tag:blogger.com,1999:blog-34152527205746026482024-03-19T05:32:50.090+01:00BricoMathsDes bricolages pour visualiser ou trouver les théorèmes de mathématiques de collège et de lycée, pour sentir et toucher les maths . ( entre autres)Olivier Longuethttp://www.blogger.com/profile/17956431908495478881noreply@blogger.comBlogger74125tag:blogger.com,1999:blog-3415252720574602648.post-22024632838107951602023-10-14T19:37:00.004+02:002023-10-14T19:37:37.028+02:00puzzles découpés à la découpeuse laser<p> Bine que je ne poste plus sur ce blog, je continue à bricoler des objets pour la classe, même si je les poste davantage sur X, qui offre plus de contacts avec les collègues .</p><p>Voila quatre objets que j'ai découpés dans un fablab avec la découpeuse laser Avec du médium 3mm, pour ces exemples, à deux faces de couleurs différentes.</p><p>J'ai utilisé Geogebra pour créer ces objets , puis inkscape afin de pouvoir découper.</p><p><br /></p><p>Identité remarquable a²-b² = ( a +b) (a- b)<br /></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-aZvjbdT-FCaI4in6skqTlMWfo7frDHPGdQBdjxdt1eNdZmECThHgfjqP9uYcR5Qs9OKS3e6IJA4eb3s7_fXVBYVSoba0ZLbswrUaNT-UxigaMSVLKV1d1JS7-roZmGXpLXXTP43bP8xghYaqqrvt4fWLHogUyk1aO4DwtqapPmpil9_nY6UJVnlVmxc/s4000/IMG_20231013_152649%5B1%5D.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2992" data-original-width="4000" height="478" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-aZvjbdT-FCaI4in6skqTlMWfo7frDHPGdQBdjxdt1eNdZmECThHgfjqP9uYcR5Qs9OKS3e6IJA4eb3s7_fXVBYVSoba0ZLbswrUaNT-UxigaMSVLKV1d1JS7-roZmGXpLXXTP43bP8xghYaqqrvt4fWLHogUyk1aO4DwtqapPmpil9_nY6UJVnlVmxc/w640-h478/IMG_20231013_152649%5B1%5D.jpg" width="640" /></a></div><br /><p></p><p>Somme des impairs </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyyizY4Ro8hnhCyNsh6Wyx676Mb7LCY10sNKuXAtnJAKd7N1c5IHE6fKxmw1tjarqv1RswEpqHepBWGA_MLBelT5nlqHAo6lDJ6dHmxIaF8UFQ8Shq58XEQcI6RjOkKuan4FvXEH0mGTuDSnz_VrCZhxfaPrZTKFfDd2RAeeWBaP3fzzO73iuQYfFH13I/s4000/IMG_20231013_152732%5B1%5D.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2992" data-original-width="4000" height="478" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyyizY4Ro8hnhCyNsh6Wyx676Mb7LCY10sNKuXAtnJAKd7N1c5IHE6fKxmw1tjarqv1RswEpqHepBWGA_MLBelT5nlqHAo6lDJ6dHmxIaF8UFQ8Shq58XEQcI6RjOkKuan4FvXEH0mGTuDSnz_VrCZhxfaPrZTKFfDd2RAeeWBaP3fzzO73iuQYfFH13I/w640-h478/IMG_20231013_152732%5B1%5D.jpg" width="640" /></a></div><div><br /></div>formules d'addition<div>cos (a+b) = cos a cos b - sin a sin b</div><div>sin(a+b) = sin a cos b + cos a sin <br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjjD75ZXrXSsYMLN_qt6ShNO9rcq-r7wMYIGEqvVKblAun1_cDJnMqpg1mGjsOIcDDPcGHRPYvfQm_EW-f6hVQSknf5fFRHMob6gEAhytZyqYcs9Z3jHusnD9QGISlcX5pAi_4H1xdnT8R0bMja2-2YErS7_V2CGCmBNBp5U7I2F-U3d-RHEa1iIbFngN8/s4000/IMG_20231013_152702%5B1%5D.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2992" data-original-width="4000" height="478" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjjD75ZXrXSsYMLN_qt6ShNO9rcq-r7wMYIGEqvVKblAun1_cDJnMqpg1mGjsOIcDDPcGHRPYvfQm_EW-f6hVQSknf5fFRHMob6gEAhytZyqYcs9Z3jHusnD9QGISlcX5pAi_4H1xdnT8R0bMja2-2YErS7_V2CGCmBNBp5U7I2F-U3d-RHEa1iIbFngN8/w640-h478/IMG_20231013_152702%5B1%5D.jpg" width="640" /></a></div><div><br /></div>Somme des entiers<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3y7jVdBHF-WzncZ0U65BbLqfl9TguFoGoNryyYjZ0R91A9o25itmlduHYCurbdEOatuWSsbEa-8aqOl4AGOF85GzhoV40Yc9ajYcupuOLzwbaHOLfPC8osGWSH_CIWNxrVeUVVgAErgFbhmTJcxcJUEWJUNXIRFqTgy2slhROzKu6bWFzhh1PHYklOf8/s4000/IMG_20231013_152747%5B1%5D.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2992" data-original-width="4000" height="478" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3y7jVdBHF-WzncZ0U65BbLqfl9TguFoGoNryyYjZ0R91A9o25itmlduHYCurbdEOatuWSsbEa-8aqOl4AGOF85GzhoV40Yc9ajYcupuOLzwbaHOLfPC8osGWSH_CIWNxrVeUVVgAErgFbhmTJcxcJUEWJUNXIRFqTgy2slhROzKu6bWFzhh1PHYklOf8/w640-h478/IMG_20231013_152747%5B1%5D.jpg" width="640" /></a></div>J'ai aussi découpé quelques tangrams.</div><div><br /></div>Olivier Longuethttp://www.blogger.com/profile/17956431908495478881noreply@blogger.com0tag:blogger.com,1999:blog-3415252720574602648.post-23117525168534152602023-09-23T19:43:00.002+02:002023-09-23T19:43:11.006+02:00racines carrés des nombres entiers<p> <span style="background-color: white; color: #050505; font-family: "Segoe UI Historic", "Segoe UI", Helvetica, Arial, sans-serif; font-size: 15px; white-space-collapse: preserve;">Pour construire les racines carrées des nombres entiers, je connaissais l'escargot de Pythagore, mais connaissiez vous les dents de requin, en traçant y=0, y=1, et en traçant les arcs de cercle en alternant les centres entre (0;0) et (0;1) ?</span></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEilN4S2YmJCjJSokNG7tN8Bo5zPNOR7kYAppHjytMmChgaevi2RcVw2P-DGF9-dXE5JS9XmdvD_Vg0WQtEldU3AmgjQd7k7uUiRwzHHYrvXL8Lhkb61BW9ycI7CGnNVchHck8L8EEF5GvE9sW4JQTkMUhoGa1y7wZ-wEqQlriAc4NQ5lUWmHlq7E4-Y1xc/s1128/dentsderequin.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="720" data-original-width="1128" height="408" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEilN4S2YmJCjJSokNG7tN8Bo5zPNOR7kYAppHjytMmChgaevi2RcVw2P-DGF9-dXE5JS9XmdvD_Vg0WQtEldU3AmgjQd7k7uUiRwzHHYrvXL8Lhkb61BW9ycI7CGnNVchHck8L8EEF5GvE9sW4JQTkMUhoGa1y7wZ-wEqQlriAc4NQ5lUWmHlq7E4-Y1xc/w640-h408/dentsderequin.png" width="640" /></a></div><br /><span style="background-color: white; color: #050505; font-family: "Segoe UI Historic", "Segoe UI", Helvetica, Arial, sans-serif; font-size: 15px; white-space-collapse: preserve;"><br /></span><p></p>Olivier Longuethttp://www.blogger.com/profile/17956431908495478881noreply@blogger.com2tag:blogger.com,1999:blog-3415252720574602648.post-48287927012303671662020-10-26T20:02:00.000+01:002020-11-17T16:06:49.733+01:00J'ai démontré le théorème de Pythagore ! ( ? ) <p><span style="font-family: arial;">Je vais vous relater une aventure mathématique qui m'est arrivée il y a deux jours, non pour me vanter, mais parce qu'elle est chargée d'émotions en montagnes russes et que ça m'aidera peut être à faire le point sur ce que j'ai trouvé ou pas... Une narration de recherche de prof et ses conséquences.</span></p><p><span style="font-family: arial;">Pendant les vacances, pour des raisons que je dévoilerai plus tard, je me suis penché sur le théorème de Pythagore. </span></p><p><span style="font-family: arial;">Je l'aime bien ce théorème. </span></p><p><span style="font-family: arial;">Premièrement, c'est l'un des résultats dont on a la trace depuis le plus longtemps, sur des tablettes d'argile . A Babylone, il était connu bien avant la naissance de Pythagore. D'ailleurs, je ne sais pas pourquoi il porte ce nom.</span></p><p><span style="font-family: arial;">Deuxièmement, c'est un résultat très pratique, dont il y a des applications dans de nombreux domaines, et on s'en sert tout le temps sans le savoir dès qu'on fait de la géométrie repérée.</span></p><p><span style="font-family: arial;">Troisièmement, il y a beaucoup de démonstrations de ce théorème . Beaucoup. plus de 200. Ce qui laisse le champ à l'imagination quand on veut démontrer ce théorème par jeu. Je savais qu'il existait un site ( https://www.cut-the-knot.org/pythagoras/# , écrit par <span style="background-color: white; color: #333333; font-size: small;">Alexander Bogomolny</span><span style="background-color: white; color: #333333; font-size: small;"> , décédé en 2018 ) qui en récensait plus d'une centaine même si j'avais oublié l'adresse. </span><span style="background-color: white; color: #333333; font-size: small;">Il existe aussi </span><span face=""Open Sans", sans-serif" style="background-color: white; color: #444444; text-align: justify;">un recueil de 256 démonstrations différentes dans le livre </span><i style="background-color: white; box-sizing: border-box; color: #444444; outline: 0px; text-align: justify;"><a class="spip_out" href="https://files.eric.ed.gov/fulltext/ED037335.pdf" rel="external" style="background: 0px 0px; box-sizing: border-box; color: #d13827; outline: 0px; text-decoration-line: none;">The Pythagorean Proposition</a></i><span face=""Open Sans", sans-serif" style="background-color: white; color: #444444; text-align: justify;"> (en anglais), de Elisha Loomis, qui date de 1927 mais ça aussi, j'ai retrouvé la référence plus tard.<br /></span></span></p><p><span face=""Open Sans", sans-serif" style="background-color: white; color: #444444; font-family: arial; text-align: justify;">Bref, démontrer le théorème de Pythagore, c'est un vaste sujet. Il y a moyen .</span></p><p><span face=""Open Sans", sans-serif" style="background-color: white; color: #444444; font-family: arial; text-align: justify;">Au collège, une démonstration classique se base sur un puzzle carré.</span></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhe9oLsSScc5kRS2O8qdvg5D1i9lNw48Ze2I6JnEVZZT2Kq8VxkP1_SK1rd2La_MhOtuuLKG7yasb000GOi-WGxEstKltPFt8UCM9Er2mOkubtK_7LiskUUxJ_WrHVRUg1AuTunz_eeDkQ/s935/pythagored%25C3%25A9mocarr%25C3%25A9.jpg" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: arial;"><img border="0" data-original-height="399" data-original-width="935" height="274" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhe9oLsSScc5kRS2O8qdvg5D1i9lNw48Ze2I6JnEVZZT2Kq8VxkP1_SK1rd2La_MhOtuuLKG7yasb000GOi-WGxEstKltPFt8UCM9Er2mOkubtK_7LiskUUxJ_WrHVRUg1AuTunz_eeDkQ/w640-h274/pythagored%25C3%25A9mocarr%25C3%25A9.jpg" width="640" /></span></a></div><span style="font-family: arial;"><br /></span><div style="text-align: justify;"><span face="Open Sans, sans-serif" style="color: #444444;"><span style="background-color: white; font-family: arial;">Deux positions différentes de placer 4 triangles rectangles identiques de côté a, b et c dans un carré de côté a +b laisse apparaitre un carré de côté c d'une part et deux carrés de côtés a et b, d'autre part . On a enlevé les mêmes triangles aux même carré, donc a² +b² = c² .</span></span></div><div style="text-align: justify;"><span face="Open Sans, sans-serif" style="color: #444444;"><span style="background-color: white; font-family: arial;"><br /></span></span></div><div style="text-align: justify;"><span face="Open Sans, sans-serif" style="color: #444444;"><span style="background-color: white; font-family: arial;">J'aime bien la figure du moulin à vent qui illustre bien le théorème de Pythagore. Il est à la base de nombreux raisonnements.</span></span></div><div style="text-align: justify;"><span style="font-family: arial;"><span face="Open Sans, sans-serif" style="color: #444444;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEit16wwOcKWwDxhtOoGrz__PBVTIZg87c4z82kA_mObfbbsWQD2dvMhhXqM7gXMUAHh14yCBcCCn0MTyu5aOZadKj3m5snFPRo9e8x5DtrCnPjAhGzmwbRnQ9uAq9Te5dw7jbjK-miCBeM/s436/pythagoremoulinavent.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="436" data-original-width="372" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEit16wwOcKWwDxhtOoGrz__PBVTIZg87c4z82kA_mObfbbsWQD2dvMhhXqM7gXMUAHh14yCBcCCn0MTyu5aOZadKj3m5snFPRo9e8x5DtrCnPjAhGzmwbRnQ9uAq9Te5dw7jbjK-miCBeM/w341-h400/pythagoremoulinavent.jpg" width="341" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">Si on réussit à découper le grand carré avec des pièces de même aire que la somme des aires des deux autres carrés, on aura démontré que c² = a² + b²</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">Une démonstration classique qui en découle est celle donnée dans les éléments d'Euclide, que je me suis amusé à transformer en gif .</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2w5gqp9Sqkw71bcWTyWTJs0idFM6VRf20axoU4JFSCrHxR_eZFT892OG-mideKPc-ZHSXjdl6WWAM6NXoQ-wtxfato8GcJ-vlTryPG71AiHmuWDgV25m_nQ75poXKNzyIYrdbQU7QJZ8/s563/pythagore3.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="563" data-original-width="555" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2w5gqp9Sqkw71bcWTyWTJs0idFM6VRf20axoU4JFSCrHxR_eZFT892OG-mideKPc-ZHSXjdl6WWAM6NXoQ-wtxfato8GcJ-vlTryPG71AiHmuWDgV25m_nQ75poXKNzyIYrdbQU7QJZ8/w630-h640/pythagore3.gif" width="630" /></a></div></span>les triangles rouges ont toujours la même aire, ils évoluent suivant trois manières : 1) en gardant la même base et la hauteur restant constante, les triangles gardent la même aire.</span></div><div style="text-align: justify;"><span style="font-family: arial;">2) on effectue une rotation, le triangle garde la même aire.</span></div><div style="text-align: justify;"><span style="font-family: arial;">3) On garde la même base, et la hauteur restant constante, les triangles gardent la même aire .</span></div><div style="text-align: justify;"><span style="font-family: arial;">Ainsi, on a dessiné dans le grand carré un triangle de même aire que la moitié du carré moyen .</span></div><div style="text-align: justify;"><span style="font-family: arial;">SI on ajoute l'aire du triangle bleu (égale à celle du triangle rouge), on a une aire équivalente au carré moyen.</span></div><div style="text-align: justify;"><span style="font-family: arial;">En raisonnant de même avec le triangle jaune et le vert, on montre que l'aire du grand carré est égale à la somme des aires des deux autres carrés.</span></div><div style="text-align: justify;"><span style="font-family: arial;"><br /></span></div><div style="text-align: justify;"><span style="font-family: arial;">J'aime bien cette interprétation géométrique du moulin à vent et j'ai essayé de la retrouver autrement.</span></div><div style="text-align: justify;"><span style="font-family: arial;">J'y ai pensé avant de me coucher et du coup, je n'arrive pas bien à dormir. </span></div><div style="text-align: justify;"><span style="font-family: arial;">Je saute de mon lit, avec une intuition qu'il me faut vérifier sur le champ.</span></div><div style="text-align: justify;"><span style="font-family: arial;">Je l'ai peut être appris ou lu quelque part, mais je redécouvre le fait que les aires des triangles entourant les carrés du moulin à vent ont la même aire.</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgncxwo-m5Du9M7z7mfa12TlSbqAiaiPS4sx-E9OXvIsP2G3SA2M5OZkbW9NUjV598WxEOG8J6vG8scFEY_ikcw4xz4U5-AdZTxplXOe_FL3a0rATOxudHTQQ1PHBU9EkPkD6xn8EBYE90/s555/triangle+pythagore.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: arial;"><img border="0" data-original-height="555" data-original-width="497" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgncxwo-m5Du9M7z7mfa12TlSbqAiaiPS4sx-E9OXvIsP2G3SA2M5OZkbW9NUjV598WxEOG8J6vG8scFEY_ikcw4xz4U5-AdZTxplXOe_FL3a0rATOxudHTQQ1PHBU9EkPkD6xn8EBYE90/s320/triangle+pythagore.gif" /></span></a></div><span style="font-family: arial;">Après avoir vérifié mon intuition sur geogebra, je me dis que je verrai la justification le lendemain et ses éventuelles applications. Cela peut-il servir à justifier le théorème de Pythagore ?</span><div><span style="font-family: arial;"><br /></span></div><div><span style="font-family: arial;">Le lendemain, je démontre ce résultat à l'aide de la formule de l'aire d'un triangle A= 1/2 a b sin(alpha) et de la formule des sinus des angles associés, même s'il y sans doute plus simple et continue l'exploration grâce à geogebra.</span></div><div><span style="font-family: arial;"><br /></span></div><div><span style="font-family: arial;">je poste la figure sur Twitter, avec un très bon retour, ce qui me fait dire que le fait n'est pas forcément connu. Mon inspecteur m'apprend alors qu'on parle d'extriangles, et de moulin à vents.</span></div><div><span style="font-family: arial;"><br /></span></div><div><span style="font-family: arial;">Est il possible d'obtenir une figure dont on peut facilement calculer l'aire à partir de cette figure? Par symétrie centrale des milieux des côtés extérieurs, je construis les parallélogrammes pour voir ce que ça donne.</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfy6P7GGATA5bnzGD6XGu4P_kCaCWwm_wX8Cirp9AkB_SIRCDsXJS0N9MSwJvAGVWmVMpX5BkFDuBLxK_GWwOMx8ba1ftRt0Z1eLOmwChLjF5AY_HeYS2R5i658HhKvJvv0XByKkgnsqo/s384/pyth4.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: arial;"><img border="0" data-original-height="364" data-original-width="384" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfy6P7GGATA5bnzGD6XGu4P_kCaCWwm_wX8Cirp9AkB_SIRCDsXJS0N9MSwJvAGVWmVMpX5BkFDuBLxK_GWwOMx8ba1ftRt0Z1eLOmwChLjF5AY_HeYS2R5i658HhKvJvv0XByKkgnsqo/s320/pyth4.jpg" width="320" /></span></a></div><span style="font-family: arial;"><br /></span><div><span style="font-family: arial;"><br /></span></div><div><span style="font-family: arial;"><br /></span></div><div><span style="font-family: arial;">En apercevant des droites parallèles, je me demande si on peut construire un rectangle en prolongeant certains côtés.</span><p></p></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglSf4O3ug-6oAWc8b6eBRXm2XMjtJYNrR_I4Cj2YLmiLPjxXYlVEN_96CywMmQEWjo9uI1KHxy-HBLUOQHymTEavgYOJ5h4naZ0C6m3qL7i43n2E4vokzT0spWCO4HbESOvJiIwloaveY/s492/pyth5.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: arial;"><img border="0" data-original-height="490" data-original-width="492" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglSf4O3ug-6oAWc8b6eBRXm2XMjtJYNrR_I4Cj2YLmiLPjxXYlVEN_96CywMmQEWjo9uI1KHxy-HBLUOQHymTEavgYOJ5h4naZ0C6m3qL7i43n2E4vokzT0spWCO4HbESOvJiIwloaveY/s320/pyth5.jpg" width="320" /></span></a></div><span style="font-family: arial;"><br /></span><div class="separator" style="clear: both; text-align: center;"><span style="font-family: arial;"><br /></span></div><span style="font-family: arial;"><br /></span><div><span style="font-family: arial;"><br /></span></div><div><span style="font-family: arial;">Surprise, les triangles manquants ont tous les mêmes dimensions !</span></div><div><span style="font-family: arial;">Ca se vérifie facilement</span></div><div><span style="font-family: arial;">On peut alors calculer l'aire du rectangle obtenu de deux manières différentes, longueur * largeur et comme somme des aires des carrés et des triangles.</span></div><div><span style="font-family: arial;">Eureka ! Ca marche !</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5LXZO4I7FglZZPae_D_wiiSocsOkzO_IdDUIUQhXMyAnGX3czA46tawyAHrh0Ol2L3ABT9MRZ4AlWaYqbs0yU8qUfQ7PqseChBWurxUa_LtQ1b6fVQwKqQsT0qTL3DJdaVHgMpr5JKCs/s929/preuvethmpythagore.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: arial;"><img border="0" data-original-height="538" data-original-width="929" height="370" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5LXZO4I7FglZZPae_D_wiiSocsOkzO_IdDUIUQhXMyAnGX3czA46tawyAHrh0Ol2L3ABT9MRZ4AlWaYqbs0yU8qUfQ7PqseChBWurxUa_LtQ1b6fVQwKqQsT0qTL3DJdaVHgMpr5JKCs/w640-h370/preuvethmpythagore.jpg" width="640" /></span></a></div><div class="separator" style="clear: both; text-align: center;"><span style="font-family: arial;"><br /></span></div><span style="font-family: arial;"><br /></span><div><span style="font-family: arial;">Chouette, j'ai réussi à démontrer le théorème de Pythagore, je suis content, parce que j'avais lu des démonstrations, je savais les reproduire, mais je ne m'étais pas attelé à le démontrer moi même . Je suis assez fier .</span></div><div><span style="font-family: arial;">Je sais que Vincent Pantaloni avait mentionné sur Twitter le site avec une centaine de démonstrations, je lui demande l'adresse pour voir d'autres stratégies.</span></div><div><span style="font-family: arial;">En première lecture, je ne trouve pas la mienne dans la liste .</span></div><div><span style="font-family: arial;">En particulier, il y en a peu qui entourent le moulin à vent d'un rectangle et je trouve ça intéressant.</span></div><div><span style="font-family: arial;">ouah, aurais je trouvé une nouvelle démo? j'en doute encore, je sais qu'il y en a d'autres qui ne sont pas dans le site</span></div><div><span style="font-family: arial;">Je poste mon résultat sur twitter encore une fois, parce que je trouve ma stratégie assez amusante, pour voir ce qu'il en découlera. Elle est de fait un peu retweetée et assez commentée.</span></div><div><span style="font-family: arial;">Avec le retweet de Vincent Pantaloni, l'idée traverse même l'Atlantique.</span></div><div><span style="font-family: arial;"><br /></span></div><div><div class="css-1dbjc4n r-18u37iz r-d0pm55" data-testid="tweet" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: horizontal; align-items: stretch; background-color: #15202b; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: row; flex-shrink: 0; font-size: 16px; margin: 0px 0px 5px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-1awozwy r-18kxxzh r-1rq6c10" style="-webkit-box-align: center; -webkit-box-direction: normal; -webkit-box-flex: 0; -webkit-box-orient: vertical; align-items: center; border: 0px solid black; box-sizing: border-box; display: flex; flex-direction: column; flex: 0 0 53px; margin: 0px 11px 0px 0px; 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min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-901oao css-bfa6kz r-jwli3a r-1qd0xha r-ubezar r-vw2c0b r-ad9z0x r-bcqeeo r-3s2u2q r-qvutc0" dir="auto" style="border: 0px solid black; box-sizing: border-box; color: white; display: inline; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: bold; line-height: 1.3125; margin: 0px; max-width: 100%; min-width: 0px; overflow-wrap: break-word; overflow: hidden; padding: 0px; text-overflow: ellipsis; white-space: nowrap;"><span class="css-901oao css-16my406 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" style="border: 0px solid black; box-sizing: border-box; color: inherit; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: inherit;"><span style="font-family: arial;"><span class="css-901oao css-16my406 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" style="border: 0px solid black; 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top: 0px; width: 19.1875px; z-index: -1;"></div><img alt="Donut" class="css-9pa8cd" draggable="false" src="https://abs-0.twimg.com/emoji/v2/svg/1f369.svg" style="bottom: 0px; height: 19.1875px; left: 0px; opacity: 0; position: absolute; right: 0px; top: 0px; width: 19.1875px; z-index: -1;" /></div></span><span class="css-901oao css-16my406 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" style="border: 0px solid black; box-sizing: border-box; color: inherit; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: inherit;">ni</span></span></span></div><div class="css-901oao r-jwli3a r-18u37iz r-1q142lx r-1qd0xha r-ubezar r-16dba41 r-ad9z0x r-bcqeeo r-qvutc0" dir="auto" style="-webkit-box-direction: normal; -webkit-box-orient: horizontal; border: 0px solid black; box-sizing: border-box; color: white; display: inline; flex-direction: row; 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margin: 0px; max-width: 100%; min-width: 0px; overflow-wrap: break-word; overflow: hidden; padding: 0px; text-overflow: ellipsis; white-space: nowrap;"><span class="css-901oao css-16my406 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" style="border: 0px solid black; box-sizing: border-box; color: inherit; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: inherit;"><span style="font-family: arial;">@panlepan</span></span></div></div></div></a></div><div class="css-1dbjc4n r-18u37iz r-1h0z5md r-mlyl9t" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: horizontal; -webkit-box-pack: start; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: row; flex-shrink: 0; justify-content: flex-start; margin: 0px 0px 0px 21px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div aria-expanded="false" aria-haspopup="true" aria-label="Plus" class="css-18t94o4 css-1dbjc4n r-1777fci r-11cpok1 r-1ny4l3l r-bztko3 r-lrvibr" data-focusable="true" data-testid="caret" role="button" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; -webkit-box-pack: center; align-items: stretch; border: 0px solid black; box-sizing: border-box; cursor: pointer; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; justify-content: center; margin: 0px; min-height: 0px; min-width: 0px; outline-style: none; overflow: visible; padding: 0px; position: relative; user-select: none; z-index: 0;" tabindex="0"><div class="css-901oao r-1awozwy r-111h2gw r-6koalj r-1qd0xha r-ubezar r-16dba41 r-1h0z5md r-ad9z0x r-bcqeeo r-o7ynqc r-clp7b1 r-3s2u2q r-qvutc0" dir="ltr" style="-webkit-box-align: center; -webkit-box-pack: start; align-items: center; border: 0px solid black; box-sizing: border-box; color: #8899a6; display: flex; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; justify-content: flex-start; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; transition-duration: 0.2s; transition-property: color; white-space: nowrap;"><div class="css-1dbjc4n r-xoduu5" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: inline-flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-sdzlij r-1p0dtai r-xoduu5 r-1d2f490 r-xf4iuw r-1ny4l3l r-u8s1d r-zchlnj r-ipm5af r-o7ynqc r-6416eg" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border-radius: 9999px; border: 0px solid black; bottom: 0px; box-sizing: border-box; display: inline-flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; left: 0px; margin: -8px; min-height: 0px; min-width: 0px; outline-style: none; padding: 0px; position: absolute; right: 0px; top: 0px; transition-duration: 0.2s; transition-property: background-color, box-shadow; z-index: 0;"></div><svg class="r-4qtqp9 r-yyyyoo r-1xvli5t r-dnmrzs r-bnwqim r-1plcrui r-lrvibr r-1hdv0qi" viewbox="0 0 24 24"><g></g></svg><span style="font-family: arial;"><path d="M19.39 14.882c-1.58 0-2.862-1.283-2.862-2.86s1.283-2.862 2.86-2.862 2.862 1.283 2.862 2.86-1.284 2.862-2.86 2.862zm0-4.223c-.75 0-1.362.61-1.362 1.36s.61 1.36 1.36 1.36 1.362-.61 1.362-1.36-.61-1.36-1.36-1.36zM12 14.882c-1.578 0-2.86-1.283-2.86-2.86S10.42 9.158 12 9.158s2.86 1.282 2.86 2.86S13.578 14.88 12 14.88zm0-4.223c-.75 0-1.36.61-1.36 1.36s.61 1.362 1.36 1.362 1.36-.61 1.36-1.36-.61-1.363-1.36-1.363zm-7.39 4.223c-1.577 0-2.86-1.283-2.86-2.86S3.034 9.16 4.61 9.16s2.862 1.283 2.862 2.86-1.283 2.862-2.86 2.862zm0-4.223c-.75 0-1.36.61-1.36 1.36s.61 1.36 1.36 1.36 1.362-.61 1.362-1.36-.61-1.36-1.36-1.36z"></path></span></div></div></div></div></div></div></div></div></div><div class="css-1dbjc4n" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; background-color: #15202b; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; font-size: 16px; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-a1ub67" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 11px 0px 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-901oao r-jwli3a r-1qd0xha r-1x35g6 r-16dba41 r-ad9z0x r-bcqeeo r-bnwqim r-qvutc0" dir="auto" id="tweet-text" lang="en" style="border: 0px solid black; box-sizing: border-box; color: white; display: inline; font-size: 24px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; position: relative; white-space: pre-wrap;"><span style="font-family: arial;"><span class="css-901oao css-16my406 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" style="border: 0px solid black; box-sizing: border-box; color: inherit; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: inherit;">A new (?) proof of the Pythagorean theorem by </span><div class="css-1dbjc4n r-xoduu5" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: inline-flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><span class="r-18u37iz" style="-webkit-box-direction: normal; -webkit-box-orient: horizontal; flex-direction: row;"><a class="css-4rbku5 css-18t94o4 css-901oao css-16my406 r-1n1174f r-1loqt21 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" data-focusable="true" dir="ltr" href="https://twitter.com/OLonguet" role="link" style="background-color: rgba(0, 0, 0, 0); border: 0px solid black; box-sizing: border-box; color: #1b95e0; cursor: pointer; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; list-style: none; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; text-align: inherit; text-decoration-line: none; white-space: inherit;">@OLonguet</a></span></div><span class="css-901oao css-16my406 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" style="border: 0px solid black; box-sizing: border-box; color: inherit; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: inherit;">.</span></span></div><div aria-expanded="false" class="css-18t94o4 css-901oao r-1n1174f r-6koalj r-1w6e6rj r-1qd0xha r-1b43r93 r-16dba41 r-6itf4e r-1g94qm0 r-bcqeeo r-qvutc0" data-focusable="true" dir="auto" role="button" style="border: 0px solid black; box-sizing: border-box; color: #1b95e0; cursor: pointer; display: flex; flex-wrap: wrap; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: calc(21px); margin: 5px 0px 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: pre-wrap;" tabindex="0"><span class="css-901oao css-16my406 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" style="border: 0px solid black; box-sizing: border-box; color: inherit; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: inherit;"><span style="font-family: arial;">Traduire le Tweet</span></span></div></div></div><div class="css-1dbjc4n" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div aria-labelledby="quote-tweet-label tweet-card-label" class="css-1dbjc4n" id="tweet-rich-content-label" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-a1ub67" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 11px 0px 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n" id="quote-tweet-label" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-901oao r-4iw3lz r-1xk2f4g r-jwli3a r-1qd0xha r-ubezar r-16dba41 r-109y4c4 r-ad9z0x r-bcqeeo r-1udh08x r-wwvuq4 r-u8s1d r-92ng3h r-qvutc0" dir="auto" style="border: 0px solid black; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); color: white; display: inline; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; height: 1px; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; overflow: hidden; padding: 0px; position: absolute; white-space: pre-wrap; width: 1px;"><span class="css-901oao css-16my406 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" style="border: 0px solid black; box-sizing: border-box; color: inherit; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: inherit;"><span style="font-family: arial;">Citer le Tweet</span></span></div><div class="css-1dbjc4n r-18bvks7 r-1867qdf r-rs99b7 r-1loqt21 r-1q3ze6u r-1ny4l3l r-1udh08x r-o7ynqc r-6416eg" data-focusable="true" role="link" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border-radius: 16px; border: 1px solid rgb(56, 68, 77); box-sizing: border-box; cursor: pointer; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 0px; min-height: 63px; min-width: 0px; outline-style: none; overflow: hidden; padding: 0px; position: relative; transition-duration: 0.2s; transition-property: background-color, box-shadow; z-index: 0;" tabindex="0"><div class="css-1dbjc4n" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-1awozwy r-18u37iz r-1wbh5a2 r-1mi5vxm r-a1ub67" style="-webkit-box-align: center; -webkit-box-direction: normal; -webkit-box-orient: horizontal; align-items: center; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: row; flex-shrink: 1; margin: 11px 11px 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-1wbh5a2 r-1udh08x" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 1; margin: 0px; min-height: 0px; min-width: 0px; overflow: hidden; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-1habvwh r-dnmrzs" style="-webkit-box-align: start; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: flex-start; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 0px; max-width: 100%; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-1wbh5a2 r-dnmrzs" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 1; margin: 0px; max-width: 100%; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-1wbh5a2 r-dnmrzs r-1ny4l3l" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 1; margin: 0px; max-width: 100%; min-height: 0px; min-width: 0px; outline-style: none; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-1awozwy r-18u37iz r-1wbh5a2 r-dnmrzs r-1ny4l3l" style="-webkit-box-align: center; -webkit-box-direction: normal; -webkit-box-orient: horizontal; align-items: center; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: row; flex-shrink: 1; margin: 0px; max-width: 100%; min-height: 0px; min-width: 0px; outline-style: none; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-1awozwy r-18u37iz r-dnmrzs" style="-webkit-box-align: center; -webkit-box-direction: normal; -webkit-box-orient: horizontal; align-items: center; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: row; flex-shrink: 0; margin: 0px; max-width: 100%; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-sdzlij r-1q142lx r-76blku r-7o8qx1 r-1ny4l3l r-1udh08x r-64lmo0" role="presentation" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border-radius: 9999px; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; height: 21px; margin: 0px 5px 0px 0px; min-height: 0px; min-width: 0px; outline-style: none; overflow: hidden; padding: 0px; position: relative; width: 21px; z-index: 0;"><div class="css-1dbjc4n r-1mlwlqe r-76blku r-1udh08x r-64lmo0 r-417010" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; background-color: #aab8c2; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; height: 21px; margin: 0px; min-height: 0px; min-width: 0px; overflow: hidden; padding: 0px; position: relative; width: 21px; z-index: 0;"><div class="css-1dbjc4n r-1niwhzg r-vvn4in r-u6sd8q r-4gszlv r-1p0dtai r-1pi2tsx r-1d2f490 r-u8s1d r-zchlnj r-ipm5af r-13qz1uu r-1wyyakw" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; background-color: rgba(0, 0, 0, 0); background-image: url("https://pbs.twimg.com/profile_images/1248645377793773571/IfIzeSXR_normal.jpg"); background-position: center center; background-repeat: no-repeat; background-size: cover; border: 0px solid black; bottom: 0px; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; height: 21px; left: 0px; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: absolute; right: 0px; top: 0px; width: 21px; z-index: -1;"></div><img alt="" class="css-9pa8cd" draggable="false" src="https://pbs.twimg.com/profile_images/1248645377793773571/IfIzeSXR_normal.jpg" style="bottom: 0px; height: 21px; left: 0px; opacity: 0; position: absolute; right: 0px; top: 0px; width: 21px; z-index: -1;" /></div><div class="css-1dbjc4n r-19z6qd4 r-sdzlij r-rs99b7 r-1p0dtai r-1mi75qu r-76blku r-1d2f490 r-u8s1d r-zchlnj r-ipm5af r-64lmo0" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border-radius: 9999px; border: 1px solid rgba(0, 0, 0, 0.08); bottom: 0px; box-shadow: rgba(0, 0, 0, 0.02) 0px 0px 2px inset; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; height: 21px; left: 0px; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: absolute; right: 0px; top: 0px; width: 21px; z-index: 0;"></div><div class="css-1dbjc4n r-19z6qd4 r-sdzlij r-rs99b7 r-1p0dtai r-1mi75qu r-1d2f490 r-1ny4l3l r-u8s1d r-zchlnj r-ipm5af" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border-radius: 9999px; border: 1px solid rgba(0, 0, 0, 0.08); bottom: 0px; box-shadow: rgba(0, 0, 0, 0.02) 0px 0px 2px inset; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; left: 0px; margin: 0px; min-height: 0px; min-width: 0px; outline-style: none; padding: 0px; position: absolute; right: 0px; top: 0px; z-index: 0;"></div></div><div class="css-901oao css-bfa6kz r-jwli3a r-1qd0xha r-ubezar r-vw2c0b r-ad9z0x r-bcqeeo r-3s2u2q r-qvutc0" dir="auto" style="border: 0px solid black; box-sizing: border-box; color: white; display: inline; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: bold; line-height: 1.3125; margin: 0px; max-width: 100%; min-width: 0px; overflow-wrap: break-word; overflow: hidden; padding: 0px; text-overflow: ellipsis; white-space: nowrap;"><span class="css-901oao css-16my406 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" style="border: 0px solid black; box-sizing: border-box; color: inherit; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: inherit;"><span style="font-family: arial;">Olivier Longuet</span></span></div><div class="css-901oao r-jwli3a r-18u37iz r-1q142lx r-1qd0xha r-ubezar r-16dba41 r-ad9z0x r-bcqeeo r-qvutc0" dir="auto" style="-webkit-box-direction: normal; -webkit-box-orient: horizontal; border: 0px solid black; box-sizing: border-box; color: white; display: inline; flex-direction: row; flex-shrink: 0; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: pre-wrap;"></div></div><div class="css-1dbjc4n r-18u37iz r-1wbh5a2 r-1f6r7vd" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: horizontal; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: row; flex-shrink: 1; margin: 0px 0px 0px 5px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-901oao css-bfa6kz r-111h2gw r-18u37iz r-1qd0xha r-ubezar r-16dba41 r-ad9z0x r-bcqeeo r-qvutc0" dir="ltr" style="-webkit-box-direction: normal; -webkit-box-orient: horizontal; border: 0px solid black; box-sizing: border-box; color: #8899a6; display: inline; flex-direction: row; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.3125; margin: 0px; max-width: 100%; min-width: 0px; overflow-wrap: break-word; overflow: hidden; padding: 0px; text-overflow: ellipsis; white-space: nowrap;"><span class="css-901oao css-16my406 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" style="border: 0px solid black; box-sizing: border-box; color: inherit; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: inherit;"><span style="font-family: arial;">@OLonguet</span></span></div></div></div></div></div></div></div><div class="css-901oao r-111h2gw r-1q142lx r-1qd0xha r-ubezar r-16dba41 r-ad9z0x r-bcqeeo r-yrgyi6 r-qvutc0" dir="ltr" style="border: 0px solid black; box-sizing: border-box; color: #8899a6; display: inline; flex-shrink: 0; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: pre;"><span style="font-family: arial;"> · <span aria-label="23 oct." class="r-111h2gw r-1q142lx r-1qd0xha r-ad9z0x r-bcqeeo r-3s2u2q r-qvutc0 css-901oao css-16my406" style="border: 0px solid black; box-sizing: border-box; display: inline; flex-shrink: 0; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: nowrap;" title="4:51 PM · 23 oct. 2020"><time datetime="2020-10-23T14:51:14.000Z">23 oct.</time></span></span></div></div><div class="css-1dbjc4n r-1a8r3js r-1mi5vxm" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 0px 11px 11px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-901oao r-jwli3a r-1qd0xha r-ubezar r-16dba41 r-ad9z0x r-1g94qm0 r-bcqeeo r-bnwqim r-qvutc0" dir="auto" lang="fr" style="border: 0px solid black; box-sizing: border-box; color: white; display: inline; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.3125; margin: 5px 0px 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; position: relative; white-space: pre-wrap;"><span class="css-901oao css-16my406 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" style="border: 0px solid black; box-sizing: border-box; color: inherit; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: inherit;"><span style="font-family: arial;">Une démonstration du théorème de Pythagore... je ne sais pas si elle est répertoriée ...</span></span></div><div class="css-901oao r-1n1174f r-1qd0xha r-ubezar r-16dba41 r-ad9z0x r-1g94qm0 r-bcqeeo r-qvutc0" dir="auto" style="border: 0px solid black; box-sizing: border-box; color: #1b95e0; display: inline; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.3125; margin: 5px 0px 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: pre-wrap;"><span class="css-901oao css-16my406 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" style="border: 0px solid black; box-sizing: border-box; color: inherit; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: inherit;"><span style="font-family: arial;">Afficher cette discussion</span></span></div></div><div class="css-1dbjc4n r-1g94qm0" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 5px 0px 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-1ny4l3l r-o7ynqc r-6416eg" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 0px; min-height: 0px; min-width: 0px; outline-style: none; padding: 0px; position: relative; transition-duration: 0.2s; transition-property: background-color, box-shadow; z-index: 0;"><div class="css-1dbjc4n" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><a class="css-4rbku5 css-18t94o4 css-1dbjc4n r-1loqt21 r-1ny4l3l" data-focusable="true" href="https://twitter.com/OLonguet/status/1319652608110460930/photo/1" role="link" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; background-color: rgba(0, 0, 0, 0); border: 0px solid black; box-sizing: border-box; cursor: pointer; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; list-style: none; margin: 0px; min-height: 0px; min-width: 0px; outline-style: none; padding: 0px; position: relative; text-align: inherit; text-decoration-line: none; z-index: 0;"><div class="css-1dbjc4n r-1adg3ll r-1udh08x" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 0px; min-height: 0px; min-width: 0px; overflow: hidden; padding: 0px; position: relative; z-index: 0;"><div class="r-1adg3ll r-13qz1uu" style="padding-bottom: 317.25px; width: 564px;"></div><div class="r-1p0dtai r-1pi2tsx r-1d2f490 r-u8s1d r-ipm5af r-13qz1uu" style="bottom: 0px; height: 317.25px; left: 0px; position: absolute; top: 0px; width: 564px;"><div aria-label="Image" class="css-1dbjc4n r-1p0dtai r-1mlwlqe r-1d2f490 r-11wrixw r-61z16t r-1mnahxq r-1udh08x r-u8s1d r-zchlnj r-ipm5af r-417010" data-testid="tweetPhoto" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; bottom: 0px; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; left: 0px; margin: 0px 0px -5.625px; min-height: 0px; min-width: 0px; overflow: hidden; padding: 0px; position: absolute; right: 0px; top: 0px; z-index: 0;"><div class="css-1dbjc4n r-1niwhzg r-vvn4in r-u6sd8q r-4gszlv r-1p0dtai r-1pi2tsx r-1d2f490 r-u8s1d r-zchlnj r-ipm5af r-13qz1uu r-1wyyakw" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; background-color: rgba(0, 0, 0, 0); background-image: url("https://pbs.twimg.com/media/ElBY2D7XgAINpzi?format=jpg&name=small"); background-position: center center; background-repeat: no-repeat; background-size: cover; border: 0px solid black; bottom: 0px; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; height: 322.875px; left: 0px; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: absolute; right: 0px; top: 0px; width: 564px; z-index: -1;"></div><img alt="Image" class="css-9pa8cd" draggable="true" src="https://pbs.twimg.com/media/ElBY2D7XgAINpzi?format=jpg&name=small" style="bottom: 0px; height: 322.875px; left: 0px; opacity: 0; position: absolute; right: 0px; top: 0px; width: 564px; z-index: -1;" /></div></div></div></a></div></div></div></div></div></div></div></div></div></div><div class="css-1dbjc4n r-1r5su4o" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 16px 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-1awozwy r-18u37iz r-1wtj0ep" style="-webkit-box-align: center; -webkit-box-direction: normal; -webkit-box-orient: horizontal; -webkit-box-pack: justify; align-items: center; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: row; flex-shrink: 0; justify-content: space-between; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-901oao r-111h2gw r-1qd0xha r-ubezar r-16dba41 r-ad9z0x r-1rq6c10 r-bcqeeo r-qvutc0" dir="auto" style="border: 0px solid black; box-sizing: border-box; color: #8899a6; display: inline; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.3125; margin: 0px 11px 0px 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: pre-wrap;"><span style="font-family: arial;"><a class="css-4rbku5 css-18t94o4 css-901oao css-16my406 r-111h2gw r-1loqt21 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" data-focusable="true" href="https://twitter.com/panlepan/status/1319697553852608513" role="link" style="background-color: rgba(0, 0, 0, 0); border: 0px solid black; box-sizing: border-box; color: #8899a6; cursor: pointer; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; list-style: none; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; text-align: inherit; text-decoration-line: none; white-space: inherit;">7:49 PM · 23 oct. 2020</a><span aria-hidden="true" class="css-901oao css-16my406 r-111h2gw r-1q142lx r-1qd0xha r-ad9z0x r-bcqeeo r-ou255f r-qvutc0" style="border: 0px solid black; box-sizing: border-box; display: inline; flex-shrink: 0; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px 5px; white-space: inherit;"><span class="css-901oao css-16my406 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" style="border: 0px solid black; box-sizing: border-box; color: inherit; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: inherit;">·</span></span><a class="css-4rbku5 css-18t94o4 css-901oao css-16my406 r-111h2gw r-1loqt21 r-1qd0xha r-ad9z0x r-bcqeeo r-1jeg54m r-qvutc0" data-focusable="true" href="https://help.twitter.com/using-twitter/how-to-tweet#source-labels" rel=" noopener noreferrer" role="link" style="background-color: rgba(0, 0, 0, 0); border: 0px solid black; box-sizing: border-box; color: #8899a6; cursor: pointer; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; list-style: none; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; text-align: inherit; text-decoration-line: none; white-space: normal;" target="_blank">Twitter for Android</a></span></div></div></div></div></div><div><span style="font-family: arial;"><br /></span></div><div><span style="font-family: arial;">Trois remarques me font réfléchir : les deux parallélogrammes ennuient un peu certaines personnes, inutilement compliqués, un twitto sous entendant peut être que j'ai maquillé une démo simple en quelque chose de plus compliqué.</span></div><div><span style="background-color: black;"><span style="font-family: arial;"><br /></span></span></div><div><div class="css-1dbjc4n r-18u37iz r-d0pm55" data-testid="tweet" style="-webkit-box-align: stretch; 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flex-direction: column; flex-shrink: 0; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-wr9vkk" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 0px 0px 3px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-k4xj1c r-18u37iz r-1wtj0ep" style="-webkit-box-align: start; -webkit-box-direction: normal; -webkit-box-orient: horizontal; -webkit-box-pack: justify; align-items: start; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: row; flex-shrink: 0; justify-content: space-between; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-18u37iz r-1h0z5md r-mlyl9t" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: horizontal; -webkit-box-pack: start; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: row; flex-shrink: 0; justify-content: flex-start; margin: 0px 0px 0px 21px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div aria-expanded="false" aria-haspopup="true" aria-label="Plus" class="css-18t94o4 css-1dbjc4n r-1777fci r-11cpok1 r-1ny4l3l r-bztko3 r-lrvibr" data-focusable="true" data-testid="caret" role="button" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; -webkit-box-pack: center; align-items: stretch; border: 0px solid black; box-sizing: border-box; cursor: pointer; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; justify-content: center; margin: 0px; min-height: 0px; min-width: 0px; outline-style: none; overflow: visible; padding: 0px; position: relative; user-select: none; z-index: 0;" tabindex="0"><div class="css-901oao r-1awozwy r-111h2gw r-6koalj r-1qd0xha r-ubezar r-16dba41 r-1h0z5md r-ad9z0x r-bcqeeo r-o7ynqc r-clp7b1 r-3s2u2q r-qvutc0" dir="ltr" style="-webkit-box-align: center; -webkit-box-pack: start; align-items: center; border: 0px solid black; box-sizing: border-box; color: #8899a6; display: flex; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; justify-content: flex-start; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; transition-duration: 0.2s; transition-property: color; white-space: nowrap;"><div class="css-1dbjc4n r-xoduu5" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: inline-flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-sdzlij r-1p0dtai r-xoduu5 r-1d2f490 r-xf4iuw r-1ny4l3l r-u8s1d r-zchlnj r-ipm5af r-o7ynqc r-6416eg" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border-radius: 9999px; border: 0px solid black; bottom: 0px; box-sizing: border-box; display: inline-flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; left: 0px; margin: -8px; min-height: 0px; min-width: 0px; outline-style: none; padding: 0px; position: absolute; right: 0px; top: 0px; transition-duration: 0.2s; transition-property: background-color, box-shadow; z-index: 0;"><span style="font-family: arial;"><br /></span></div></div></div></div></div></div></div></div></div></div><div class="css-1dbjc4n" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; background-color: #15202b; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; font-size: 16px; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-a1ub67" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 11px 0px 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-901oao r-jwli3a r-1qd0xha r-1x35g6 r-16dba41 r-ad9z0x r-bcqeeo r-bnwqim r-qvutc0" dir="auto" id="tweet-text" lang="en" style="border: 0px solid black; box-sizing: border-box; color: white; display: inline; font-size: 24px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; position: relative; white-space: pre-wrap;"><span class="css-901oao css-16my406 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" style="border: 0px solid black; box-sizing: border-box; color: inherit; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: inherit;"><span style="font-family: arial;">Took me a while to see what was going on here, but I like it! Whatever a, b and c are, you can construct these nine extra triangles, each with the same area, plus the squares on each side, to form a square.
I mean, it’s a bit Heath-Robinson, but it’s still neat :-)</span></span></div><div class="css-901oao css-bfa6kz r-jwli3a r-6koalj r-1w6e6rj r-1qd0xha r-ubezar r-16dba41 r-ad9z0x r-1g94qm0 r-bcqeeo r-q4m81j r-qvutc0" dir="ltr" style="border: 0px solid black; box-sizing: border-box; color: white; display: flex; flex-wrap: wrap; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.3125; margin: 5px 0px 0px; max-width: 100%; min-width: 0px; overflow-wrap: break-word; overflow: hidden; padding: 0px; text-align: center; text-overflow: ellipsis; white-space: nowrap;"><span aria-expanded="true" aria-label="Masquer le Tweet traduit" class="css-18t94o4 css-901oao css-16my406 r-1n1174f r-1loqt21 r-1qd0xha r-1b43r93 r-6itf4e r-bcqeeo r-qvutc0" data-focusable="true" role="button" style="border: 0px solid black; box-sizing: border-box; color: #1b95e0; cursor: pointer; display: inline; font-size: 14px; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: calc(21px); margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: inherit;" tabindex="0"><span class="css-901oao css-16my406 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" style="border: 0px solid black; box-sizing: border-box; color: inherit; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: inherit;"><span style="font-family: arial;">À l'origine en anglais et traduit par</span></span></span><a aria-label="À l'origine en anglais et traduit par Google" class="css-4rbku5 css-18t94o4 css-901oao css-16my406 r-111h2gw r-1loqt21 r-1qd0xha r-1b43r93 r-6itf4e r-5f2r5o r-enhg6t r-bcqeeo r-qvutc0" data-focusable="true" href="https://translate.google.com/" rel=" noopener noreferrer" role="link" style="background-color: rgba(0, 0, 0, 0); border: 0px solid black; box-sizing: border-box; color: #8899a6; cursor: pointer; display: inline; font-size: 14px; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: calc(21px); list-style: none; margin: 0.1em 5px 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; text-align: inherit; text-decoration-line: none; white-space: inherit;" target="_blank"><svg class="r-4qtqp9 r-hp0c3x r-1xvli5t r-dnmrzs r-bnwqim r-1plcrui r-lrvibr" viewbox="0 0 74 24"><g></g></svg><span style="font-family: arial;"><path d="M9.827 17.667c-4.82 0-8.873-3.927-8.873-8.747S5.007.173 9.827.173c2.667 0 4.567 1.047 5.993 2.413l-1.687 1.687c-1.027-.96-2.413-1.707-4.307-1.707-3.52 0-6.273 2.84-6.273 6.36s2.753 6.36 6.273 6.36c2.28 0 3.587-.92 4.413-1.747.68-.68 1.132-1.668 1.3-3.008H10v-2.4h7.873c.087.428.127.935.127 1.495 0 1.793-.493 4.013-2.067 5.587-1.54 1.6-3.5 2.453-6.106 2.453zm20.806-5.627c0 3.24-2.533 5.633-5.633 5.633-3.107 0-5.633-2.387-5.633-5.633 0-3.267 2.527-5.633 5.633-5.633 3.1.006 5.633 2.373 5.633 5.633zm-2.466 0c0-2.027-1.467-3.413-3.167-3.413-1.7 0-3.167 1.387-3.167 3.413 0 2.007 1.467 3.413 3.167 3.413 1.7 0 3.167-1.406 3.167-3.413zm15.133-.007c0 3.24-2.527 5.633-5.633 5.633s-5.633-2.387-5.633-5.633c0-3.267 2.527-5.633 5.633-5.633S43.3 8.773 43.3 12.033zm-2.467 0c0-2.027-1.467-3.413-3.167-3.413S34.5 10.007 34.5 12.033c0 2.007 1.467 3.413 3.167 3.413s3.166-1.406 3.166-3.413zm14.5-5.286V16.86c0 4.16-2.453 5.867-5.353 5.867-2.733 0-4.373-1.833-4.993-3.327l2.153-.893c.387.92 1.32 2.007 2.84 2.007 1.853 0 3.007-1.153 3.007-3.307v-.813H52.9c-.553.68-1.62 1.28-2.967 1.28-2.813 0-5.267-2.453-5.267-5.613 0-3.18 2.453-5.652 5.267-5.652 1.347 0 2.413.6 2.967 1.26h.087v-.92h2.346zm-2.173 5.306c0-1.987-1.32-3.433-3.007-3.433-1.707 0-3.007 1.453-3.007 3.433 0 1.96 1.3 3.393 3.007 3.393 1.68 0 3.007-1.426 3.007-3.393zM59.807.78v16.553h-2.473V.78h2.473zm9.886 13.113l1.92 1.28c-.62.92-2.113 2.493-4.693 2.493-3.2 0-5.587-2.473-5.587-5.633 0-3.347 2.413-5.633 5.313-5.633 2.92 0 4.353 2.327 4.82 3.587l.253.64-7.534 3.113c.573 1.133 1.473 1.707 2.733 1.707s2.133-.62 2.773-1.554zm-5.906-2.026l5.033-2.093c-.28-.707-1.107-1.193-2.093-1.193-1.254 0-3.007 1.107-2.94 3.287z"></path></span></a></div><div class="css-1dbjc4n r-1g94qm0" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 5px 0px 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-901oao r-jwli3a r-1qd0xha r-1x35g6 r-16dba41 r-ad9z0x r-bcqeeo r-bnwqim r-qvutc0" dir="auto" id="tweet-text" lang="fr" style="border: 0px solid black; box-sizing: border-box; color: white; display: inline; font-size: 24px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; position: relative; white-space: pre-wrap;"><span class="css-901oao css-16my406 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" style="border: 0px solid black; box-sizing: border-box; color: inherit; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: inherit;"><span style="font-family: arial;">Il m'a fallu un certain temps pour voir ce qui se passait ici, mais j'aime ça! Quels que soient a, b et c, vous pouvez construire ces neuf triangles supplémentaires, chacun avec la même aire, plus les carrés de chaque côté, pour former un carré.
Je veux dire, c'est un peu Heath-Robinson, mais c'est toujours chouette :-)</span></span></div><div class="css-901oao r-jwli3a r-1qd0xha r-1x35g6 r-16dba41 r-ad9z0x r-bcqeeo r-bnwqim r-qvutc0" dir="auto" id="tweet-text" lang="fr" style="border: 0px solid black; box-sizing: border-box; color: white; display: inline; font-size: 24px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; position: relative; white-space: pre-wrap;"><span class="css-901oao css-16my406 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" style="border: 0px solid black; box-sizing: border-box; color: inherit; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: inherit;"><span style="font-family: arial;"><br /></span></span></div></div></div></div></div></div><div><div class="css-1dbjc4n r-18u37iz r-d0pm55" data-testid="tweet" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: horizontal; align-items: stretch; background-color: #15202b; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: row; flex-shrink: 0; font-size: 16px; margin: 0px 0px 5px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-1iusvr4 r-16y2uox r-1777fci" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-flex: 1; -webkit-box-orient: vertical; -webkit-box-pack: center; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-direction: column; flex: 1 0 0px; justify-content: center; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; 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-webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 1; margin: 0px; max-width: 100%; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><a class="css-4rbku5 css-18t94o4 css-1dbjc4n r-1loqt21 r-1wbh5a2 r-dnmrzs r-1ny4l3l" data-focusable="true" href="https://twitter.com/BenHambrecht" role="link" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; background-color: rgba(0, 0, 0, 0); border: 0px solid black; box-sizing: border-box; cursor: pointer; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 1; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; list-style: none; margin: 0px; max-width: 100%; min-height: 0px; min-width: 0px; outline-style: none; padding: 0px; position: relative; text-align: inherit; text-decoration-line: none; z-index: 0;"><div class="css-1dbjc4n r-1wbh5a2 r-dnmrzs r-1ny4l3l" id="tweet-user-name" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 1; margin: 0px; max-width: 100%; min-height: 0px; min-width: 0px; outline-style: none; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-1awozwy r-18u37iz r-dnmrzs" style="-webkit-box-align: center; -webkit-box-direction: normal; -webkit-box-orient: horizontal; align-items: center; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: row; flex-shrink: 0; margin: 0px; max-width: 100%; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-901oao css-bfa6kz r-jwli3a r-1qd0xha r-ubezar r-vw2c0b r-ad9z0x r-bcqeeo r-1ddef8g r-3s2u2q r-qvutc0" dir="auto" style="border: 0px solid black; box-sizing: border-box; color: white; display: inline; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: bold; line-height: 1.3125; margin: 0px; max-width: 100%; min-width: 0px; overflow-wrap: break-word; overflow: hidden; padding: 0px; text-decoration-line: underline; text-overflow: ellipsis; white-space: nowrap;"><span style="font-family: arial;"><br /></span></div></div></div></a></div><div class="css-1dbjc4n r-18u37iz r-1h0z5md r-mlyl9t" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: horizontal; -webkit-box-pack: start; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: row; flex-shrink: 0; justify-content: flex-start; margin: 0px 0px 0px 21px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div aria-expanded="false" aria-haspopup="true" aria-label="Plus" class="css-18t94o4 css-1dbjc4n r-1777fci r-11cpok1 r-1ny4l3l r-bztko3 r-lrvibr" data-focusable="true" data-testid="caret" role="button" style="-webkit-box-align: stretch; 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z-index: 0;"></div><svg class="r-4qtqp9 r-yyyyoo r-1xvli5t r-dnmrzs r-bnwqim r-1plcrui r-lrvibr r-1hdv0qi" viewbox="0 0 24 24"><g></g></svg><span style="font-family: arial;"><path d="M19.39 14.882c-1.58 0-2.862-1.283-2.862-2.86s1.283-2.862 2.86-2.862 2.862 1.283 2.862 2.86-1.284 2.862-2.86 2.862zm0-4.223c-.75 0-1.362.61-1.362 1.36s.61 1.36 1.36 1.36 1.362-.61 1.362-1.36-.61-1.36-1.36-1.36zM12 14.882c-1.578 0-2.86-1.283-2.86-2.86S10.42 9.158 12 9.158s2.86 1.282 2.86 2.86S13.578 14.88 12 14.88zm0-4.223c-.75 0-1.36.61-1.36 1.36s.61 1.362 1.36 1.362 1.36-.61 1.36-1.36-.61-1.363-1.36-1.363zm-7.39 4.223c-1.577 0-2.86-1.283-2.86-2.86S3.034 9.16 4.61 9.16s2.862 1.283 2.862 2.86-1.283 2.862-2.86 2.862zm0-4.223c-.75 0-1.36.61-1.36 1.36s.61 1.36 1.36 1.36 1.362-.61 1.362-1.36-.61-1.36-1.36-1.36z"></path></span></div></div></div></div></div></div></div></div></div><div class="css-1dbjc4n" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; background-color: #15202b; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; font-size: 16px; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-4qtqp9 r-18u37iz r-1wtj0ep r-p1pxzi r-a1ub67" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: horizontal; -webkit-box-pack: justify; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: inline-block; flex-basis: auto; flex-direction: row; flex-shrink: 0; justify-content: space-between; margin: 11px 0px 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-901oao r-111h2gw r-1qd0xha r-ubezar r-16dba41 r-ad9z0x r-bcqeeo r-qvutc0" dir="auto" style="border: 0px solid black; box-sizing: border-box; color: #8899a6; display: inline; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: pre-wrap;"><a class="css-4rbku5 css-18t94o4 css-1dbjc4n r-1loqt21 r-1wbh5a2 r-dnmrzs r-1ny4l3l" data-focusable="true" href="https://twitter.com/BenHambrecht" role="link" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; background-color: rgba(0, 0, 0, 0); border: 0px solid black; box-sizing: border-box; cursor: pointer; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 1; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; list-style: none; margin: 0px; max-width: 100%; min-height: 0px; min-width: 0px; outline-style: none; padding: 0px; position: relative; text-align: inherit; text-decoration-line: none; white-space: normal; z-index: 0;"><div class="css-1dbjc4n r-1wbh5a2 r-dnmrzs r-1ny4l3l" id="tweet-user-name" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 1; margin: 0px; max-width: 100%; min-height: 0px; min-width: 0px; outline-style: none; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-1awozwy r-18u37iz r-dnmrzs" style="-webkit-box-align: center; -webkit-box-direction: normal; -webkit-box-orient: horizontal; align-items: center; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: row; flex-shrink: 0; margin: 0px; max-width: 100%; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-901oao css-bfa6kz r-jwli3a r-1qd0xha r-ubezar r-vw2c0b r-ad9z0x r-bcqeeo r-1ddef8g r-3s2u2q r-qvutc0" dir="auto" style="border: 0px solid black; box-sizing: border-box; color: white; display: inline; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: bold; line-height: 1.3125; margin: 0px; max-width: 100%; min-width: 0px; overflow-wrap: break-word; overflow: hidden; padding: 0px; text-decoration-line: underline; text-overflow: ellipsis; white-space: nowrap;"><span style="font-family: arial;"><br /></span></div></div></div></a></div></div><div class="css-1dbjc4n r-4qtqp9 r-18u37iz r-1wtj0ep r-p1pxzi r-a1ub67" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: horizontal; -webkit-box-pack: justify; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: inline-block; flex-basis: auto; flex-direction: row; flex-shrink: 0; justify-content: space-between; margin: 11px 0px 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-901oao r-111h2gw r-1qd0xha r-ubezar r-16dba41 r-ad9z0x r-bcqeeo r-qvutc0" dir="auto" id="tweet-reply-context" style="border: 0px solid black; box-sizing: border-box; color: #8899a6; display: inline; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: pre-wrap;"><span style="font-family: arial;">En réponse à <div class="css-1dbjc4n r-xoduu5" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: inline-flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><a class="css-4rbku5 css-18t94o4 css-901oao css-16my406 r-1n1174f r-1loqt21 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" data-focusable="true" href="https://twitter.com/OLonguet" role="link" style="background-color: rgba(0, 0, 0, 0); border: 0px solid black; box-sizing: border-box; color: #1b95e0; cursor: pointer; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; list-style: none; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; text-align: inherit; text-decoration-line: none; white-space: inherit;"><span class="css-901oao css-16my406 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" style="border: 0px solid black; box-sizing: border-box; color: inherit; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: inherit;">@OLonguet</span></a></div></span></div></div><div class="css-1dbjc4n" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-a1ub67" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 11px 0px 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-901oao r-jwli3a r-1qd0xha r-1x35g6 r-16dba41 r-ad9z0x r-bcqeeo r-bnwqim r-qvutc0" dir="auto" id="tweet-text" lang="fr" style="border: 0px solid black; box-sizing: border-box; color: white; display: inline; font-size: 24px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; position: relative; white-space: pre-wrap;"><span class="css-901oao css-16my406 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" style="border: 0px solid black; box-sizing: border-box; color: inherit; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: inherit;"><span style="font-family: arial;">Je ne vois pas pq les parallélogrammes sont décomposés en triangles obtus plutôt que rectangles, comme l‘indique le calcul</span></span></div></div></div></div></div><div><span style="font-family: arial;"><br /></span></div><div><div class="css-1dbjc4n r-18u37iz r-d0pm55" data-testid="tweet" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: horizontal; align-items: stretch; background-color: #15202b; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: row; flex-shrink: 0; font-size: 16px; margin: 0px 0px 5px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-1iusvr4 r-16y2uox r-1777fci" style="-webkit-box-align: stretch; 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position: relative; z-index: 0;"><div class="css-1dbjc4n r-1awozwy r-18u37iz r-dnmrzs" style="-webkit-box-align: center; -webkit-box-direction: normal; -webkit-box-orient: horizontal; align-items: center; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: row; flex-shrink: 0; margin: 0px; max-width: 100%; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-901oao css-bfa6kz r-jwli3a r-1qd0xha r-ubezar r-vw2c0b r-ad9z0x r-bcqeeo r-3s2u2q r-qvutc0" dir="auto" style="border: 0px solid black; box-sizing: border-box; color: white; display: inline; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: bold; line-height: 1.3125; margin: 0px; max-width: 100%; min-width: 0px; overflow-wrap: break-word; overflow: hidden; padding: 0px; text-overflow: ellipsis; white-space: nowrap;"><span style="font-family: arial;"><br /></span></div></div></div></a></div><div class="css-1dbjc4n r-18u37iz r-1h0z5md r-mlyl9t" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: horizontal; -webkit-box-pack: start; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: row; flex-shrink: 0; justify-content: flex-start; margin: 0px 0px 0px 21px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div aria-expanded="false" aria-haspopup="true" aria-label="Plus" class="css-18t94o4 css-1dbjc4n r-1777fci r-11cpok1 r-1ny4l3l r-bztko3 r-lrvibr" data-focusable="true" data-testid="caret" role="button" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; -webkit-box-pack: center; align-items: stretch; border: 0px solid black; box-sizing: border-box; cursor: pointer; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; justify-content: center; margin: 0px; min-height: 0px; min-width: 0px; outline-style: none; overflow: visible; padding: 0px; position: relative; user-select: none; z-index: 0;" tabindex="0"><div class="css-901oao r-1awozwy r-111h2gw r-6koalj r-1qd0xha r-ubezar r-16dba41 r-1h0z5md r-ad9z0x r-bcqeeo r-o7ynqc r-clp7b1 r-3s2u2q r-qvutc0" dir="ltr" style="-webkit-box-align: center; -webkit-box-pack: start; align-items: center; border: 0px solid black; box-sizing: border-box; color: #8899a6; display: flex; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; justify-content: flex-start; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; transition-duration: 0.2s; transition-property: color; white-space: nowrap;"><div class="css-1dbjc4n r-xoduu5" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: inline-flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-sdzlij r-1p0dtai r-xoduu5 r-1d2f490 r-xf4iuw r-1ny4l3l r-u8s1d r-zchlnj r-ipm5af r-o7ynqc r-6416eg" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border-radius: 9999px; border: 0px solid black; bottom: 0px; box-sizing: border-box; display: inline-flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; left: 0px; margin: -8px; min-height: 0px; min-width: 0px; outline-style: none; padding: 0px; position: absolute; right: 0px; top: 0px; transition-duration: 0.2s; transition-property: background-color, box-shadow; z-index: 0;"><span style="font-family: arial;"><br /></span></div></div></div></div></div></div></div></div></div></div><div class="css-1dbjc4n" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; background-color: #15202b; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; font-size: 16px; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-4qtqp9 r-18u37iz r-1wtj0ep r-p1pxzi r-a1ub67" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: horizontal; -webkit-box-pack: justify; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: inline-block; flex-basis: auto; flex-direction: row; flex-shrink: 0; justify-content: space-between; margin: 11px 0px 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-901oao r-111h2gw r-1qd0xha r-ubezar r-16dba41 r-ad9z0x r-bcqeeo r-qvutc0" dir="auto" id="tweet-reply-context" style="border: 0px solid black; box-sizing: border-box; color: #8899a6; display: inline; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: pre-wrap;"><span style="font-family: arial;">En réponse à <div class="css-1dbjc4n r-xoduu5" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: inline-flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><a class="css-4rbku5 css-18t94o4 css-901oao css-16my406 r-1n1174f r-1loqt21 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" data-focusable="true" href="https://twitter.com/OLonguet" role="link" style="background-color: rgba(0, 0, 0, 0); border: 0px solid black; box-sizing: border-box; color: #1b95e0; cursor: pointer; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; list-style: none; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; text-align: inherit; text-decoration-line: none; white-space: inherit;"><span class="css-901oao css-16my406 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" style="border: 0px solid black; box-sizing: border-box; color: inherit; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: inherit;">@OLonguet</span></a></div></span></div></div><div class="css-1dbjc4n" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-a1ub67" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 11px 0px 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-901oao r-jwli3a r-1qd0xha r-1x35g6 r-16dba41 r-ad9z0x r-bcqeeo r-bnwqim r-qvutc0" dir="auto" id="tweet-text" lang="en" style="border: 0px solid black; box-sizing: border-box; color: white; display: inline; font-size: 24px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; position: relative; white-space: pre-wrap;"><span class="css-901oao css-16my406 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" style="border: 0px solid black; box-sizing: border-box; color: inherit; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: inherit;"><span style="font-family: arial;">You can get 4 more by reposition that square. I see what was done. This is an augmentation of the original proof. The original proof is sitting in the bottom left corner.</span></span></div><div class="css-901oao css-bfa6kz r-jwli3a r-6koalj r-1w6e6rj r-1qd0xha r-ubezar r-16dba41 r-ad9z0x r-1g94qm0 r-bcqeeo r-q4m81j r-qvutc0" dir="ltr" style="border: 0px solid black; box-sizing: border-box; color: white; display: flex; flex-wrap: wrap; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.3125; margin: 5px 0px 0px; max-width: 100%; min-width: 0px; overflow-wrap: break-word; overflow: hidden; padding: 0px; text-align: center; text-overflow: ellipsis; white-space: nowrap;"><span aria-expanded="true" aria-label="Masquer le Tweet traduit" class="css-18t94o4 css-901oao css-16my406 r-1n1174f r-1loqt21 r-1qd0xha r-1b43r93 r-6itf4e r-bcqeeo r-qvutc0" data-focusable="true" role="button" style="border: 0px solid black; box-sizing: border-box; color: #1b95e0; cursor: pointer; display: inline; font-size: 14px; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: calc(21px); margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: inherit;" tabindex="0"><span class="css-901oao css-16my406 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" style="border: 0px solid black; box-sizing: border-box; color: inherit; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: inherit;"><span style="font-family: arial;">À l'origine en anglais et traduit par</span></span></span><a aria-label="À l'origine en anglais et traduit par Google" class="css-4rbku5 css-18t94o4 css-901oao css-16my406 r-111h2gw r-1loqt21 r-1qd0xha r-1b43r93 r-6itf4e r-5f2r5o r-enhg6t r-bcqeeo r-qvutc0" data-focusable="true" href="https://translate.google.com/" rel=" noopener noreferrer" role="link" style="background-color: rgba(0, 0, 0, 0); border: 0px solid black; box-sizing: border-box; color: #8899a6; cursor: pointer; display: inline; font-size: 14px; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: calc(21px); list-style: none; margin: 0.1em 5px 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; text-align: inherit; text-decoration-line: none; white-space: inherit;" target="_blank"><svg class="r-4qtqp9 r-hp0c3x r-1xvli5t r-dnmrzs r-bnwqim r-1plcrui r-lrvibr" viewbox="0 0 74 24"><g></g></svg><span style="font-family: arial;"><path d="M9.827 17.667c-4.82 0-8.873-3.927-8.873-8.747S5.007.173 9.827.173c2.667 0 4.567 1.047 5.993 2.413l-1.687 1.687c-1.027-.96-2.413-1.707-4.307-1.707-3.52 0-6.273 2.84-6.273 6.36s2.753 6.36 6.273 6.36c2.28 0 3.587-.92 4.413-1.747.68-.68 1.132-1.668 1.3-3.008H10v-2.4h7.873c.087.428.127.935.127 1.495 0 1.793-.493 4.013-2.067 5.587-1.54 1.6-3.5 2.453-6.106 2.453zm20.806-5.627c0 3.24-2.533 5.633-5.633 5.633-3.107 0-5.633-2.387-5.633-5.633 0-3.267 2.527-5.633 5.633-5.633 3.1.006 5.633 2.373 5.633 5.633zm-2.466 0c0-2.027-1.467-3.413-3.167-3.413-1.7 0-3.167 1.387-3.167 3.413 0 2.007 1.467 3.413 3.167 3.413 1.7 0 3.167-1.406 3.167-3.413zm15.133-.007c0 3.24-2.527 5.633-5.633 5.633s-5.633-2.387-5.633-5.633c0-3.267 2.527-5.633 5.633-5.633S43.3 8.773 43.3 12.033zm-2.467 0c0-2.027-1.467-3.413-3.167-3.413S34.5 10.007 34.5 12.033c0 2.007 1.467 3.413 3.167 3.413s3.166-1.406 3.166-3.413zm14.5-5.286V16.86c0 4.16-2.453 5.867-5.353 5.867-2.733 0-4.373-1.833-4.993-3.327l2.153-.893c.387.92 1.32 2.007 2.84 2.007 1.853 0 3.007-1.153 3.007-3.307v-.813H52.9c-.553.68-1.62 1.28-2.967 1.28-2.813 0-5.267-2.453-5.267-5.613 0-3.18 2.453-5.652 5.267-5.652 1.347 0 2.413.6 2.967 1.26h.087v-.92h2.346zm-2.173 5.306c0-1.987-1.32-3.433-3.007-3.433-1.707 0-3.007 1.453-3.007 3.433 0 1.96 1.3 3.393 3.007 3.393 1.68 0 3.007-1.426 3.007-3.393zM59.807.78v16.553h-2.473V.78h2.473zm9.886 13.113l1.92 1.28c-.62.92-2.113 2.493-4.693 2.493-3.2 0-5.587-2.473-5.587-5.633 0-3.347 2.413-5.633 5.313-5.633 2.92 0 4.353 2.327 4.82 3.587l.253.64-7.534 3.113c.573 1.133 1.473 1.707 2.733 1.707s2.133-.62 2.773-1.554zm-5.906-2.026l5.033-2.093c-.28-.707-1.107-1.193-2.093-1.193-1.254 0-3.007 1.107-2.94 3.287z"></path></span></a></div><div class="css-1dbjc4n r-1g94qm0" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 5px 0px 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-901oao r-jwli3a r-1qd0xha r-1x35g6 r-16dba41 r-ad9z0x r-bcqeeo r-bnwqim r-qvutc0" dir="auto" id="tweet-text" lang="fr" style="border: 0px solid black; box-sizing: border-box; color: white; display: inline; font-size: 24px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; position: relative; white-space: pre-wrap;"><span class="css-901oao css-16my406 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" style="border: 0px solid black; box-sizing: border-box; color: inherit; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: inherit;"><span style="font-family: arial;">Vous pouvez en obtenir 4 supplémentaires en repositionnant ce carré. Je vois ce qui a été fait. Ceci est une augmentation de la preuve originale. La preuve originale se trouve dans le coin inférieur gauche.</span></span></div></div></div></div></div></div><div><span style="font-family: arial;"> On peut remplacer les parallélogrammes par des triangles rectangles. C'est vrai, je n'avais pas remarqué, j'avais pris un autre chemin . On obtient une figure plus simple.</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9nS6bsqnt4voiT4Q-UGQxPJFYEmb9VJYC_jEG6BhD8UFdE9asR7PU5QAhgvix3FEDEWUZ9s3MU9DXz-LqregvGswIUL5PRgbkHO-J4XKDFip5knZHFdDTE8B8QK5LyR-jJaFSJzsWoDY/s952/preuvpythagore3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: arial;"><img border="0" data-original-height="525" data-original-width="952" height="352" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9nS6bsqnt4voiT4Q-UGQxPJFYEmb9VJYC_jEG6BhD8UFdE9asR7PU5QAhgvix3FEDEWUZ9s3MU9DXz-LqregvGswIUL5PRgbkHO-J4XKDFip5knZHFdDTE8B8QK5LyR-jJaFSJzsWoDY/w640-h352/preuvpythagore3.jpg" width="640" /></span></a></div><span style="font-family: arial;">Là dessus, la figure est bien simplifiée, et on remarque la même figure que la première démonstration de ce post, ce que me fait remarquer Jason-automaths</span><div><span style="font-family: arial;"><br /></span></div><div><div class="css-1dbjc4n" style="-webkit-box-align: stretch; 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font-weight: inherit; line-height: inherit; list-style: none; margin: 0px; max-width: 100%; min-height: 0px; min-width: 0px; outline-style: none; padding: 0px; position: relative; text-align: inherit; text-decoration-line: none; z-index: 0;"><div class="css-1dbjc4n r-1wbh5a2 r-dnmrzs r-1ny4l3l" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 1; margin: 0px; max-width: 100%; min-height: 0px; min-width: 0px; outline-style: none; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-1awozwy r-18u37iz r-dnmrzs" style="-webkit-box-align: center; -webkit-box-direction: normal; -webkit-box-orient: horizontal; align-items: center; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: row; flex-shrink: 0; margin: 0px; max-width: 100%; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-901oao css-bfa6kz r-jwli3a r-1qd0xha r-ubezar r-vw2c0b r-ad9z0x r-bcqeeo r-3s2u2q r-qvutc0" dir="auto" style="border: 0px solid black; box-sizing: border-box; color: white; display: inline; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: bold; line-height: 1.3125; margin: 0px; max-width: 100%; min-width: 0px; overflow-wrap: break-word; overflow: hidden; padding: 0px; text-overflow: ellipsis; white-space: nowrap;"><span class="css-901oao css-16my406 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" style="border: 0px solid black; box-sizing: border-box; color: inherit; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: inherit;"><span style="font-family: arial;">Jason - Automaths</span></span></div><div class="css-901oao r-jwli3a r-18u37iz r-1q142lx r-1qd0xha r-ubezar r-16dba41 r-ad9z0x r-bcqeeo r-qvutc0" dir="auto" style="-webkit-box-direction: normal; -webkit-box-orient: horizontal; border: 0px solid black; box-sizing: border-box; color: white; display: inline; flex-direction: row; flex-shrink: 0; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: pre-wrap;"></div></div><div class="css-1dbjc4n r-18u37iz r-1wbh5a2" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: horizontal; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: row; flex-shrink: 1; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-901oao css-bfa6kz r-111h2gw r-18u37iz r-1qd0xha r-ubezar r-16dba41 r-ad9z0x r-bcqeeo r-qvutc0" dir="ltr" style="-webkit-box-direction: normal; -webkit-box-orient: horizontal; border: 0px solid black; box-sizing: border-box; color: #8899a6; display: inline; flex-direction: row; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.3125; margin: 0px; max-width: 100%; min-width: 0px; overflow-wrap: break-word; overflow: hidden; padding: 0px; text-overflow: ellipsis; white-space: nowrap;"><span class="css-901oao css-16my406 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" style="border: 0px solid black; box-sizing: border-box; color: inherit; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: inherit;"><span style="font-family: arial;">@paljasn</span></span></div></div></div></a></div><div class="css-1dbjc4n r-18u37iz r-1h0z5md r-mlyl9t" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: horizontal; -webkit-box-pack: start; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: row; flex-shrink: 0; justify-content: flex-start; margin: 0px 0px 0px 21px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div aria-expanded="false" aria-haspopup="true" aria-label="Plus" class="css-18t94o4 css-1dbjc4n r-1777fci r-11cpok1 r-1ny4l3l r-bztko3 r-lrvibr" data-focusable="true" data-testid="caret" role="button" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; -webkit-box-pack: center; align-items: stretch; border: 0px solid black; box-sizing: border-box; cursor: pointer; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; justify-content: center; margin: 0px; min-height: 0px; min-width: 0px; outline-style: none; overflow: visible; padding: 0px; position: relative; user-select: none; z-index: 0;" tabindex="0"><div class="css-901oao r-1awozwy r-111h2gw r-6koalj r-1qd0xha r-ubezar r-16dba41 r-1h0z5md r-ad9z0x r-bcqeeo r-o7ynqc r-clp7b1 r-3s2u2q r-qvutc0" dir="ltr" style="-webkit-box-align: center; -webkit-box-pack: start; align-items: center; border: 0px solid black; box-sizing: border-box; color: #8899a6; display: flex; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; justify-content: flex-start; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; transition-duration: 0.2s; transition-property: color; white-space: nowrap;"><div class="css-1dbjc4n r-xoduu5" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: inline-flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-sdzlij r-1p0dtai r-xoduu5 r-1d2f490 r-xf4iuw r-1ny4l3l r-u8s1d r-zchlnj r-ipm5af r-o7ynqc r-6416eg" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border-radius: 9999px; border: 0px solid black; bottom: 0px; box-sizing: border-box; display: inline-flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; left: 0px; margin: -8px; min-height: 0px; min-width: 0px; outline-style: none; padding: 0px; position: absolute; right: 0px; top: 0px; transition-duration: 0.2s; transition-property: background-color, box-shadow; z-index: 0;"></div><svg class="r-4qtqp9 r-yyyyoo r-1xvli5t r-dnmrzs r-bnwqim r-1plcrui r-lrvibr r-1hdv0qi" viewbox="0 0 24 24"><g></g></svg><span style="font-family: arial;"><path d="M19.39 14.882c-1.58 0-2.862-1.283-2.862-2.86s1.283-2.862 2.86-2.862 2.862 1.283 2.862 2.86-1.284 2.862-2.86 2.862zm0-4.223c-.75 0-1.362.61-1.362 1.36s.61 1.36 1.36 1.36 1.362-.61 1.362-1.36-.61-1.36-1.36-1.36zM12 14.882c-1.578 0-2.86-1.283-2.86-2.86S10.42 9.158 12 9.158s2.86 1.282 2.86 2.86S13.578 14.88 12 14.88zm0-4.223c-.75 0-1.36.61-1.36 1.36s.61 1.362 1.36 1.362 1.36-.61 1.36-1.36-.61-1.363-1.36-1.363zm-7.39 4.223c-1.577 0-2.86-1.283-2.86-2.86S3.034 9.16 4.61 9.16s2.862 1.283 2.862 2.86-1.283 2.862-2.86 2.862zm0-4.223c-.75 0-1.36.61-1.36 1.36s.61 1.36 1.36 1.36 1.362-.61 1.362-1.36-.61-1.36-1.36-1.36z"></path></span></div></div></div></div></div></div></div></div></div><div class="css-1dbjc4n" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; background-color: #15202b; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; font-size: 16px; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-4qtqp9 r-18u37iz r-1wtj0ep r-p1pxzi r-a1ub67" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: horizontal; -webkit-box-pack: justify; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: inline-block; flex-basis: auto; flex-direction: row; flex-shrink: 0; justify-content: space-between; margin: 11px 0px 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-901oao r-111h2gw r-1qd0xha r-ubezar r-16dba41 r-ad9z0x r-bcqeeo r-qvutc0" dir="auto" style="border: 0px solid black; box-sizing: border-box; color: #8899a6; display: inline; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: pre-wrap;"><span style="font-family: arial;">En réponse à <div class="css-1dbjc4n r-xoduu5" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: inline-flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><a class="css-4rbku5 css-18t94o4 css-901oao css-16my406 r-1n1174f r-1loqt21 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" data-focusable="true" href="https://twitter.com/OLonguet" role="link" style="background-color: rgba(0, 0, 0, 0); border: 0px solid black; box-sizing: border-box; color: #1b95e0; cursor: pointer; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; list-style: none; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; text-align: inherit; text-decoration-line: none; white-space: inherit;"><span class="css-901oao css-16my406 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" style="border: 0px solid black; box-sizing: border-box; color: inherit; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: inherit;">@OLonguet</span></a></div></span></div></div><div class="css-1dbjc4n" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-a1ub67" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 11px 0px 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-901oao r-jwli3a r-1qd0xha r-1x35g6 r-16dba41 r-ad9z0x r-bcqeeo r-bnwqim r-qvutc0" dir="auto" lang="fr" style="border: 0px solid black; box-sizing: border-box; color: white; display: inline; font-size: 24px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; position: relative; white-space: pre-wrap;"><span class="css-901oao css-16my406 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" style="border: 0px solid black; box-sizing: border-box; color: inherit; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: inherit;"><span style="font-family: arial;">Ça me donne l'impression d'avoir une combinaison de ces deux figures là</span></span></div></div></div><div class="css-1dbjc4n" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-18bvks7 r-1867qdf r-1phboty r-rs99b7 r-a1ub67 r-1ny4l3l r-1udh08x r-o7ynqc r-6416eg" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border-radius: 16px; border: 1px solid rgb(56, 68, 77); box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 11px 0px 0px; min-height: 0px; min-width: 0px; outline-style: none; overflow: hidden; padding: 0px; position: relative; transition-duration: 0.2s; transition-property: background-color, box-shadow; z-index: 0;"><div class="css-1dbjc4n" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><a class="css-4rbku5 css-18t94o4 css-1dbjc4n r-1loqt21 r-1ny4l3l" data-focusable="true" href="https://twitter.com/paljasn/status/1319730776485863424/photo/1" role="link" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; background-color: rgba(0, 0, 0, 0); border: 0px solid black; box-sizing: border-box; cursor: pointer; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; list-style: none; margin: 0px; min-height: 0px; min-width: 0px; outline-style: none; padding: 0px; position: relative; text-align: inherit; text-decoration-line: none; z-index: 0;"><div class="css-1dbjc4n r-1adg3ll r-1udh08x" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 0px; min-height: 0px; min-width: 0px; overflow: hidden; padding: 0px; position: relative; z-index: 0;"><div class="r-1adg3ll r-13qz1uu" style="padding-bottom: 458.094px; width: 564px;"></div><div class="r-1p0dtai r-1pi2tsx r-1d2f490 r-u8s1d r-ipm5af r-13qz1uu" style="bottom: 0px; height: 458.094px; left: 0px; position: absolute; top: 0px; width: 564px;"><div aria-label="Image" class="css-1dbjc4n r-1p0dtai r-1mlwlqe r-1d2f490 r-p1pxzi r-11wrixw r-61z16t r-1mnahxq r-1udh08x r-u8s1d r-zchlnj r-ipm5af r-417010" data-testid="tweetPhoto" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; bottom: 0px; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; left: 0px; margin: 0px; min-height: 0px; min-width: 0px; overflow: hidden; padding: 0px; position: absolute; right: 0px; top: 0px; z-index: 0;"><div class="css-1dbjc4n r-1niwhzg r-vvn4in r-u6sd8q r-4gszlv r-1p0dtai r-1pi2tsx r-1d2f490 r-u8s1d r-zchlnj r-ipm5af r-13qz1uu r-1wyyakw" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; background-color: rgba(0, 0, 0, 0); background-image: url("https://pbs.twimg.com/media/ElCgJXwXUAAk5Bp?format=png&name=small"); background-position: center center; background-repeat: no-repeat; background-size: cover; border: 0px solid black; bottom: 0px; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; height: 458.094px; left: 0px; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: absolute; right: 0px; top: 0px; width: 564px; z-index: -1;"></div><img alt="Image" class="css-9pa8cd" draggable="true" src="https://pbs.twimg.com/media/ElCgJXwXUAAk5Bp?format=png&name=small" style="bottom: 0px; height: 458.094px; left: 0px; opacity: 0; position: absolute; right: 0px; top: 0px; width: 564px; z-index: -1;" /></div></div></div></a></div></div></div></div></div><div class="css-1dbjc4n r-1r5su4o" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; margin: 16px 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-1dbjc4n r-1awozwy r-18u37iz r-1wtj0ep" style="-webkit-box-align: center; -webkit-box-direction: normal; -webkit-box-orient: horizontal; -webkit-box-pack: justify; align-items: center; border: 0px solid black; box-sizing: border-box; display: flex; flex-basis: auto; flex-direction: row; flex-shrink: 0; justify-content: space-between; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: relative; z-index: 0;"><div class="css-901oao r-111h2gw r-1qd0xha r-ubezar r-16dba41 r-ad9z0x r-1rq6c10 r-bcqeeo r-qvutc0" dir="auto" style="border: 0px solid black; box-sizing: border-box; color: #8899a6; display: inline; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.3125; margin: 0px 11px 0px 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: pre-wrap;"><span style="font-family: arial;"><a class="css-4rbku5 css-18t94o4 css-901oao css-16my406 r-111h2gw r-1loqt21 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" data-focusable="true" href="https://twitter.com/paljasn/status/1319730776485863424" role="link" style="background-color: rgba(0, 0, 0, 0); border: 0px solid black; box-sizing: border-box; color: #8899a6; cursor: pointer; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; list-style: none; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; text-align: inherit; text-decoration-line: none; white-space: inherit;">10:01 PM · 23 oct. 2020</a><span aria-hidden="true" class="css-901oao css-16my406 r-111h2gw r-1q142lx r-1qd0xha r-ad9z0x r-bcqeeo r-ou255f r-qvutc0" style="border: 0px solid black; box-sizing: border-box; display: inline; flex-shrink: 0; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px 5px; white-space: inherit;"><span class="css-901oao css-16my406 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" style="border: 0px solid black; box-sizing: border-box; color: inherit; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space: inherit;">·</span></span><a class="css-4rbku5 css-18t94o4 css-901oao css-16my406 r-111h2gw r-1loqt21 r-1qd0xha r-ad9z0x r-bcqeeo r-1jeg54m r-qvutc0" data-focusable="true" href="https://help.twitter.com/using-twitter/how-to-tweet#source-labels" rel=" noopener noreferrer" role="link" style="background-color: rgba(0, 0, 0, 0); border: 0px solid black; box-sizing: border-box; color: #8899a6; cursor: pointer; display: inline; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.3125; list-style: none; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; text-align: inherit; text-decoration-line: none; white-space: normal;" target="_blank">Twitter for Android</a></span></div></div></div></div><div><span style="font-family: arial;"><br /></span></div><div><span style="font-family: arial;">Ah oui, est ce que ma démonstration est encore intéressante, alors ? J'ai tendance à le penser encore, parce que le moulin à vents, clef de la démonstration reste tout à fait visible, mais bon, vu comme ça, c'est vrai que ça fait un peu bricolage.</span></div><div><span style="font-family: arial;">Quoique, j'aurai tendance à penser que c'est possible que la démonstration a été trouvée ainsi, avec le moulin à vents, puis simplifiée juste dans le carré.</span></div><div><span style="font-family: arial;"><br /></span></div><div><span style="font-family: arial;">Là dessus, je revérifie sur le site https://www.cut-the-knot.org/pythagoras/ et je trouve que ma démo ressemble un peu à la #87</span></div><div><span style="font-family: arial;">https://www.cut-the-knot.org/pythagoras/Pyth3Trapezoids.shtml</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOrnnn3VE2HZoqsu0VmPTU6QLtyat7_F8vsPl-vfuwj1sSfVHPx2j6nYkaGiwKVu8FPW0_p-2fJkXCdYFQ96ePLOz4d1SWeVPGR8eZTOR5TyRbnLkUX0am_gG3abs3oKrT_vkKCkhZ6FM/s677/2020_10_26_19_34_24_Th%25C3%25A9or%25C3%25A8me_de_Pythagore_une_preuve_alg%25C3%25A9brique_%25C3%25A0_trois_trap%25C3%25A8zes.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: arial;"><img border="0" data-original-height="317" data-original-width="677" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOrnnn3VE2HZoqsu0VmPTU6QLtyat7_F8vsPl-vfuwj1sSfVHPx2j6nYkaGiwKVu8FPW0_p-2fJkXCdYFQ96ePLOz4d1SWeVPGR8eZTOR5TyRbnLkUX0am_gG3abs3oKrT_vkKCkhZ6FM/w640-h300/2020_10_26_19_34_24_Th%25C3%25A9or%25C3%25A8me_de_Pythagore_une_preuve_alg%25C3%25A9brique_%25C3%25A0_trois_trap%25C3%25A8zes.jpg" width="640" /></span></a></div><div class="separator" style="clear: both; text-align: center;"><span style="font-family: arial;">Bien que j'aie du mal à comprendre le découpage pour obtenir un trapèze, mais j'ai fait aussi des choix qui ont surpris.</span></div><div class="separator" style="clear: both; text-align: center;"><span style="font-family: arial;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><span style="font-family: arial;">Au final, j'ai démontré le théorème de Pythagore par mes propres moyens. Que cette démonstration existe ou pas est finalement de peu d'importance, le résultat est vrai de toute façon. Que la démonstration soit nouvelle ou pas, je n'ai pas vraiment réussi à trancher. C'est une amusette comme j'aime bien en tout cas .</span></div><div class="separator" style="clear: both; text-align: center;"><span style="font-family: arial;">Le débat qui a suivi sur Twitter était aussi intéressant.</span></div><div class="separator" style="clear: both; text-align: center;"><span style="font-family: arial;"> Cela m'a montré en tout cas une fois de plus qu'on peut s'amuser avec les maths et en ressentir bien des émotions .</span></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div></div>Olivier Longuethttp://www.blogger.com/profile/17956431908495478881noreply@blogger.com0tag:blogger.com,1999:blog-3415252720574602648.post-1169240869388920822020-09-30T21:01:00.004+02:002020-11-17T16:06:36.422+01:00origami<p> j'aime bien l'origami pour fabriquer des formes géométriques, notamment des solides de Platon. Sur ce blog, j'ai déjà parlé de ce pliage classique de la page A4 pour obtenir le tétraèdre régulier.</p><p>j'aime bien faire aussi le dodécaèdre régulier, qui pose des questions intéressantes.</p><p>Depuis très longtemps, j'essaye de faire le pliage de l'octaèdre, en partant d'une feuille carrée, voire une feuille A4, sans résultat satisfaisant.</p><p>Je me suis rendu compte qu'on pouvait facilement en obtenir un, à partir d'une feuille hexagonale. C'est très satisfaisant</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnZPA7lafBvoxJ4ZCOjZIdke7kyBWXWxCRZyizLLVPUmf2_ZvtkoqjJaIPf0uvQxmQ0kERPzer5bDpil1KYI5iIT_xzfbIAwG8fa2qaHhwKAYEMcVG6abnZop-xvUMpHDXusG9SvAZ6EU/s680/octaedreorigami.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="360" data-original-width="680" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnZPA7lafBvoxJ4ZCOjZIdke7kyBWXWxCRZyizLLVPUmf2_ZvtkoqjJaIPf0uvQxmQ0kERPzer5bDpil1KYI5iIT_xzfbIAwG8fa2qaHhwKAYEMcVG6abnZop-xvUMpHDXusG9SvAZ6EU/w569-h300/octaedreorigami.jpg" width="569" /></a></div><p>J'ai dessiné la construction pas à pas.</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKA4lAwUjoc2Ej42iqXujS0J603hVd1FO49kM_drRCTSVG5GxK0ChWTBHCCMTQms3Cc_HDi74-BZkRH1JdspSkVNEPxaiN2Dln3o9-i0I5Rbafp5jl_G8Rpomd1XIZ-msTqJzEhHbJTsM/s863/origamioctaedre.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="601" data-original-width="863" height="426" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKA4lAwUjoc2Ej42iqXujS0J603hVd1FO49kM_drRCTSVG5GxK0ChWTBHCCMTQms3Cc_HDi74-BZkRH1JdspSkVNEPxaiN2Dln3o9-i0I5Rbafp5jl_G8Rpomd1XIZ-msTqJzEhHbJTsM/w611-h426/origamioctaedre.jpg" width="611" /></a></div><br /><br /><p></p><p><br /></p>Olivier Longuethttp://www.blogger.com/profile/17956431908495478881noreply@blogger.com0tag:blogger.com,1999:blog-3415252720574602648.post-66747871108954356382020-06-20T13:50:00.001+02:002020-11-17T16:06:10.064+01:00pixel artCe blog est un peu trop au repos. Pourtant, je n'ai pas cessé de bricoler des objets pour la classe, je me suis servi de certains devant ma webcam pour la classe virtuelle, mais ça n'a pas le même goût ni la même efficacité que quand les élèves le manipulent. Mais il y a des trucs assez jolis, donc j'en fais profiter quand même, d'abord sur Twitter, mais pour un peu plus qu'une photo sur ce blog.<br />
Enfin, c'est mon projet du jour : faire un bilan des objets que j'ai fabriqués et utilisés depuis quelques mois et que j'ai tus sur ce blog .<br />
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Un petit jeu de grilles qui correspond à un nouveau point du programme de seconde :<br />
Notation |a|. Distance entre deux nombres réels.<br />
Représentation de l’intervalle [a - r , a + r]<br />
puis caractérisation par la condition
|x - a| ⩽ r.<br />
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J'avais entendu parler par les collègues de collèges de pixel art, et même si sa mise en oeuvre en est totalement différente (travail collaboratif, le choix pour griser une case dépend de réponses à des questions indépendantes), je me suis inspiré du concept de cases à griser pour entraîner les élèves aux équations avec les valeurs absolues . Il reste un code mathématique à traduire de manière graphique, et la satisfaction pour l'élève d'obtenir un résultat dont la cohérence s'établit peu à peu.<br />
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La réponse tient en un dessin. Le professeur peut voir en un coup d'oeil si le dessin montre la bonne réponse.<br />
Une erreur commune est la non compréhension du signe - dans l'expression<br />
|x - a| . Parfois pour toutes les expressions, parfois juste quand on soustrait un nombre négatif |x+3| = |x - (-3) | <br />
Si l'élève traduit |x - 2| par la distance au point d'abscisse 2, alors le bonhomme de neige aura le bras à gauche, s'il pense que c'est la distance au point d'abscisse -2, alors le bras du bonhomme de neige sera dans l'autre sens . S'il traduit bien<br />
|x - 2| mais pas |x +3|, alors le dessin est brouillé, n'existe que d'un côté.<br />
L'une des questions posées par les élèves est l'emploi du OU, qui n'est pas habituel pour eux . Faut-il colorier l'une des zones au choix ? Comme la choisir ?<br />
On doit expliciter : tu colories une zone si une condition ou si une autre est réalisée . Cela aboutit à colorier la zone 1 et la zone 2. Donc beaucoup d'élèves auraient préféré écrire un ET . L'écriture de la solution avec la réunion d'intervalles et sa traduction permet de clarifier cette écriture.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYX3ainR3BOX9MzoGi1a72r1X8ZBqq7bu-h7Ys8EGYQvDCPd-I5TJ84D3IeCMmDFQWTLBxgUqB3hm4p7UI-fFGVT7Qc-s7lUNVvlJYA3SP4a3dZ2rX_tZCM3nbsKsU9WVEoZIrkeQBE3c/s1600/dessincod%25C3%25A9valeur_absolue.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="497" data-original-width="988" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYX3ainR3BOX9MzoGi1a72r1X8ZBqq7bu-h7Ys8EGYQvDCPd-I5TJ84D3IeCMmDFQWTLBxgUqB3hm4p7UI-fFGVT7Qc-s7lUNVvlJYA3SP4a3dZ2rX_tZCM3nbsKsU9WVEoZIrkeQBE3c/s640/dessincod%25C3%25A9valeur_absolue.jpg" width="640" /></a></div>
<br />Olivier Longuethttp://www.blogger.com/profile/17956431908495478881noreply@blogger.com2tag:blogger.com,1999:blog-3415252720574602648.post-14187337177059969742020-06-20T11:12:00.001+02:002020-06-20T11:12:12.074+02:00découpage de gâteauDernièrement, nous étions cinq à la maison, et nous avions acheté un gâteau à base carrée et de crème, sans croûte. J'ai demandé à le couper .<br />
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On peut aussi découper en 3 parties égales en suscitant le même étonnement.<br />
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On pourra remarquer que c'est dommage d'avoir une part aussi charcutée, mais le plaisir d'avoir fait le malin à peu de frais rend le gâteau meilleur .<br />
<br />Olivier Longuethttp://www.blogger.com/profile/17956431908495478881noreply@blogger.com0tag:blogger.com,1999:blog-3415252720574602648.post-76529582372939892712020-01-09T19:39:00.002+01:002020-01-12T19:16:08.172+01:00identité remarquabledans le livre preuve en images ( Kangourou ), j'ai trouvé une preuve sans mots de l'identité remarquable a² - b² = ( a + b) ( a - b) .<br />
Autant l'illustration de (a+b)² = a²+2 ab +b²<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhN_7LT4h39ILmDtcLlpyhitzk2l1ExVwPs673_96t9bO4hYI9zxM1tIt7Hcet66qoqMtPDFuqL-Q58dOoVj8tFqPhzZA20iowt66DbEuGW0s9QFiMppnR0LDBLddWRApNi6iKS_j_bQ_oN/s1600/acarremoinbcarrec.gif" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="381" data-original-width="635" height="192" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhN_7LT4h39ILmDtcLlpyhitzk2l1ExVwPs673_96t9bO4hYI9zxM1tIt7Hcet66qoqMtPDFuqL-Q58dOoVj8tFqPhzZA20iowt66DbEuGW0s9QFiMppnR0LDBLddWRApNi6iKS_j_bQ_oN/s320/acarremoinbcarrec.gif" width="320" /></a> tombe sous le sens et est très facile à expliquer aux élèves, autant les deux autres identités sont laborieuses à illustrer. Donc j'étais assez content pour en faire un petit gif animé .<br />
Pour apprendre à faire de tels gifs, la video de Vincent Pantaloni est très bien faite :<br />
<a href="https://www.youtube.com/watch?v=2XzPlaz9D-8">https://www.youtube.com/watch?v=2XzPlaz9D-8</a><br />
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Ce gif a été très apprécié des collègues sur Twitter et je me suis dit que c'était aussi un petit puzzle sympathique que j'ai découpé au fablab .<br />
Matériau médium 3 mm<br />
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<br />Olivier Longuethttp://www.blogger.com/profile/17956431908495478881noreply@blogger.com0tag:blogger.com,1999:blog-3415252720574602648.post-8293597561907359652019-08-24T14:14:00.000+02:002019-08-24T17:17:29.067+02:00Ensembles de nombresDepuis un an que je poste sur Twitter, j'ai concentré mon attention sur des photos et images les plus parlantes possibles, ce qui est un exercice intéressant mais j'ai négligé le blog, pourtant il me semble que l'apport du texte pour expliciter la démarche, donner un mode de construction, faire le bilan de l'activité est important. Je vais essayer de coupler les deux, je vois que des collègues le font très bien. Quand j'aurai une idée nouvelle à proposer, je posterai l'image et une brève explication sur Twitter ( comme d'habitude) et je mettra un lien sur l'article du blog qui contiendra des explications supplémentaires.<br />
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Ma première activité en seconde à la rentrée: ranger les nombres dans des boites encastrées.</div>
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Mon épouse qui a été longtemps professeur de SVT utilisait différentes boites en bois afin de faire une activité sur la classification du vivant et l'arbre phylogénétique. Elle faisait utiliser ensuite des bambous et pitons pour transformer ces encastrements en graphes.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhD4sEcidIF_XcNYwkblwd1dGRR_ucapklPjlYsE9-V0g80356SmLUNuc8c5lgJfFsyEfPfYCVTOaNbF_vyU4h9muKbXqNN9Tw7k7x5iRjeudcUelSVlFUgdGXm30MJtdEwYnCM3Plns9w/s1600/DbiiMIpXUAE9tHU.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="678" data-original-width="1003" height="432" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhD4sEcidIF_XcNYwkblwd1dGRR_ucapklPjlYsE9-V0g80356SmLUNuc8c5lgJfFsyEfPfYCVTOaNbF_vyU4h9muKbXqNN9Tw7k7x5iRjeudcUelSVlFUgdGXm30MJtdEwYnCM3Plns9w/s640/DbiiMIpXUAE9tHU.jpg" width="640" /></a></div>
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On peut facilement fabriquer de telles boites dans un fablab, à différentes tailles, avec du médium 3mm ou 6mm .</div>
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Une vingtaine de nombres marqués sur des bouchons .</div>
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La consigne est de ranger ma collection de nombres le mieux possible dans les boites, et d'expliciter la technique de rangement, à l'écrit d'abord puis à l'oral.</div>
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Variable didactique: on peut donner le bon nombre de boites imbriquées pour R, Q, D, Z et N, ou on peut en donner davantage en demandant de faire le rangement qui utilisera le moins de boites.</div>
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J'ai déjà pratiqué cette activité, il faut s'attendre à des propositions un peu différentes de celles qu'on veut à la fin, mais cela suscite un beau débat. </div>
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erreurs classiques: les plus d'un côté , le moins de l'autre</div>
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les nombres faciles d'un côté, les plus compliqués de l'autre</div>
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les fractions d'un côté, les autres de l'autre</div>
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Temps de rangement estimé: 20 minutes.</div>
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Temps de débat estimé:15 minutes.</div>
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Il y a quelques pièges , comme sqrt 3 et sqrt 25 qui se ressemblent <i>a priori .</i></div>
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Je pense distribuer un papier avec quelques conseils, comme : écrire ces nombres avec un écriture à virgule( calculatrice autorisée) pour différencier plus facilement les différences de forme.</div>
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Il est possible dans le bilan de classe de coupler les explications avec quelques repères historiques sur une frise.</div>
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Olivier Longuethttp://www.blogger.com/profile/17956431908495478881noreply@blogger.com1tag:blogger.com,1999:blog-3415252720574602648.post-52389642927999206742018-06-16T17:45:00.001+02:002018-06-16T18:05:11.391+02:00gabarits pour patrons de polyèdres ou pavagesIl y a quelques années, j'avais trouvé dans une brocante, six petites règles avec quelques gabarits de formes,parmi lesquelles un pentagone régulier et un hexagone régulier qui avaient la même longueur de côté. On pouvait donc avec un peu de concentration et de méthode tracer des patrons de dodécaèdres ou d'icosaèdres tronqués en ne concentrant que sur la position des faces et non sur la construction des faces. Ce qui m'intéresse dans leur utilisation, c'est la réflexion et les stratégies que l'on peut mener pour trouver des patrons , peut être par la suite pour appréhender la foultitude des manières de réaliser ces patrons .<br />
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Au fil du temps, j'ai donné quelques unes de ces règles et perdu quelques autres, mais je trouve que c'est un joli objet et ça délasse de se concentrer sur ce genre de construction.</div>
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La semaine dernière, j'ai passé quelques heures au fablab du dôme à Caen pour réaliser avec le découpeuse laser des masques pour une pièce de théâtre. C'était assez répétitif, et j'ai eu le temps de bricoler sur geogebra en ligne, puis sur inkscape un jeu de gabarits pour dessiner des patrons de polyèdres. </div>
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Il restait quelques chutes de polyprolpylène, une sorte de plastique plutôt fin et assez rigide pour ne pas s'abimer lorsqu'on passe plusieurs fois le stylo .Le matériel idéal .<br />
Je me suis limité à 6 côtés, je n'ai pas fait l'octogone ou le dodécacagone qu'on voit sur certains solides d'Archimède pour des raisons de place sur la plaque de plastique comme sur la feuille . Le patron deviendrait lui aussi trop grand .<br />
étape 1 : travail sur geogebra</div>
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dessiner 4 segments de longueur donnée ( 2 cm) et tracer les polygones réguliers à 3 , 4 , 5 , 6 côtés .Les placer dans un carré. </div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIH-7k6ezXFPhp1O_wUN0rwJ4sHJ6EnkC7ZvLGa7hPhKHwPN2ySs3KmttOo53zVNJP8awi-OjE7vmuowX74ubvoRzO1XCWm4eAuDYkgkOr0s18BLAYQX3n7skYU737d2SrII8hNW9fNPk/s1600/tutogabarits.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="994" data-original-width="1102" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIH-7k6ezXFPhp1O_wUN0rwJ4sHJ6EnkC7ZvLGa7hPhKHwPN2ySs3KmttOo53zVNJP8awi-OjE7vmuowX74ubvoRzO1XCWm4eAuDYkgkOr0s18BLAYQX3n7skYU737d2SrII8hNW9fNPk/s400/tutogabarits.jpg" width="400" /></a></div>
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étape 2 : nettoyer la figure, enlever les poins , les étiquettes . </div>
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colorier les polygones en rouge pur avec une opacité 0 </div>
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Une fois la figure terminée, exporter le gaphique en tant qu'image</div>
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Etape 3 : exporter le graphique en tant qu'iamge vectorielle . SVG .</div>
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Etape 4 : le format est maintenant lisible sur un logiciel comme inskape qui permet le dialogue avec la découpeuse . Inkscape est un logiciel libre et gratuit .<br />
Ouvrir Inkscape .</div>
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cliquer sur propriétés du document et choisir la taille adaptée à celle de la feuille de polypropylene que vous voulez découper . ( adaptée aussi à la taille de la découpeuse ).</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgadLQIkgLxi0aDaQcTsoUW8CPMhvDr9mNSYqGs92qXZgPc2BeN9SNp11K2v2X5b8UGlhqmtsThuj7AjDMdRMy7yXOVLqxLGyVKqCq0YU5C6u5EcF2yCp6F1zYIfHl-wM46Bia3HjCsVdQ/s1600/tutogabarits5.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="431" data-original-width="550" height="500" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgadLQIkgLxi0aDaQcTsoUW8CPMhvDr9mNSYqGs92qXZgPc2BeN9SNp11K2v2X5b8UGlhqmtsThuj7AjDMdRMy7yXOVLqxLGyVKqCq0YU5C6u5EcF2yCp6F1zYIfHl-wM46Bia3HjCsVdQ/s640/tutogabarits5.jpg" width="640" /></a></div>
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Etape 5 : copier coller plusieurs objets à découper, sélectionner tout, puis cliquer sur une couleur de la palette en bas, afin de sélectionner le style de contour ., vérifier que c'est du rouge pur . L'épaisseur du trait est 0.1 ou 0.2 mm .</div>
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Etape 6 : lancer l'impression sur le logiciel de la découpeuse . Je n'ai pas ce logiciel sur mon PC . A ce moment là, une personne dans le fablab vous aidera sûrement .</div>
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Je me suis servi de ces 8 gabarits que j'ai pu fabriquer pour les deux derniers jours de classe en seconde, j'avais axé ces cours sur les solides de Platon et d'Archimède . J'ai proposé ces objets à qui voulait dessiner des patrons de l''icosaèdre, du dodécaèdre et de l'icosaèdre tronqué . En parallèle, j'ai apporté 12 pentagones en bambou et des élèves ont fabriqué le dodécaèdre. Mais ceci est une autre histoire . Avec un peu plus d'anticipation, je pense que j'aurai pu facilement fabriquer un gabarit pour chaque élève et qu'on aurait pu les utiliser pour beaucoup de problèmes passionnants.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3KxyvX8DEtgyrwok46qZ3lfsCV_g6rIXk43GJJuKDomq5WIZLPD8kZnUqMiUDJIMkA824WlkVZlYJxcC2uaE0zN6nCbDmHD6gODnsKyAZcfSru6-oZJ0uVGJ91AwW1uxL9pvf8gQbiSY/s1600/gabarits.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1160" data-original-width="696" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3KxyvX8DEtgyrwok46qZ3lfsCV_g6rIXk43GJJuKDomq5WIZLPD8kZnUqMiUDJIMkA824WlkVZlYJxcC2uaE0zN6nCbDmHD6gODnsKyAZcfSru6-oZJ0uVGJ91AwW1uxL9pvf8gQbiSY/s1600/gabarits.jpg" /></a></div>
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Pour s'aider dans la construction des patrons, on peut par exemple s'aider de dés numérotés à 4 , 6 , 8 , 12 et 20 faces . Il devient alors plus facile de repérer les faces voisines . On peut alors les relier pour qu'elles ne servent plus .</div>
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A noter que la longueur de côté choisie pour la fabrication est un peu grande, il faudra prévoir des feuilles A3 pour dessiner l'icoaèdre tronqué. Pour se repérer ,j'ai acheté un jouet pour chien en forme de ballon de foot . pas très cher, on peut écrire dessus les numéros des faces .</div>
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Olivier Longuethttp://www.blogger.com/profile/17956431908495478881noreply@blogger.com1tag:blogger.com,1999:blog-3415252720574602648.post-77148060318725711302018-05-05T12:54:00.003+02:002020-11-17T16:05:09.290+01:00Fraction d'un nombreJ'étais inscrit sur twitter depuis des années, sans beaucoup l'utiliser . Depuis deux semaines, je l'utilise enfin pour poster des idées qui semblent plaire à des collègues . Ca me redonne en1vie de reposter d'autres idées .<br />
Parmi les objets que j'avais fabriqués au début, il y en a un que j'aimais nettement moins, celui illustrant le théorème de Thalès . Remarquer que les rapports sont proches pour vérifier que le théorème est plausible, pourquoi pas . Mais en prenant les choses à l'envers, en supposant le théorème de Thalès vrai, on peut utiliser l'objet pour calculer des ordres de grandeurs de fractions d'un nombre, et ça, ça me parait plus pertinent .<br />
utilisation: on veut par exemple calculer (11 / 7 ) * 20 . On place les fils à plomb sur les points 7 et 11 de la règle mobile . on tourne cette règle de manière à ce que le fil à plomb arrive sur 20 sur la règle graduée . On lit une valeur approchée de la valeur désirée en regardant le résultat sur le fil 11.<br />
7 est à 20 ce que 11 est à ...<br />
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Voilà l'objet que j'ai fabriqué en démontant celui pour le théorème de Thalès, l'un des premiers de ce blog, mais qui ne m'avait jamais convaincu .</div>
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<br />Olivier Longuethttp://www.blogger.com/profile/17956431908495478881noreply@blogger.com1tag:blogger.com,1999:blog-3415252720574602648.post-27985374207369019002018-04-11T10:36:00.001+02:002018-04-11T10:54:30.577+02:00tutoriel video fabrication du puzzle "pavage du Caire" dans un fablab<div class="separator" style="clear: both; text-align: center;">
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Suite à un article précédent, j'ai pensé qu'il pouvait être judicieux de filmer les étapes principales de fabrication du découpage d'un pavage avec la découpeuse laser dans un fablab . Au vu du résultat, je m'aperçois que monter un film, ça s'apprend aussi . Excusez moi des quelques défauts, le but de cette vidéo est de montrer un exemple de fabrication , et qu'en tout cas, ce n'est pas très difficile, et que le fab lab est aussi un endroit d'apprentissage, où on est conseillé et où on acquiert peu à peu de l'autonomie. Merci à Camille Lejosne, qui m'a bien accompagné pendant ces heures au fablab de Nonant ( Bayeux intercom)</div>
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Renseignez vous sur les fablabs près de chez vous, les prix peuvent être très différents, parfois très intéressants et attractifs. La carte des fablabs est disponible ici.</div>
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http://www.fablab.fr/les-fablabs/carte-des-fablabs/</div>
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Pour l'instant, je travaille différents projets autant personnels que professionnels, j'y vais à mes frais. Sans doute pourrait-on obtenir un abonnement au nom de l'établissement scolaire pour les projets pédagogiques. </div>
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A l'avenir, je fabriquerai sans doute quelques objets avec la découpeuse laser, mon joujou préféré, voire avec l'imprimante 3D, et je joindrai à mes articles les fichiers correspondants au format adéquat. </div>
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<br />Olivier Longuethttp://www.blogger.com/profile/17956431908495478881noreply@blogger.com0tag:blogger.com,1999:blog-3415252720574602648.post-61948644668853533072018-04-08T15:14:00.002+02:002018-04-08T21:01:47.346+02:00Atelier pendant la journée régionale de l'APMEPHier, la régionale de l'APMEP a eu lieu dans mon lycée . Une belle journée. Ca fait plaisir de croiser des professeurs motivés et les discussions étaient passionnantes.<br />
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Quelques photos de l'atelier que j'ai animé . Merci à Nathalie, Virginie, Alice, Chantal et Jacques<br />
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de les avoir prises . Je n'y pense jamais .<br />
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La plupart des objets que j'ai utilisés dans mes cours, les collègues les ont essayés.</div>
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Ensuite, je les présentais les uns après les autres, en demandant, à l'aide de post-it s'il s'agissait plutôt d'un objet théorème (rose), d'un objet problème (bleu), d'un objet de mesure (vert), ou simplement c'est beau et c'est déjà pas mal(rose) . Transversalement, l'objet peut être un théorème en action (jaune) . </div>
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A ma grande surprise, les votes pour certains des objets étaient très variés. ce lecteur de cosinus, par exemple, ayant eu des votes de toutes les couleurs. </div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCfA6M54gPsoAJs4V3f6hZgIVpA_HURCm26VYaPerzP0KIkpEfxxZjFDsj_4Zw_erDAljs2KNej4bg1CI-e7NpjY-zBMR3OFoJWiA43IVjSvvPWzhRaDPTZ5nUAaaoee4osI8jZa7wjDE/s1600/DaKze6jXUAI22tB.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="675" data-original-width="1024" height="419" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCfA6M54gPsoAJs4V3f6hZgIVpA_HURCm26VYaPerzP0KIkpEfxxZjFDsj_4Zw_erDAljs2KNej4bg1CI-e7NpjY-zBMR3OFoJWiA43IVjSvvPWzhRaDPTZ5nUAaaoee4osI8jZa7wjDE/s640/DaKze6jXUAI22tB.jpg" width="640" /></a></div>
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Construire la section d'un cube en direct est parfois acrobatique . Un nouveauté par rapport à l'objet présenté il y a quelques années dans ce blog, j'ai collé du film blanc velleda sur le cube afin de pouvoir écrire dessus. </div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYnjTsOs6WwXgaVAoS07178_X8_RVY-boKcDAzplUcblSnb07PB1FIZ-b7HLHsKiMatNy_12m7R0tIrAxpMaO0gJei5GSkci6CXqPK4JquQXlU6IEpL8N-a2BrXj2EmSa1x0PeOHaMJwA/s1600/DaK9M1kX4AE6TId.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1199" data-original-width="677" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYnjTsOs6WwXgaVAoS07178_X8_RVY-boKcDAzplUcblSnb07PB1FIZ-b7HLHsKiMatNy_12m7R0tIrAxpMaO0gJei5GSkci6CXqPK4JquQXlU6IEpL8N-a2BrXj2EmSa1x0PeOHaMJwA/s640/DaK9M1kX4AE6TId.jpg" width="360" /></a></div>
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La fin de l'atelier avec la construction de l'icosaèdre tronqué .</div>
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Demain, la suite du stage toucher les maths, avec une heure consacrée à la main à la pate avec la construction en direct du dodécaèdre avec tous les calculs et les bricolages par les stagiaires . J'espère que ça va marcher !</div>
<br />Olivier Longuethttp://www.blogger.com/profile/17956431908495478881noreply@blogger.com0tag:blogger.com,1999:blog-3415252720574602648.post-35129040647822731262017-12-22T10:31:00.002+01:002020-11-17T16:04:12.863+01:00Décomposition de vecteurs ( première S)<br />
Pour faire réfléchir à la décomposition de vecteurs, j'ai utilisé un jeu de baguettes en bambou (60 cm et 90 cm) et de tourillon de 2 mètres .<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3mRTduCDu4HnyallEWmUh9Z-TDeb9M9ZTUI7m8qJPwSHNuFtmSy4eMeI7aw-lhXdxtiHM0qySSJ7GDCaFWNYa7aJcEMvndxX6UbmUJAkeXNVuFw39fBMY7V6rpfqshV3uStbG7biUbhI/s1600/IMG_0024.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="594" data-original-width="911" height="208" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3mRTduCDu4HnyallEWmUh9Z-TDeb9M9ZTUI7m8qJPwSHNuFtmSy4eMeI7aw-lhXdxtiHM0qySSJ7GDCaFWNYa7aJcEMvndxX6UbmUJAkeXNVuFw39fBMY7V6rpfqshV3uStbG7biUbhI/s320/IMG_0024.JPG" width="320" /></a></div>
En origami, j'ai fabriqué des triangles équilatéraux, que j'ai placés au bout de mes tiges, afin de figurer le sens des vecteurs . Sur cette flèche, j'ai nommé les vecteurs u , v, w .<br />
Avec du Patafix, j'ai collé un vecteur u (tige de 60 cm ), un vecteur v ( tige de 90 cm) et un vecteur w (tige de 2 mètres) , non colinéaires 2 à 2, en faisant en sorte que les extrémités correspondent à peu près au carrelage du sol. (au besoin, ajuster en enfonçant plus ou moins la flèche ).<br />
La consigne était de trouver les valeurs de x et de y telles que w = x u + y v .<br />
Le matériel à leur disposition: un mètre , des tiges de deux mètres, des vecteurs u et v mobiles posés à côté des vecteurs u et v fixés . <br />
En poussant les tables, j'ai pu trouver la place de mettre deux jeux différents et en demi groupe, j'ai donc fait travailler deux groupes de 7 personnes qui ont débattu et établi des stratégies pour répondre à la consigne . certains ont utilisé le tableau pour noter leurs calculs .<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjW1hkr5s7C-VmuEKEZ6DOesVCJhYG3E3iY6mLBDuR84sWm-kTkGKXGtAntx3GE3wiA6BVXJAYGfGKxA1Pglta1SXjZ_vHBf04LdJEkm-ZE2ZUoWtOnwh3-4eeZAt20_E6yYYdflzVLN0w/s1600/IMG_0023.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="774" data-original-width="662" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjW1hkr5s7C-VmuEKEZ6DOesVCJhYG3E3iY6mLBDuR84sWm-kTkGKXGtAntx3GE3wiA6BVXJAYGfGKxA1Pglta1SXjZ_vHBf04LdJEkm-ZE2ZUoWtOnwh3-4eeZAt20_E6yYYdflzVLN0w/s320/IMG_0023.JPG" width="273" /></a></div>
Plusieurs stratégies se sont mises en place au bout d'un certain temps: une approche purement géométrique et une approche analytique .<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivdiDLrZhxPrAkGcNCGBE5plvdD11rXudZuxv66JGP16QuyKtjTOjAykmjNIAtmDlfmIFdGQhsPjYg9D-Fx4HXYsidEfuaFBuaM-zYWnpviHrebEgWaUK36FqjLTSxhgEsbCeyStnD2l8/s1600/vecteurs.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="597" data-original-width="838" height="452" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivdiDLrZhxPrAkGcNCGBE5plvdD11rXudZuxv66JGP16QuyKtjTOjAykmjNIAtmDlfmIFdGQhsPjYg9D-Fx4HXYsidEfuaFBuaM-zYWnpviHrebEgWaUK36FqjLTSxhgEsbCeyStnD2l8/s640/vecteurs.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">L'une des situations étudiées</td></tr>
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En posant le problème sur le sol, j'ai pu observer d'autres comportements de mes élèves que ceux que j'ai d'habitude avec un problème sur le papier . Le débat était plus vivant, parce que souvent, <b>ils joignaient le geste à la parole</b> ( tu vas dans cette direction, tu prends deux carreaux par là, six carreaux par là, ... ). Parfois , les élèves dessinaient sur le sol avec un marqueur effaçable les vecteurs i et j correspondants aux carreaux .<br />
La taille des vecteurs aussi pose le problème d'une manière inhabituelle pour les élèves qui ont l'habitude de travailler sur le cahier.<br />
Sans doute le travail aurait-il été encore plus riche avec des groupes de 4, mais j'ai manqué de temps et de place pour déplacer les tables et positionner mes jeux de vecteurs .<br />
La position des vecteurs était un peu due au hasard, avec les contraintes suivantes : coordonnées entières sur les carreaux de la salle, non colinéarité. Les résultats ne tombaient pas juste, ce qui ne me dérangeait pas, au contraire.<br />
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En sortant le problème du cadre habituel, j'aime à penser que les élèves se souviendront mieux des techniques , pour deux raisons : il sera facile de rappeler le problème ( vous vous souvenez, les vecteurs sur le sol), et les débats ont été riches de propositions, chacun ayant mis la main à la pâte.<br />
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<br />Olivier Longuethttp://www.blogger.com/profile/17956431908495478881noreply@blogger.com0tag:blogger.com,1999:blog-3415252720574602648.post-16028779818118712972017-12-21T22:46:00.001+01:002017-12-21T23:07:09.347+01:00Animation gifGeospace, c'etait quand même un sacré logiciel .<br />
Voici un patron de l'icosaèdre tronqué qui se déplie.<br />
Je ne sais pas si Geogebra peut faire pareil .<br />
Images fabriquées à l'aide de geospace, retouche avec paint, création du gif avec gimp.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigZYhFHVwMbctmWJQyXyRTS0SBrNWt2bjXJO0094cfrO2_qlQ-kKXsO2ZkTHYJ1ODK2sTJKrZ-Rsvz-GlJMaH3ielCEq8hgN3y6LL-lP_ZOy7NewxKmZbSjUsO0TRC-OZ9Q85tFhxSz4Q/s1600/icosaedretronque.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="581" data-original-width="445" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigZYhFHVwMbctmWJQyXyRTS0SBrNWt2bjXJO0094cfrO2_qlQ-kKXsO2ZkTHYJ1ODK2sTJKrZ-Rsvz-GlJMaH3ielCEq8hgN3y6LL-lP_ZOy7NewxKmZbSjUsO0TRC-OZ9Q85tFhxSz4Q/s400/icosaedretronque.gif" width="306" /></a></div>
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Je me demande si les commentateurs sportifs ont déjà prononcé les mots icosaèdre tronqué</div>
Olivier Longuethttp://www.blogger.com/profile/17956431908495478881noreply@blogger.com0tag:blogger.com,1999:blog-3415252720574602648.post-58013568167834494232017-12-08T20:15:00.000+01:002017-12-14T22:17:11.379+01:00Pavages et découpeuse laser .<div class="separator" style="clear: both; text-align: center;">
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Je suis allé au Fablab proche de chez moi . On peut y trouver des imprimantes 3D, une découpeuse vinyl et une découpeuse laser, ainsi que d'autres outils pour aider à la fabrication.<br />
Mon projet était de fabriquer un jeu de pavés pour un puzzle .<br />
La bonne surprise c'est qu'on peut utiliser geogebra, qui permet de faire des fichiers en vectoriel SVG (fichier/exporter/graphique en tant qu'image, choisir le format SVG ) . Ensuite, on nettoie le fichier avec Inkscape ( en particulier pour éviter les doublons, lorsqu'on crée des pavages, on dessine deux fois chaque coté des pavés, ce qui occasionnerait une double découpe inutile ) . Ensuite, je ne sais pas encore bien me servir de la découpeuse, mais Camille qui encadre la FabLab a finalisé la programmation de la coupe .<br />
Comme matériau, j'ai utilisé du matériel de récupération, à savoir deux plaques qu'on trouve derrière les cadres photos .<br />
J'ai choisi deux pavages du plan , le premier composé de carrés et de losanges composés de triangles équilatéraux parce que ces losanges peuvent permettre bien d'autres possibilités<br />
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width="640" /><br />
et le pavage du Caire, l'un des 15 pavages pentagonaux que je trouve très élégant .<br />
<img alt="" height="495" src="data:image/png;base64,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" width="640" /><br />
<br />
La construction du pavé du Caire . Construire ABC triangle rectangle isocèle , le point D, tel que BD= AB et CD=CB<br />
<img alt="" height="400" 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" width="351" /><br />
Au final, après 5 minutes de découpe effective pour chaque planche, j'ai obtenu mon jeu de pavés .<br />
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<br />Olivier Longuethttp://www.blogger.com/profile/17956431908495478881noreply@blogger.com0tag:blogger.com,1999:blog-3415252720574602648.post-71478192837923665052017-03-14T22:49:00.003+01:002017-03-14T23:05:14.560+01:00PI day : maths et langage Le nombre Pi est sans doute un nombre univers, ce qui veut dire que toute séquence de chiffres de votre choix est inscrite dans ses décimales . Il faut imaginer qu'il possède une infinité de décimales .<br />
Oui, comme 1/3, c'est vrai, mais les nombres rationnels ne sont pas des nombres univers, car on ne peut pas avoir toutes les séquences de chiffres possibles, les décimales se répétant en séquences à l'infini . Le nombre de Champernowe 0.12345678910111213... possède par construction toutes les séquences de chiffres possibles, mais est un peu prévisible.<br />
<br />
En cette année, la semaine des maths a pour thème maths et langage . Si Pi est un nombre univers, en transformant ses décimales en lettres, on pourrait aussi avoir toutes les séquences de lettres possibles, un peu comme dans "la bibliothèque de Babel", la nouvelle de Borges. Votre prénom, les paroles de votre chanson préférée s'y trouvent, à condition de les chercher assez loin .<br />
Bon, il faut quand même trouver une méthode pour transformer ces décimales en lettres de l'alphabet. J'ai demandé à mes élèves de seconde de réfléchir à des méthodes pour trouver les séquences de lettres, de les essayer sur les premières lettres, et d'anticiper les propriétés de cette transformation, les avantages et les inconvénients.<br />
J'ai trouvé sur un site internet les 2400 premières décimales de pi, que j'ai données aux élèves.<br />
Voici les 100 premières pour avoir une idée de la forme :<br />
<span style="background-color: white; font-size: x-small;">3,141 592 653 589 793 238 462 643 383 279 502 884 197 169 399 375 105 820 974 944 592 307 816 406 286 208 998 628 034 825 3</span><br />
<span style="background-color: white;"><span style="font-family: inherit;">Le fait que les décimales soient rangées en paquet de trois a influencé beaucoup d'élèves, on le verra plus tard .</span></span><br />
En utilisant les idées des élèves, j'ai programmé ensuite les algorithmes sur Python et nous avons analysé les résultats des fréquences des lettres. J'ai recopié les algorithmes en limitant le nombre de décimales de pi parce que c'est déjà assez long, mais dans le programme j'ai recopié les 2400 décimales. Sur d'autres sites, j'ai trouvé 100000 décimales, mais ça plantait python quand je les recopiais.<br />
<br />
<b>Méthode 1</b> on prend les décimales 2 par 2 , et on regard le reste de la division par 26<br />
from math import *<br />
pid="3.14159265358979323846264338327950288419716939937510582097494459230781640"<br />
for i in range(2,2399,2):<br />
A= (10*int(pid[i])+int(pid[i+1]))%26<br />
if A ==0:<br />
L="A"<br />
elif A ==1:<br />
L="B"<br />
elif A ==2:<br />
L="C"<br />
elif A ==3:<br />
L="D"<br />
elif A ==4:<br />
L="E"<br />
elif A ==5:<br />
L="F"<br />
elif A ==6:<br />
L="G"<br />
elif A ==7:<br />
L="H"<br />
elif A ==8:<br />
L="I"<br />
elif A ==9:<br />
L="J"<br />
elif A ==10:<br />
L="K"<br />
elif A ==11:<br />
L="L"<br />
elif A ==12:<br />
L="M"<br />
elif A ==13:<br />
L="N"<br />
elif A ==14:<br />
L="O"<br />
elif A ==15:<br />
L="P"<br />
elif A ==16:<br />
L="Q"<br />
elif A ==17:<br />
L="R"<br />
elif A ==18:<br />
L="S"<br />
elif A ==19:<br />
L="T"<br />
elif A ==20:<br />
L="U"<br />
elif A ==21:<br />
L="V"<br />
elif A ==22:<br />
L="W"<br />
elif A ==23:<br />
L="X"<br />
elif A==24:<br />
L="Y"<br />
elif A==25:<br />
L="Z"<br />
OPONJLBGMUARMGBYCGTTRNPXKGUTXSHXHDMGCKIVICDWZIVRGBEOCIZGEEOVJMSIRYGWFUBHODCWLRTCGKBBPHVKDHMUWQLCPDDSSCDJXOHHSJCVEWXLIAFNBMBMNTMHOOIIIIKTRAMENNKHACXOMVUTJAOGFDKRWDAJUSCDZONTBMKAOHDIBNEBFWEEOANGORZQPLIQHFUSKFHHTBJVILVDPALBFFLHWHSKLVKWRPJSHXBYLMBPDFBTXMUHPHKSGEMEICNQQLRWVLTHCRUIQLCZFNVTYDFYXXGPWSUYROZGAFQMTTAJIEZHZNQXZLINVLTAUOQSJBWXBRBUCRHLKYBWBQOGOJQBVELVDCTIIOIPDHDKDZVTEVIZJHVNXVVULDAEVZFTFVCQJLSHYYTQDIRIEAQAXIZHSQYJATFSDTBADNAMXCIGXHUFDQGRRYROVDHEBXECXCQVLHECLKXBAXPXTFASFAFGRMACONATBJOLTHJVMUTLMJAFUKNWGLBKNPJBMSBSEEETADBBHDQVFVKZVPMNYTVZAFVNFZDWHUQTPYRHYERHLQJUADKMXJFDXULUXNFODGEAOZBPLNAUWEOMHFJIJLSYIKVKSTQRDSTLUYALSQWZBBZVAGTEEXIMKIEOGZMRXMPFKZCLLPVEXVKFROCOGDDYTJLZHERAJGYOYWSVGLNPVBAEAVWBPEJVDLIJIRVMMTOTIFYECJETTDSPXFHFXTKGRAVEMOUKBXJEDDGLNIXJUBDSCKWGNXNTKSIBZBELRCWACZBIZZDGRFUULJZZBPCADMSIBJTYNORGRVVUJBPSTVEHWQNJPVADVHVFPGQQRHXGNHNPRHTVYYQIZSUJRWDKJOTWVGBZYZQEKYTBEQIQBUQEUIBXBNAIHARFEBPTODTPARMFALIRGCGQZMAFLVOUWSIPCWIAQEEYTNCYWVGJSLGWQAKUNTXTETXTLISJEKRTNUJUZMNXVSYNLINFATVGNNEACXMJQNYOARMRUFUJZRSUZEAUAYLOZATQAAGEIOYVJCMBKNSLTBFGEDXKATRXNSZRODCNMNOYPUVRMJZFJHFJPFTKHHZDXXLEQRBOGQNEQQMQQBWPHNHHZYHBRQFEVUAUCGHJBKSRGWNMKVKWKIVMUIFMRKRMTMSNNXYBCBZPROJVZAMSQIQPRWQDGWOLBQUUWGCWIWPGECH<br />
<br />
Remarque : Chaque lettre a presque la même probabilité d'apparition . est ce un avantage, est ce un inconvénient ? Borges l'aurait accepté, surtout avec 25 caractères, toutes les lettres auuraient eu la même probabilté...<br />
<br />
<b>Méthode 2 :</b> addition des chiffres 3 par 3 et codage avec l’alphabet<br />
from math import *<br />
pid="3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280..."<br />
<br />
for i in range(2,2399,3):<br />
A= (int(pid[i])+int(pid[i+1])+int(pid[i+2]))<br />
if A ==0 or A==26:<br />
L="A"<br />
elif A ==1 or A==27:<br />
L="B"<br />
elif A ==2:<br />
L="C"<br />
elif A ==3:<br />
L="D"<br />
elif A ==4:<br />
L="E"<br />
elif A ==5:<br />
L="F"<br />
elif A ==6:<br />
L="G"<br />
elif A ==7:<br />
L="H"<br />
elif A ==8:<br />
L="I"<br />
elif A ==9:<br />
L="J"<br />
elif A ==10:<br />
L="K"<br />
elif A ==11:<br />
L="L"<br />
elif A ==12:<br />
L="M"<br />
elif A ==13:<br />
L="N"<br />
elif A ==14:<br />
L="O"<br />
elif A ==15:<br />
L="P"<br />
elif A ==16:<br />
L="Q"<br />
elif A ==17:<br />
L="R"<br />
elif A ==18:<br />
L="S"<br />
elif A ==19:<br />
L="T"<br />
elif A ==20:<br />
L="U"<br />
elif A ==21:<br />
L="V"<br />
elif A ==22:<br />
L="W"<br />
elif A ==23:<br />
L="X"<br />
elif A==24:<br />
L="Y"<br />
elif A==25:<br />
L="Z"<br />
print(L, end='')<br />
GQOWTNMNOSHURQVPGKURQKPKQKAQHPJJNTNOJMJRMQPKPGORMLNJJODIUIGTOKVSMMTOJVRPOLQSIVSMKDSKSROKPHNLSGPNIPGMNUGMJVMRHLRTLKNNQTOJCGIRKQIPLPOHPKMJOVPRLPJMOITGKRLMTRUSJVONSLUMCWMOQLIRNODQTRIRKJROQJORKOOOOPRRRVJGATKKLLRUPJTYPLQQKSIKIRHLSSLFSSXPOLKUEMDPSHNPMRSPMPOOEQBAMYNPOLMPPMTGSONRFMJLKLTIJNRJBDLTOWULKMGOPVMGWKNORSLPNRSLWRNVQUPKJKOKBSVIPSJGSUOODLRRRTSJMRXFEQIEPXXRKXISPKTNUFLQUINGUOTLIPQSZMRMQQOVNMGESIONJUODVKJOOMFIKPTUSTUSRQMTSPTFLMQKKSQPOOHUKAIFOJLVGNLGNHKNHIUKNTOLOTLKRNWRMQPJIKLMPTJDQLUPNUTKRVTRXPSDXOFTGMLYERPLMRWLRPXPRSPMLOQLRMQPRXQTIJRGHKPMLKHQIGJTTRIKNKMHQMVSPKIQQIKQPLQOUURNSMGNLKLNXOQRHOQMZPHRVNTORWWPNBRTVJOOKJIHJOVXMLUOSKHUPEDNPJPRKMOSLGLVPUNLRRRRSPRIRTNPXMMTJOSPRPPRSUKTQPMIJVLPRTQOHRSLKKQOOIOFTJKUVMIPRKUHTFVLLQVSFVVXQVVMIPTSMQRWPSLTSQLRXINSLORYMOUUORQGOSHOGJUMKKKSPPXNQMZHMNRJTWPUKLIJJSUSOPK<br />
<br />
Remarque : Beaucoup d'élèves ont été tentés par cette méthode, après avoir remarqué que 9+9+9 = 27 , que c'est presque 26 , qu'on ne va pas trop s'embêter avec ces détails . Les nombres vont de 0 à 27, ce qui fait 28 possiilités . En regardant les fréquences des lettres, on se rend compte que les lettres au début et à la fin de l'alphabet avaient moins de chances d'apparaitre, et que cette méthode avantage les lettres du milieu de l'alphabet.<br />
<br />
<b>Méthode 3 </b>: on prend les décimales une par une et on code par une lettre .<br />
from math import *<br />
pid="3.141592653589793238462643383279502884197169399375105820974944592307816…"<br />
<br />
for i in range(2,2399,1):<br />
A= (int(pid[i])<br />
if A ==0<br />
L="A"<br />
elif A ==1<br />
L="B"<br />
elif A ==2:<br />
L="C"<br />
elif A ==3:<br />
L="D"<br />
elif A ==4:<br />
L="E"<br />
elif A ==5:<br />
L="F"<br />
elif A ==6:<br />
L="G"<br />
elif A ==7:<br />
L="H"<br />
elif A ==8:<br />
L="I"<br />
elif A ==9:<br />
L="J"<br />
<br />
print(L, end='')<br />
<br />
<br />
BEBFJCGFDFIJHJDCDIEGCGEDDIDCHJFACIIEBJHBGJDJJDHFBAFICAJHEJEEFJCDAHIBGEAGCIGCAIJJIGCIADEICFDECBBHAGHJICBEIAIGFBDCICDAGGEHAJDIEEGAJFFAFICCDBHCFDFJEAIBCIEIBBBHEFACIEBACHABJDIFCBBAFFFJGEEGCCJEIJFEJDADIBJGEECIIBAJHFGGFJDDEEGBCIEHFGEICDDHIGHIDBGFCHBCABJAJBEFGEIFGGJCDEGADEIGBAEFEDCGGEICBDDJDGAHCGACEJBEBCHDHCEFIHAAGGAGDBFFIIBHEIIBFCAJCAJGCICJCFEAJBHBFDGEDGHIJCFJADGAABBDDAFDAFEIICAEGGFCBDIEBEGJFBJEBFBBGAJEDDAFHCHADGFHFJFJBJFDAJCBIGBBHDIBJDCGBBHJDBAFBBIFEIAHEEGCDHJJGCHEJFGHDFBIIFHFCHCEIJBCCHJDIBIDABBJEJBCJIDDGHDDGCEEAGFGGEDAIGACBDJEJEGDJFCCEHDHBJAHACBHJIGAJEDHACHHAFDJCBHBHGCJDBHGHFCDIEGHEIBIEGHGGJEAFBDCAAAFGIBCHBEFCGDFGAICHHIFHHBDECHFHHIJGAJBHDGDHBHIHCBEGIEEAJABCCEJFDEDABEGFEJFIFDHBAFAHJCCHJGIJCFIJCDFECABJJFGBBCBCJACBJGAIGEADEEBIBFJIBDGCJHHEHHBDAJJGAFBIHAHCBBDEJJJJJJIDHCJHIAEJJFBAFJHDBHDCIBGAJGDBIFJFACEEFJEFFDEGJAIDACGECFCCDAICFDDEEGIFADFCGBJDBBIIBHBABAAADBDHIDIHFCIIGFIHFDDCAIDIBECAGBHBHHGGJBEHDADFJICFDEJAECIHFFEGIHDBBFJFGCIGDIICDFDHIHFJDHFBJFHHIBIFHHIAFDCBHBCCGIAGGBDAABJCHIHGGBBBJFJAJCBGECABJIJDIAJFCFHCABAGFEIFIGDCHIIGFJDGBFDDIBICHJGICDADABJFCADFDABIFCJGIJJFHHDGCCFJJEBDIJBCEJHCBHHFCIDEHJBDBFBFFHEIFHCECEFEBFAGJFJFAICJFDDBBGIGBHCHIFFIIJAHFAJIDIBHFEGDHEGEJDJDBJCFFAGAEAAJCHHABGHBBDJAAJIEIICEABCIFIDGBGADFGDHAHGGABAEHBABIBJECJFFFJGBJIJEGHGHIDHEEJEEICFFDHJHHEHCGIEHBAEAEHFDEGEGCAIAEGGIECFJAGJEJBCJDDBDGHHACIJIJBFCBAEHFCBGCAFGJGGACEAFIADIBFABJDFBBCFDDICEDAADFFIHGEACEHEJGEHDCGDJBEBJJCHCGAECGJJCCHJGHICDFEHIBGDGAAJDEBHCBGEBCBJJCEFIGDBFADACIGBICJHEFFFHAGHEJIDIFAFEJEFIIFIGJCGJJFGJAJCHCBAHJHFAJDACJFFDCBBGFDEEJIHCACHFFJGACDGEIAGGFEJJBBJIIBIDEHJHHFDFGGDGJIAHECGFECFCHIGCFFBIBIEBHFHEGHCIJAJHHHHCHJDIAAAIBGEHAGAABGBEFCEJBJCBHDCBHCBEHHCDFABEBEEBJHDFGIFEIBGBDGBBFHDFCFFCBDDEHFHEBIEJEGIEDIFCDDCDJAHDJEBEDDDEFEHHGCEBGIGCFBIJIDFGJEIFFGCAJJCBJCCCBIECHCFFACFECFGIIHGHBHJAEJEGABGFDEGGIAEJIIGCHCDCHJBHIGAIFHIEDIDICHJGHJHGGIBEFEBAAJFDIIDHIGDGAJFAGIAAGECCFBCFCAFBBHDJCJIEIJGAIEBCIEIIGCGJEFGAECEBJGFCIFACCCBAGGBBIGDAGHEECHIGCCADJBJEJEFAEHBCDHBDHIGJGAJFGDGEDHBJBHCIHEGHHGEGFHFHDJGCEBDIJAIGFIDCGEFJJFIBDDJAEHIACHFJAAJJEGFHGEAHIJFBCGJEGIDJIDFCFJFHAJICFICCGCAFCCEIJEAHHCGHBJEHICGIEICGABEHGJJAJACGEABDGDJEEDHEFFDAFAGICADEJGCFCEFBHEJDJJGFBEDBECJIAJBJAGFJCFAJDHCCBGJGEGBFBFHAJIFIDIHEBAFJHIIFJFJHHCJHFEJIJDABGBHFDJCIEGIBDICGIGIDIGIJECHHEBFFJJBIFFJCFCEFJFDJFJEDBAEJJHCFCEGIAIEFJIHCHDGEEGJFIEIGFDIDGHDGCCCGCGAJJBCEGAIAFBCEDIIEDJAEFBCEEBDGFEJHGCHIAHJHHBFGJBEDFJJHHAABCJGBGAIJEEBGJEIGIFFFIEIEAGDFDECCAHCCCFICIEIIGEIBFIEFGACI<br />
<br />
<br />
Remarque : c'est simple, mais on ne pourra pas coder tout ce qu'on veut, car l'alphabet s'arrête à J . Sinon, on code plus de lettres, c'est appréciable .<br />
<br />
<b>Méthode 4 :</b> on prend les décimales 3 par 3 . En remarquant que 1000 / 26 vaut environ 38,5 , on crée 26 intervalles d'amplitude 38 ou 39, qui correspondent chacun à une lettre de l'alphabet .<br />
<br />
from math import *<br />
pid="3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408"<br />
<br />
for i in range(2,2399,3):<br />
A= (100*int(pid[i])+10*int(pid[i+1])+int(pid[i+2]))<br />
if A <38: p=""> <38 38:="" :=""></38></38:><br />
<38: p=""> L="A"<br />
elif A <77: p=""> <77 77:="" :=""></77></77:></38:><br />
<38: p=""><77: p=""> L="B"<br />
elif A <115: p=""> < 115:</115:></77:></38:><br />
<38: p=""><77: p=""><115: p=""> L="C"<br />
elif A <154: p=""> <154 154:="" :=""></154></154:></115:></77:></38:><br />
<38: p=""><77: p=""><115: p=""><154: p=""> L="D"<br />
elif A < 192:<br />
L="E"<br />
elif A <230: p=""> <230: 230:=""></230:></230:></154:></115:></77:></38:><br />
<38: p=""><77: p=""><115: p=""><154: p=""><230: p=""> L="F"<br />
elif A <259: p=""> < 269:</259:></230:></154:></115:></77:></38:><br />
<38: p=""><77: p=""><115: p=""><154: p=""><230: p=""><259: p=""> L="G"<br />
elif A <307: p=""> <307: 307:=""></307:></307:></259:></230:></154:></115:></77:></38:><br />
<38: p=""><77: p=""><115: p=""><154: p=""><230: p=""><259: p=""><307: p=""> L="H"<br />
elif A <346: p=""> < 346:</346:></307:></259:></230:></154:></115:></77:></38:><br />
<38: p=""><77: p=""><115: p=""><154: p=""><230: p=""><259: p=""><307: p=""><346: p=""> L="I"<br />
elif A <384: 346:=""></384:></346:></307:></259:></230:></154:></115:></77:></38:><br />
<38: p=""><77: p=""><115: p=""><154: p=""><230: p=""><259: p=""><307: p=""><346: p=""><384: p=""> L="J"<br />
elif A <; 422:<br />
L="K"<br />
elif A <461: 384:=""></461:></384:></346:></307:></259:></230:></154:></115:></77:></38:><br />
<38: p=""><77: p=""><115: p=""><154: p=""><230: p=""><259: p=""><307: p=""><346: p=""><384: p=""><461: p=""> L="L"<br />
elif A <499: p=""> <499: 499:=""></499:></499:></461:></384:></346:></307:></259:></230:></154:></115:></77:></38:><br />
<38: p=""><77: p=""><115: p=""><154: p=""><230: p=""><259: p=""><307: p=""><346: p=""><384: p=""><461: p=""><499: p=""> L="M"<br />
elif A <538: p=""> <538: 538:=""></538:></538:></499:></461:></384:></346:></307:></259:></230:></154:></115:></77:></38:><br />
<38: p=""><77: p=""><115: p=""><154: p=""><230: p=""><259: p=""><307: p=""><346: p=""><384: p=""><461: p=""><499: p=""><538: p=""> L="N"<br />
elif A <576: p=""> <576: 576:=""></576:></576:></538:></499:></461:></384:></346:></307:></259:></230:></154:></115:></77:></38:><br />
<38: p=""><77: p=""><115: p=""><154: p=""><230: p=""><259: p=""><307: p=""><346: p=""><384: p=""><461: p=""><499: p=""><538: p=""><576: p=""> L="O"<br />
elif A <614: p=""> <614: 614:=""></614:></614:></576:></538:></499:></461:></384:></346:></307:></259:></230:></154:></115:></77:></38:><br />
<38: p=""><77: p=""><115: p=""><154: p=""><230: p=""><259: p=""><307: p=""><346: p=""><384: p=""><461: p=""><499: p=""><538: p=""><576: p=""><614: p=""> L="P"<br />
elif A <653: p=""> <653: 653:=""></653:></653:></614:></576:></538:></499:></461:></384:></346:></307:></259:></230:></154:></115:></77:></38:><br />
<38: p=""><77: p=""><115: p=""><154: p=""><230: p=""><259: p=""><307: p=""><346: p=""><384: p=""><461: p=""><499: p=""><538: p=""><576: p=""><614: p=""><653: p=""> L="Q"<br />
elif A <730: 653:=""></730:></653:></614:></576:></538:></499:></461:></384:></346:></307:></259:></230:></154:></115:></77:></38:><br />
<38: p=""><77: p=""><115: p=""><154: p=""><230: p=""><259: p=""><307: p=""><346: p=""><384: p=""><461: p=""><499: p=""><538: p=""><576: p=""><614: p=""><653: p=""><730: p=""> L="R"<br />
elif A <768: p=""> <768: 768:=""></768:></768:></730:></653:></614:></576:></538:></499:></461:></384:></346:></307:></259:></230:></154:></115:></77:></38:><br />
<38: p=""><77: p=""><115: p=""><154: p=""><230: p=""><259: p=""><307: p=""><346: p=""><384: p=""><461: p=""><499: p=""><538: p=""><576: p=""><614: p=""><653: p=""><730: p=""><768: p=""> L="S"<br />
elif A <806: p=""> <806: 806:=""></806:></806:></768:></730:></653:></614:></576:></538:></499:></461:></384:></346:></307:></259:></230:></154:></115:></77:></38:><br />
<38: p=""><77: p=""><115: p=""><154: p=""><230: p=""><259: p=""><307: p=""><346: p=""><384: p=""><461: p=""><499: p=""><538: p=""><576: p=""><614: p=""><653: p=""><730: p=""><768: p=""><806: p=""> L="T"<br />
elif A <845: p=""> <845: 845:=""></845:></845:></806:></768:></730:></653:></614:></576:></538:></499:></461:></384:></346:></307:></259:></230:></154:></115:></77:></38:><br />
<38: p=""><77: p=""><115: p=""><154: p=""><230: p=""><259: p=""><307: p=""><346: p=""><384: p=""><461: p=""><499: p=""><538: p=""><576: p=""><614: p=""><653: p=""><730: p=""><768: p=""><806: p=""><845: p=""> L="U"<br />
elif A <883: p=""> <883: 883:=""></883:></883:></845:></806:></768:></730:></653:></614:></576:></538:></499:></461:></384:></346:></307:></259:></230:></154:></115:></77:></38:><br />
<38: p=""><77: p=""><115: p=""><154: p=""><230: p=""><259: p=""><307: p=""><346: p=""><384: p=""><461: p=""><499: p=""><538: p=""><576: p=""><614: p=""><653: p=""><730: p=""><768: p=""><806: p=""><845: p=""><883: p=""> L="V"<br />
elif A <921: 883:=""></921:></883:></845:></806:></768:></730:></653:></614:></576:></538:></499:></461:></384:></346:></307:></259:></230:></154:></115:></77:></38:><br />
<38: p=""><77: p=""><115: p=""><154: p=""><230: p=""><259: p=""><307: p=""><346: p=""><384: p=""><461: p=""><499: p=""><538: p=""><576: p=""><614: p=""><653: p=""><730: p=""><768: p=""><806: p=""><845: p=""><883: p=""><921: p=""> L="W"<br />
elif A <960: p=""> <960: 960:=""></960:></960:></921:></883:></845:></806:></768:></730:></653:></614:></576:></538:></499:></461:></384:></346:></307:></259:></230:></154:></115:></77:></38:><br />
L="X"<br />
<38: p=""><77: p=""><115: p=""><154: p=""><230: p=""><259: p=""><307: p=""><346: p=""><384: p=""><461: p=""><499: p=""><538: p=""><576: p=""><614: p=""><653: p=""><730: p=""><768: p=""><806: p=""><845: p=""><883: p=""><921: p=""><960: p="">
elif A<1000: p=""> <1000: 1000:=""></1000:></1000:></960:></921:></883:></845:></806:></768:></730:></653:></614:></576:></538:></499:></461:></384:></346:></307:></259:></230:></154:></115:></77:></38:><br />
<38: p=""><77: p=""><115: p=""><154: p=""><230: p=""><259: p=""><307: p=""><346: p=""><384: p=""><461: p=""><499: p=""><538: p=""><576: p=""><614: p=""><653: p=""><730: p=""><768: p=""><806: p=""><845: p=""><883: p=""><921: p=""><960: p=""><1000: p=""> L="Y"<br />
else::<br />
L="Z"<br />
<br />
<br />
print(L, end='')<br />
<br />
<br />
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br />
<br />
Remarque : les lettres sont équiréparties.<br />
<br /><b>
Méthode 5 :</b> Conversion en base 26 des décimales de pi<br />
Bon, celle-ci c'est moi qui ai voulu l'essayer. On multiplie le nombre décimal par 26, on retient la partie entière du résultat pour la convertir en lettres, puis on enlève cette partie entière, et on continue...<br />
<br />
from math import *<br />
pid="3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408..." #2400 décimales#<br />
dpi=float(pid)<br />
dpi=dpi-3<br />
for i in range(60):<br />
A= (int(dpi*26))<br />
dpi=26*dpi-A<br />
lettre=65+A<br />
L=chr(lettre)<br />
<br />
<br />
<br />
print(L, end='')<br />
<br />
DRSQLOLYRTRCLRGGUKBJKPSRFVKRODHLJRFSZSOXNHXZEWTNAAAAAAAAAAAA<br />
<br />
Bon, là, j'ai été surpris , à partir de la 49 eme lettre, plus que des A , cette méthode est vraiment gourmande en décimales.<br />
<br />
<br />
<br />
Après avoir remarqué qu'on avait peu de chances d'obtenir un mot compréhensible avec ces méthodes, parce qu'il y avait trop de lettres rares comme k ou w , nous avons recherché les fréquences des lettres en français, et essayé de respecter davantage ce critère afin d'optimiser les chances d'obtenir un mot intelligible.<br />
<br /><b>
Méthode 6 :</b><br />
Pour commencer, prenons les 100 jetons du scrabble ( hors joker ) et rangeaons les dans l'ordre alphabétique . Prenons ensuite les décimales de pi 2 par 2 , et cherchons la lettre qui correspond ( en commençant à compter à 0) :<br />
from math import *<br />
pid="3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408"# 2400 décimales#<br />
<br />
for i in range(2,2399,2):<br />
A= (10*int(pid[i])+1*int(pid[i+1]))<br />
if A <9: p=""> L="A"<br />
elif A <11: p=""> L="B"<br />
elif A <13: p=""> L="C"<br />
elif A <16: p=""> L="D"<br />
elif A < 31:<br />
L="E"<br />
elif A <33: p=""> L="F"<br />
elif A <35: p=""> L="G"<br />
elif A <37: p=""> L="H"<br />
elif A <45: p=""> L="I"<br />
elif A <46: p=""> L="J"<br />
elif A < 47:<br />
L="K"<br />
elif A <52: p=""> L="L"<br />
elif A <55: p=""> L="M"<br />
elif A <61: p=""> L="N"<br />
elif A <67: p=""> L="O"<br />
elif A <69: p=""> L="P"<br />
elif A <70: p=""> L="Q"<br />
elif A <76: p=""> L="R"<br />
elif A <82: p=""> L="S"<br />
elif A <88: p=""> L="T"<br />
elif A <94: p=""> L="U"<br />
elif A <96: p=""> L="V"<br />
elif A <97: p=""> L="W"<br />
elif A <98: p=""> L="X"<br />
elif A<99: p=""> L="Y"<br />
elif A<100: p=""> L="Z"<br />
<br />
<br />
print(L, end='')<br />
<br />
DDUOHUSFIKEIIFSLETERQIURBNEXLINEASOAEOAZTEALEGEEASTDSTLFTEOLBIINVLNEFRMNISELCEJATBEAUTEBNNOKEVUMUASWIESBRONGIOELNLEITSFOECAUUJOTOUGNGTBJIEOTDIHAEALDCRRJTAOAFNUELSMBEWEEEIURMOHSUNANADEMALTAOMDTDQLVDCNVGARRHNNNEMBETCRSUECSFACTLAIOIZORVPHETREEUCEUSTAELCYGPGOIANOETADVVOVELIEAAEYNVIASAIERSEFSRETPLEKSQILFAAPCRJEHNTSTSDIRSUNURORSRDPIBAELMIAKMVTIBLSESPUNUHIAZNCEEAENTIGISNSHESLREZNLTAEDLZZYIESAZLAXFREEBOENLEJVNGQAEEIMEAEGIPLHEEFESRAAADSIRETNRGETSIAEESQDRANTMLAERMPRCNNEOUEMSRURENSENSAFECESODAEETOCENBEOEEUIBMNEBOLNOEUOUOMIEEWTEEEMAMATEPZNROEZIIUEXESMTLUFLNRTRIJILQNLTVGCPORSNUURBTSRKIKLIFUNAAAUSAPCIAYLTICTTONHORSNBLBEEIVNWEUKSSIIVLEMSSLETRAARGOOAAOTEUQLCUFHSAUUDEAREOAQOAINASLEHCEGTIAHNSIERWLFOUIZEEAEZESPTHLSONBGEEOCEUJTFLEEOTXJNRPLTTALJUNQEZNUURBSRBEENFCOGLTEENWAHLAOLUEUEGSSMNOQSREMEETELSTENKRUBSSEUSASORNAOJEUUEFEELRHAIIERNTLEDODRMNEGLNITVPITEFIAIIIGJLSEETEEYHQLNOBUEEETEELEINUSRSAVNEMKPAYTEEEUSNTSITTSPXOSJIAVITSONVASAIECMACRUYLWAIELTEVNAEEOELEEAOEOARISOEIELJARERITWBNHIRURTKSOORRWEDUAOTEJZNDIASARUBVOSISVCQKTYHEVRYETEEMEUISERVSETTNDSZBAOAHIIIJMAATALOMJELIWLIDESUUOULUREQOOLNBTTTIAXUNNSERLUEEEMUTPDTPPIPVERDNUTNEENMVVFAZRMKSTNTEHIQNLOIHROEONZCKAACIUIUJCIDOLSESSSDQDHZSACWEAVIQLPNNLIOMIERENELTLDTNAT<br />
>>><br />
<br />
Remarques : la fréquence des lettres suit la fréquence de celles du scrabble<br />
C'est là que j'ai remarqué le premier mot, sur la deuxième ligne : BEAUTE .<br />
C'était magnifique, j'en étais ému .<br />
<br />
Méthode 8 : plus précis que le scrabble, on a utilisé les fréquences des lettres en français trouvées sur le magnifique site ars cryptographica de Didier Muller, l'un de mes sites préférés. On a pris les décimales 3 par 3 et on a utilisé les fréquences cumulées des lettres rangées par ordre croissant.<br />
from math import *<br />
pid="3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408"<br />
<br />
for i in range(2,2399,3):<br />
A= (100*int(pid[i])+10*int(pid[i+1])+int(pid[i]))<br />
if A <84: p=""> L="A"<br />
elif A <95: p=""> L="B"<br />
elif A <125: p=""> L="C"<br />
elif A <167: p=""> L="D"<br />
elif A < 339:<br />
L="E"<br />
elif A <351: p=""> L="F"<br />
elif A <363: p=""> L="G"<br />
elif A <372: p=""> L="H"<br />
elif A <446: p=""> L="I"<br />
elif A <449: p=""> L="J"<br />
elif A < 450:<br />
L="K"<br />
elif A <511: p=""> L="L"<br />
elif A <540: p=""> L="M"<br />
elif A <610: p=""> L="N"<br />
elif A <663: p=""> L="O"<br />
elif A <693: p=""> L="P"<br />
elif A <703: p=""> L="Q"<br />
elif A <769: p=""> L="R"<br />
elif A <849: p=""> L="S"<br />
elif A <920: p=""> L="T"<br />
elif A <977: p=""> L="U"<br />
elif A <991: p=""> L="V"<br />
elif A <992: p=""> L="W"<br />
elif A <996: p=""> L="X"<br />
elif A<999: p=""> L="Y"<br />
elif A<1000: p=""> L="Z"<br />
<br />
<br />
print(L, end='')<br />
<br />
DNONSELOIELTEDIICSVUNESIEEZOASFCAVDAMEEOBSNNNERGICLCLECRUMCNOOUUUIUISVPUICLOESSDEETDONULFOLEOEINEEDERNANENETMUUSEBRHHTNHAEMNSLMIDUUMNIAEHRNUBECIUOSCCNALIURNGTRRTEUEAUCSPHIOOAAIUIERERETURSMEEEERIPSLPIDANCDENSSSFRSNEOERLITEUIDNNIASEPEUNAUCCAUTAIDSOSSEUMREFZZIVAUARRSBENALLFTEOMEEFPAEUEEAADSRTNMEIIOEPDENELIRLRDNTTGSNRUSTSMEESOAUTOETEIEUBEEALTETUDISUEEUAETUZSONITERSELDMNTELDQUSMCTRTTABIROLUEEAIURPDASSATHNNRPCREUUNEURSIIEISRSCAMOEAPEALEEPAVDCRDAUAAADEMEIIANOELLETEENEUSSGSOAFROEUNEAEEVNRRSLLNNUZQUESLEUEDFVERUELPLCTSSRNHSINMTNSINPTVSSSAOAADEEEEESGDIVNNDHDGNDLRSLIMETIDENRITMVNLNBEEEENEETPSLNOLSVOESSASISUVPLCUTSHUPAECECIVTACLOUNEUEAEPEEREOAEUACRSUUHITELRONUITTSOZSILANBLRAUELIGNRSSOMLIRRLELNLZTODIILEAELELRIOIISEOEUEQLMRTIINTUSVLUDRULDEPTUSDZTUEUUIAVMPSVEOQSOSREOBCNAETILEDNRSSRQIZRCOAIQTNSIGIAESLODLA<br />
</1000:></999:></996:></992:></991:></977:></920:></849:></769:></703:></693:></663:></610:></540:></511:></449:></446:></372:></363:></351:></167:></125:></95:></84:></100:></99:></98:></97:></96:></94:></88:></82:></76:></70:></69:></67:></61:></55:></52:></46:></45:></37:></35:></33:></16:></13:></11:></9:></1000:></960:></921:></883:></845:></806:></768:></730:></653:></614:></576:></538:></499:></461:></384:></346:></307:></259:></230:></154:></115:></77:></38:><br />
<div>
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<div>
Remarque : les lettres suivent les fréquences du français .On peut commencer à reconnaitre des débuts de mots .</div>
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On peut faire quelques autres variations sur ce thème, en rangeant les lettres par fréquences croissantes ou décroissantes, par exemple . Le choix des méthodes est très varié .</div>
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Bien sûr, ce n'est pas très spectaculaire, nous n'avons pas trouvé de jolies phrases, ni même notre prénom . Mais savoir qu'en allant chercher aussi loin qu'on veut, on trouvera certainement la phrase que l'on veut, ça donne un frisson , une réflexion sur l'infini que l'on peut ressentir en se promenant dans la bibliothèque de Babel .</div>
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<br />Olivier Longuethttp://www.blogger.com/profile/17956431908495478881noreply@blogger.com0tag:blogger.com,1999:blog-3415252720574602648.post-20495592687810129362017-01-13T13:00:00.000+01:002017-01-13T13:00:39.907+01:00une rencontre imaginaireUne planche de travail pour le concours maths et BD organisé par images des maths .<br />
Je compte la refondre totalement, mais il y a des idées que j'aime bien.<br />
<br />
J'espère faire concourir deux élèves de mon lycée par ailleurs . <br />
<br />
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<a href="http://i1220.photobucket.com/albums/dd448/olonguet/pereceuler_zpswzg4lcru.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://i1220.photobucket.com/albums/dd448/olonguet/pereceuler_zpswzg4lcru.jpg" /></a></div>
<br />Olivier Longuethttp://www.blogger.com/profile/17956431908495478881noreply@blogger.com0tag:blogger.com,1999:blog-3415252720574602648.post-45794615620121917602016-10-16T23:30:00.000+02:002016-10-16T23:30:13.414+02:00Suite de pliageVoici une aide pour démarrer le pliage pour un devoir maison.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<iframe width="320" height="266" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/nPyvL-MN6fY/0.jpg" src="https://www.youtube.com/embed/nPyvL-MN6fY?feature=player_embedded" frameborder="0" allowfullscreen></iframe></div>
<br />
Et voici le <a href="http://mathslyceechartier.monsite-orange.fr/file/e27509603e7535f85ae27826d88ceb12.pdf" target="_blank">devoir associé </a><br />
Sur une idée de Ruben Rodriguez.Olivier Longuethttp://www.blogger.com/profile/17956431908495478881noreply@blogger.com0tag:blogger.com,1999:blog-3415252720574602648.post-75734710542550896712016-10-09T12:27:00.001+02:002016-10-17T14:16:56.133+02:00QCM en classeDepuis la rentrée, pour dynamiser un peu mes classes et faire se poser des bonnes questions à mes élèves, j'ai décidé de faire dans chacune des mes séances de deux heures de cours un QCM, souvent placé au milieu de la séance . Je me suis renseigné sur les méthodes qu'on peut employer, J'ai appris qu'il y avait des boitiers pour cela dans certains amphis, ou des applications sur téléphone. Chacun ayant un compte, on peut garder la trace des réponses et arriver à une note .Mon objectif étant plutôt de créer une réflexion, puis un débat en classe, et non d'évaluer, j'ai opté pour une solution plus simple. Et puis, la technologie, c'est bien quand ça marche . Je me méfie un peu des solutions compliquées ou coûteuses. <br />
La question est projetée au tableau . Quatre réponses sont proposées, dont au moins un bonne, dans des rectangles de couleur bleue, verte, jaune ou rose . J'ai donné en première séance un post it de chacune des couleurs repositionnable . Au bout d'un certain temps que j'ai défini, les élèves levent le post it en même temps . En un coup d'oeil, on voit si la notion est comprise, et on explique les pièges s'ils sont tombés dedans . Les élèves aiment beaucoup ce rituel, et me le demandent si par hasard j'ai oublié ou si on n'est pas allés assez loin pour poser la bonne question .<br />
Pour l'instant, ça me demande du temps d'imaginer les questions qui peuvent faire avancer le débat, mais j'engrange pour les années suivantes .<br />
Les questions les plus efficaces pour le moment, avant d'aborder le théorème des valeurs intermédiaires et son corollaire :<br />
<br />
<div style="text-align: center;">
QUESTION 1 ( 30 secondes ) :</div>
<div style="text-align: center;">
f est continue sur [ -5 ; 5 ] ,</div>
<div style="text-align: center;">
f(-5) = - 3 , f(5) = 3 .</div>
<div style="text-align: center;">
Alors l'équation f(x) = 0 admet </div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisxd1hRgHswqQlmV8Ilp6iYgajRdcNw1goeG46jbM98U35aYfLK3c_EBTeVbTOMPpIttSP09Lryb4RXmJVWIMrZN4_ZMsq1E8YlvVVU3yM1B59CTAAUyam0LpJ_cqJNCfhQk7ULz5ebhs/s1600/qcm1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="160" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisxd1hRgHswqQlmV8Ilp6iYgajRdcNw1goeG46jbM98U35aYfLK3c_EBTeVbTOMPpIttSP09Lryb4RXmJVWIMrZN4_ZMsq1E8YlvVVU3yM1B59CTAAUyam0LpJ_cqJNCfhQk7ULz5ebhs/s400/qcm1.png" width="400" /></a></div>
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<div class="separator" style="clear: both; text-align: center;">
QUESTION 2 ( 30 secondes )</div>
<div class="separator" style="clear: both; text-align: center;">
f est continue et strictement croissante sur[ -5 ; 5 ] .</div>
<div style="text-align: center;">
f(-5) = - 3 , f(5) = 3 .</div>
<div style="text-align: center;">
Alors l'équation f(x) = 0 admet </div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisxd1hRgHswqQlmV8Ilp6iYgajRdcNw1goeG46jbM98U35aYfLK3c_EBTeVbTOMPpIttSP09Lryb4RXmJVWIMrZN4_ZMsq1E8YlvVVU3yM1B59CTAAUyam0LpJ_cqJNCfhQk7ULz5ebhs/s1600/qcm1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="160" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisxd1hRgHswqQlmV8Ilp6iYgajRdcNw1goeG46jbM98U35aYfLK3c_EBTeVbTOMPpIttSP09Lryb4RXmJVWIMrZN4_ZMsq1E8YlvVVU3yM1B59CTAAUyam0LpJ_cqJNCfhQk7ULz5ebhs/s400/qcm1.png" width="400" /></a></div>
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<br /></div>
<div class="separator" style="clear: both; text-align: center;">
QUESTION 3 (30 secondes)</div>
<div class="separator" style="clear: both; text-align: center;">
f est strictement croissante sur[ -5 ; 5 ] .</div>
<div style="text-align: center;">
f(-5) = - 3 , f(5) = 3 .</div>
<div style="text-align: center;">
Alors l'équation f(x) = 0 admet </div>
<div style="text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisxd1hRgHswqQlmV8Ilp6iYgajRdcNw1goeG46jbM98U35aYfLK3c_EBTeVbTOMPpIttSP09Lryb4RXmJVWIMrZN4_ZMsq1E8YlvVVU3yM1B59CTAAUyam0LpJ_cqJNCfhQk7ULz5ebhs/s1600/qcm1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="160" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisxd1hRgHswqQlmV8Ilp6iYgajRdcNw1goeG46jbM98U35aYfLK3c_EBTeVbTOMPpIttSP09Lryb4RXmJVWIMrZN4_ZMsq1E8YlvVVU3yM1B59CTAAUyam0LpJ_cqJNCfhQk7ULz5ebhs/s400/qcm1.png" width="400" /></a></div>
<div style="text-align: center;">
<br /></div>
<div style="text-align: left;">
Résultat, en cinq minutes ( débat et correction compris ), le théorème des valeurs intermédiaires et son corollaire étaient prêts à l'emploi .</div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
Je compte faire en fin de chapitre sur les suites un QCM en forme de vrai ou faux, avec élimination directe en cas de mauvaise réponse ( 20 secondes par question ). Sans doute les élèves qui auront trouvé toutes les bonnes réponses auront une note bonus .</div>
<div style="text-align: left;">
<span style="color: white;">QUESTION 1 : Une suite monotone et bornée converge .</span></div>
<div style="text-align: left;">
<span style="color: white;">QUESTION 2 : Une suite minorée et croissante converge.</span></div>
<div style="text-align: left;">
<span style="color: white;">QUESTION 3 : Une suite minorée est croissante.</span></div>
<div style="text-align: left;">
<span style="color: white;">QUESTION 4 : Une suite majorée et convergente est croissante</span></div>
<div style="text-align: left;">
<span style="color: white;">QUESTION 5 Une suite convergente est bornée.</span></div>
<div style="text-align: left;">
<span style="color: white;">QUESTION 6 Une suite croissante est minorée</span></div>
<div style="text-align: left;">
<span style="color: white;">QUESTION 7 : Une suite convergente est monotone .</span></div>
<div style="text-align: left;">
<span style="color: white;">QUESTION 8 : Une suite divergente n'est pas bornée .</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgn2swRFj2G5mBWKYil5bNxgbn5-Syx4-AzLHqnGzsoszqd4FlhCnW_34jPRsL9aig9dLGl0rEeBDKeyUiNFGG-oSSY5sPVYGwFSBR-ZlRpwp69hcYM2jus3-_PnZHS1kUeJcae2JMTtD0/s1600/qcmvraifaux.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="205" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgn2swRFj2G5mBWKYil5bNxgbn5-Syx4-AzLHqnGzsoszqd4FlhCnW_34jPRsL9aig9dLGl0rEeBDKeyUiNFGG-oSSY5sPVYGwFSBR-ZlRpwp69hcYM2jus3-_PnZHS1kUeJcae2JMTtD0/s320/qcmvraifaux.png" width="320" /></a></div>
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Je crois que c'est une bonne idée d'avoir opté pour des post it repositionnables. Les élèves les recollent sur la première page de le cahier, voire sur le protège cahier, il sont toujours à disposition.</div>
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C'est amusant, quand le cours devient un peu pointu, et que certains élèves veulent passer à autre chose, je les vois ouvrir la première page en espérant ce moment un peu plus détendu. </div>
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<br />Olivier Longuethttp://www.blogger.com/profile/17956431908495478881noreply@blogger.com3tag:blogger.com,1999:blog-3415252720574602648.post-76127017695488272202016-05-12T18:36:00.000+02:002016-10-09T12:35:40.352+02:00François MorelletFrançois Morellet vient de mourir . Je ne sais rien de lui, mais je lui dois ma meilleure surprise quand j'ai visité Beaubourg .
Son oeuvre est drôle et rigoureuse à la fois, empreinte de géométrie, un régal pour l'esprit . Je voulais lui rendre hommage .
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<a href="https://francoismorellet.files.wordpress.com/2011/01/8-trames-0c2b0-22c2b05-45c2b0-67c2b05-90c2b0-112c2b05-135c2b0-157c2b05-1958-pompi1.jpg?w=654" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://francoismorellet.files.wordpress.com/2011/01/8-trames-0c2b0-22c2b05-45c2b0-67c2b05-90c2b0-112c2b05-135c2b0-157c2b05-1958-pompi1.jpg?w=654" /></a></div>
8 trames 0° - 22°55 - 45° - 67°5 - 90° - 112°5 - 135° - 157°5,
Une huile sur bois constituée de 8 familles de droites parallèles régulièrement disposées .Suivant la position d'om on regarde le tableau, on voit des fleurs, des rosaces de différentes tailles, qui vibrent .<br />
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<a href="https://s2.qwant.com/thumbr/?u=http%3A%2F%2Fwww.galerie-ajct.com%2Fb_221.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://s2.qwant.com/thumbr/?u=http%3A%2F%2Fwww.galerie-ajct.com%2Fb_221.jpg" /></a></div>
Une belle façon de simuler le hasard, et pourtant vérifiable et reproductible avec le même annuaire.
PAr ailleurs, cela peut faire l'objet d'un exercice d'algorithmique : programmer l'ordinateur (algobox? ) pour faire une image sur le même principe .<br />
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<span style="font-family: "liberation mono";"><span style="font-size: x-small;">1
VARIABLES</span></span></div>
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<span style="font-family: "liberation mono";"><span style="font-size: x-small;">2
i EST_DU_TYPE NOMBRE</span></span></div>
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j EST_DU_TYPE NOMBRE</span></span></div>
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<span style="font-family: "liberation mono";"><span style="font-size: x-small;">4
numero EST_DU_TYPE NOMBRE</span></span></div>
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DEBUT_ALGORITHME</span></span></div>
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POUR i ALLANT_DE 1 A 200</span></span></div>
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DEBUT_POUR</span></span></div>
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POUR j ALLANT_DE 1 A 200</span></span></div>
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DEBUT_POUR</span></span></div>
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numero PREND_LA_VALEUR ALGOBOX_ALEA_ENT(0,9)</span></span></div>
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SI (numero%2==0) ALORS</span></span></div>
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DEBUT_SI</span></span></div>
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TRACER_POINT (i,j) {rouge}</span></span></div>
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FIN_SI</span></span></div>
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SINON</span></span></div>
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DEBUT_SINON</span></span></div>
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TRACER_POINT (i,j) {bleu}</span></span></div>
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FIN_SINON</span></span></div>
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FIN_POUR</span></span></div>
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FIN_POUR</span></span></div>
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FIN_ALGORITHME</span></span></div>
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(réglages dessiner dans un repère : xmin =0 , xmax =200 , y min = 0 , ymax = 200)<br />
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<a href="https://francoismorellet.files.wordpress.com/2011/01/6-rc3a9partitions-alc3a9atoires-de-4-carrc3a9s-noirs-et-blancs-daprc3a8s-les-chiffres-1958-pompi.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://francoismorellet.files.wordpress.com/2011/01/6-rc3a9partitions-alc3a9atoires-de-4-carrc3a9s-noirs-et-blancs-daprc3a8s-les-chiffres-1958-pompi.jpg" /></a></div>
6 répartitions aléatoires de 4 carrés noirs et blancs d'après les chiffres pairs et impairs du nombre Pi, 1958
Ensemble de 6 éléments. 6 panneaux carrés
Huile sur bois, 80x80 cm (dimension de chaque panneau)<br />
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Je viens de m'inspirer de cette dernière installation pour proposer un exercice de seconde, dans la continuité de ce que je fais en ce moment sur les probabilités:
Un tableau de François Morellet est composé de 4 carrés peints de façon aléatoire en blanc ou noir. Calculer les probabilités des événements suivants :<br />
A : " le tableau est monochrome."<br />
B : " Le tableau comporte un seul carré noir ."<br />
C: " Le tableau dessine une bande noire ."Olivier Longuethttp://www.blogger.com/profile/17956431908495478881noreply@blogger.com0tag:blogger.com,1999:blog-3415252720574602648.post-64782309434848992932015-03-28T12:37:00.000+01:002015-03-28T12:42:40.193+01:00stella octangula<html>
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La stella octangula, nommée ainsi par Johannes Kepler, peut être vue comme l'intersection de deux tétraèdres réguliers,
<a href="http://www.mi.sanu.ac.rs/vismath/zefiro2008/stella_octangula_clino_scala5_grey_320px.png" imageanchor="1" ><img border="0" src="http://www.mi.sanu.ac.rs/vismath/zefiro2008/stella_octangula_clino_scala5_grey_320px.png" /></a><br /> ou encore comme un octaèdre étoilé, c'est à dire un octaèdre où on a posé sur chaque face un tétraèdre régulier.<br />
<a href="http://www.matematicasvisuales.com/images/geometry/space/stellatedoctahedron/stellatedoctahedron1.jpg" imageanchor="1" ><img border="0" src="http://www.matematicasvisuales.com/images/geometry/space/stellatedoctahedron/stellatedoctahedron1.jpg" /></a>
Pour le construire, j'ai utilisé des baguettes de 20 cm découpées dans des tourillons, aux bouts desquelles j'ai vissé deux pitons à vis. L'attache se fait par des collerettes .<br />
<br />
J'ai commencé par fabriquer l'octaèdre pour ne pas me perdre dans la construction : au bout du compte, sur chaque sommet, il n'y aura pas moins que 8 arêtes !<br />
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Puis j'ai posé les tétraèdres par dessus.<br />
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La construction comporte 12 + 8 * 4 = 36 baguettes.<br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjoW39mquTz37AIMjCeWsivI_rJHXmzz4YqCsr23klXCsWHfjwZNKtf4q2-hxLBdGWnUa5iuFPDx0S-3gwX719YcN1tg1TgyyQ3NEVceM8WGLXFfH-p4i1U788aFefXe4ZiPVfi-04rjWo/s1600/octangula2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjoW39mquTz37AIMjCeWsivI_rJHXmzz4YqCsr23klXCsWHfjwZNKtf4q2-hxLBdGWnUa5iuFPDx0S-3gwX719YcN1tg1TgyyQ3NEVceM8WGLXFfH-p4i1U788aFefXe4ZiPVfi-04rjWo/s400/octangula2.jpg" /></a></div>
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La troisième partie de la construction consiste à faire passer au sommet de chaque tétraèdre une ficelle de manière à faire apparaître un cube .<br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW31ItRDQ189pnjZ7_Tg6yZvo6240_L681ldbeAdz3AGwuEMK1ov81d-O-WwuXxgISyhtscXFLhyQmrGizVZM0ymMaPgsbrQT-2_J5K9xUINlkxhGs2ukSYe-845cQKDBfux2M0Rzirjg/s1600/octangula3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW31ItRDQ189pnjZ7_Tg6yZvo6240_L681ldbeAdz3AGwuEMK1ov81d-O-WwuXxgISyhtscXFLhyQmrGizVZM0ymMaPgsbrQT-2_J5K9xUINlkxhGs2ukSYe-845cQKDBfux2M0Rzirjg/s400/octangula3.jpg" /></a></div>
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A partir de là, on peut avoir une petite réflexion sur les rapports de volumes de ces trois solides de Platon, et sur les pavages de l'espace.<br />
<br />
On sait paver l'espace avec des cubes de même taille, tout le monde en a fait l'expérience depuis son plus jeune âge.<br />
Imaginons que l'on pose plusieurs cubes de cette sorte de manière à paver l'espace.<br />
Oublions alors les cubes en ficelles, on a alors construit une structure composée de tétraèdres et d'octaèdres, chaque quart d'octaèdre se complétant avec ceux qui sont dans les cubes voisins.<br />
La structure composée d'octaèdres et de tétraèdres pave donc l'espace.<br />
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On a vu dans une précédente activité que le volume de l'octaèdre est égal à quatre fis celui du tétraèdre régulier de même longueur d'arête. <div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhN5NUEfDo4i8DvT_qdn6wqHpVcdcG8sYNzxZOxQ1qnfHzXZ6uUVV9zzJOcU2md6XGgfWOLpClDbRhOfur8SswSIlLNToMO3GmcrxyDAm17kfoK3IFQaF8wIcouup2POQP-8lsGIy4g6Dg/s1600/PICT0009.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhN5NUEfDo4i8DvT_qdn6wqHpVcdcG8sYNzxZOxQ1qnfHzXZ6uUVV9zzJOcU2md6XGgfWOLpClDbRhOfur8SswSIlLNToMO3GmcrxyDAm17kfoK3IFQaF8wIcouup2POQP-8lsGIy4g6Dg/s400/PICT0009.JPG" /></a></div>
Le cube que nous avons formé a une longueur de côté égale à <span lang="latex">\sqrt 2</span>
fois celle du côté de l'octaèdre . Le volume du cube que nous obtenons est donc <span lang="latex">\( \sqrt{2})^3 = 2 \sqrt 2</span>
fois plus grande que celle du carré de même longueur d'arête .
On garde ce fait sous le coude et on continue l'exploration:
Le cube est composé d'un octaèdre entier, de 8 tétraèdres et de 12 quarts d'octaèdres, dont une diagonale est figurée par les arêtes des cubes.
On peut compléter les octaèdres si avec quelques baguettes supplémentaires .
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzyFA-ILkgo8H0X_A_z-zmHSv8Olac1ITFShzUknkRNMHWWZPxgC4-3jZkGDiULGB3C8r3Ffpa67S_yGHfvUMdLXuJ0JtX2CX6wAfSD2A0FYdG3eI1ePh3ufUN_Rod7pNpU_HYuyJEDh4/s1600/octangula4.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzyFA-ILkgo8H0X_A_z-zmHSv8Olac1ITFShzUknkRNMHWWZPxgC4-3jZkGDiULGB3C8r3Ffpa67S_yGHfvUMdLXuJ0JtX2CX6wAfSD2A0FYdG3eI1ePh3ufUN_Rod7pNpU_HYuyJEDh4/s400/octangula4.jpg" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpJhEUomS2IcLglsRdO0XBSsWXbOJ2ERe_7CmzSC2ek_KT3gy2zt2yx5RoBV5sET0hcoCzv4ZHgbVhim4TtNkYACHHO_e2Y5OE5k6sPqtG5iQwA-5rDRGdByMyHfdMwYN4fqUYas7VNVk/s1600/octangula5.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpJhEUomS2IcLglsRdO0XBSsWXbOJ2ERe_7CmzSC2ek_KT3gy2zt2yx5RoBV5sET0hcoCzv4ZHgbVhim4TtNkYACHHO_e2Y5OE5k6sPqtG5iQwA-5rDRGdByMyHfdMwYN4fqUYas7VNVk/s400/octangula5.jpg" /></a></div>
Faisons les comptes , le volume du grand cube est donc celui de 4 octaèdres et de 8 tétraèdres, ce qui équivaut au volume de 6 octaèdres ou encore de 24 tétraèdres. Le volume d'un cube de la même arête est donc <span lang="latex">\frac{6}{2 \sqrt2 } = \frac{3 \sqrt 2} {2}</span> fois plus grand que celui de l'octaèdre .
On trouve donc les formules :
<br />
Pour l'octaèdre régulier d'arête a: <span lang="latex">V = \frac{\sqrt 2}{3} a^3</span>
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Pour le tétraèdre régulier d'arête a : <span lang="latex">V = \frac{\sqrt 2}{12} a^3</span>
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On peut aussi faire le rapport du volume de la stella octangula sur celui du cube :
ainsi, le volume de l'étoile est celui du cube ôté des 12 quarts d'octaèdre. On a vu que le volume du cube est celui de 6 octaèdres. Donc la volume de l'étoile est de 3 octaèdres, soit la moitié du volume du cube qui la contient.
Encore une fois, la perception du volume n'est pas évidente, je n'aurait pas parié sur ce rapport avant le calcul.
Si on veut dessiner la stella octangula avec un logiciel de géométrie dans l'espace, il suffit de commencer en donnant les coordonnées des sommets, qui sont aussi ceux du cube. Olivier Longuethttp://www.blogger.com/profile/17956431908495478881noreply@blogger.com0tag:blogger.com,1999:blog-3415252720574602648.post-72395611925843760842015-03-23T18:42:00.004+01:002015-03-23T18:42:36.661+01:00Happening pendant la semaine des mathsAu lycée, pendant la semaine des maths, j'ai affiché quelques énigmes sur l'icosaèdre tronqué que j'ai monté dans le préau. Les élèves pouvaient accrocher leur réponses.<br />
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Il y avait une affiche qui expliquait comment construire des tétraèdres par pliage. Le but du jeu était d'en construire un maximum et de les empiler pour obtenir un tétraèdre de Sierpinki. J'ai beaucoup invité les élèves qui étaient sous le préau à en construire. Au final, vendredi midi, nous avions fabriqué 256 pièces avec des feuilles A5 et les avons empilé pour obtenir une pyramide de 1.33 mètres environ. Voici les dernières photos avant destruction.<br />
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<br />Olivier Longuethttp://www.blogger.com/profile/17956431908495478881noreply@blogger.com8tag:blogger.com,1999:blog-3415252720574602648.post-42777735896037532032015-03-15T18:09:00.001+01:002015-03-15T18:44:25.442+01:00pi day sur la plage du D dayAvec un jour de retard, comme souvent quand je fête les anniversaires, je voulais célébrer le pi day d'un manière ludique en essayant de quarrer le cercle.<br />
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Sur la plage d'Asnelles, je vais tracer de manière approximative un carré de même aire qu'un disque donné.</div>
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Dans mes bagages, une tige, une ficelle , un rateau, des coquilles de moules ramassées sur place .</div>
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Cette méthode n'est pas du tout acceptable par les grecs qui refusaient l'usage des coquilles de moule et de tout autre instrument que le compas et la règle pour résoudre ce problème . De plus, j'utilise une méthode expérimentale ,avec tous les défauts de mesure que cela peut engendrer . Mais c'est toujours jouissif de faire de la géométrie sur la plage .<br />
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La construction peut se résumer ainsi :<br />
report de la longueur de Pi sur une droite ( opération interdite par les grecs)<br />
construction géométrique de la racine carrée<br />
construction du carré.<br />
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Je décris la méthode sur ce fichier geogebra .</div>
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<a href="https://tube.geogebra.org/student/m843075" target="_blank">https://tube.geogebra.org/student/m843075</a><br />
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dans un premier temps, je choisis une unité et je trace un cercle de centre A de rayon 1 unité.<br />
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Le but du jeu sera donc de tracer un carré de la même aire que ce disque . Je l'ai ratissé parce que ça fait plus joli, je crois.<br />
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Voila l'opération que le grecs auraient bannie . Je clôture le disque à l'aide de coquilles de moules trouvées sur place .<br />
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Je trace un diamètre avec la tige [BC] .<br />
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En posant la ficelle le long de la muraille de moules pour obtenir une demie circonférence, une valeur expérimentale de pi ;<br />
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Je reporte cette longueur .<br />
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ainsi que le diamètre du cercle. L'intersection de (BC) avec cet arc de cercle est le point D .<br />
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Je veux maintenant tracer le cercle de diamètre [AD] , pour cela , j'obtiens le milieu du segment en traçant la médiatrice.<br />
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Il reste à tracer la droite perpendiculaire au diamètre passant par B . Pour cela j'ai tracé le symétrique de C par rapport à B, puis la médiatrice de [CC'].<br />
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Cette droite coupe le cercle en deux points M et N . Par construction, la longueur BM est égale à la racine carrée de pi. Il reste juste à terminer le carré de côté [BM] .<br />
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Le carré a la même aire que le disque .<br />
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Ce fut intéressant de dessiner sur la plage, même s j'avoue que c'est un peu gratuit parce que je n'avais pas d'élèves , c'était samedi. J'imagine qu'on peut essayer de faire faire des constructions sur une plage, mais après avoir pas mal anticipé, en travaillant sur la figure à la règle et au compas, et sur la transposition de la méthode de construction avec d'autres outils, dans un univers plus grand que celui de la feuille .<br />
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J'ajoute que sur les plages normandes, le 14 mars, on se gèle .<br />
Comme Archimède avait trouvé qu'une valeur fractionnaire approchée de pi était 22/7, et que ça, ça correspond à une date française, je propose qu'on fasse un jour de pi le 22 juillet . Bon, il n'y aura pas d'élèves, mais on sera mieux sur la plage .<br />
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Merci à mon fils François pour m'avoir suivi et pour avoir pris les photos ...<br />
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Olivier Longuethttp://www.blogger.com/profile/17956431908495478881noreply@blogger.com1tag:blogger.com,1999:blog-3415252720574602648.post-58970516914885532212015-02-03T22:59:00.001+01:002015-02-13T10:45:59.749+01:00arc capableUn exercice peut être hors programme, mais intéressant dans la manipulation, et qui peut amener d'intéressantes méthodes de construction une fois qu'on a admis le résultat.<br />
Un plan de la côte normande, que j'ai plastifié .<br />
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Voici l'énoncé : Un bateau navigue sur la Manche par une nuit nuageuse . Le GPS tombe en panne . Le capitaine aperçoit au loin les lumières des phares de Port en Bessin, de Courseulles et de Ouistreham . Il mesure les angles azimutaux entre ces différents phares .<br />
Entre Port en Bessin et Courseulles, il trouve un angle de + pi/6 .<br />
Entre Courseulles et Ouistreham, il trouve un angle de + pi/4<br />
Où se trouve le bateau ?<br />
Derrière la feuille plastifiée, j'ai placé trois punaises aux positions des trois phares . On dispose de plus d'un feutre effaçable et de deux équerres ( une équerre à 30°,60°, 90° et une équerre à 45° )<br />
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Je noterai B le bateau, P Port en Bessin, C Courseulles et O Ouistreham<br />
Phase d'exploration : En faisant les côtés de l'équerre autour de deux punaises, on peut déterminer la position des points qui vérifie (BC, BO) = pi/ 4 . On obtient un bel arc de cercle . De même pour le deuxième angle . Le bateau est à l'intersection des deux arcs de cercle qui n'est pas C .<br />
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On admet ensuite le théorème de l'arc capable :<br />
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<strong class="theoreme-nom" style="line-height: 22.3999996185303px;">Théorème</strong><span class="theoreme-tiret" style="line-height: 22.3999996185303px;"> — </span><span style="line-height: 22.3999996185303px;"> Soient </span><b style="line-height: 22.3999996185303px;">A</b><span style="line-height: 22.3999996185303px;"> et </span><b style="line-height: 22.3999996185303px;">B</b><span style="line-height: 22.3999996185303px;"> deux points du plan et </span><b style="line-height: 22.3999996185303px;"><img alt="\alpha" class="mwe-math-fallback-image-inline tex" src="http://upload.wikimedia.org/math/b/c/c/bccfc7022dfb945174d9bcebad2297bb.png" style="border: none; display: inline-block; margin: 0px; vertical-align: middle;" /></b><span style="line-height: 22.3999996185303px;"> un réel donné tel que </span><b style="line-height: 22.3999996185303px;"><img alt=" 0 < \alpha < {\pi}" class="mwe-math-fallback-image-inline tex" src="http://upload.wikimedia.org/math/c/7/2/c729b34e6abcb345da602659efaf9485.png" style="border: none; display: inline-block; margin: 0px; vertical-align: middle;" /></b><span style="line-height: 22.3999996185303px;">. L'ensemble des points </span><b style="line-height: 22.3999996185303px;">M</b><span style="line-height: 22.3999996185303px;"> du plan différents de </span><b style="line-height: 22.3999996185303px;">A</b><span style="line-height: 22.3999996185303px;"> et </span><b style="line-height: 22.3999996185303px;">B</b><span style="line-height: 22.3999996185303px;"> tels que </span><img alt="\scriptstyle \widehat{AMB} \, = \, \alpha " class="mwe-math-fallback-image-inline tex" src="http://upload.wikimedia.org/math/0/e/9/0e963a7c113fecd93c59b55ecd3a3439.png" style="border: none; display: inline-block; line-height: 22.3999996185303px; margin: 0px; vertical-align: 0%;" /> <span style="line-height: 22.3999996185303px;">est un arc de cercle </span><img alt=" \underset{AB}{\frown}" class="mwe-math-fallback-image-inline tex" src="http://upload.wikimedia.org/math/0/2/0/020f5312e897c8561670f2d0305817f8.png" style="border: none; display: inline-block; line-height: 22.3999996185303px; margin: 0px; vertical-align: 0%;" /><span style="line-height: 22.3999996185303px;"> ouvert ( c'est-à-dire dont les extrémités </span><b style="line-height: 22.3999996185303px;">A</b><span style="line-height: 22.3999996185303px;"> et </span><b style="line-height: 22.3999996185303px;">B</b><span style="line-height: 22.3999996185303px;"> sont exclues).</span></div>
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On peut justifier ce théorème à l'aide du théorème de l'angle inscrit.</div>
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La construction à la règle, au compas et au rapporteur ( ou bien avec <a href="http://tube.geogebra.org/student/m623289" target="_blank">geogebra</a> ) de ces arcs de cercle demande une petite réflexion . J'ai utilisé la médiatrice et le théorème de l'angle au centre pour trouver le centre des arcs de cercle, </div>
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EDIT : Lors du stage de jeudi, une collègue a immédiatement juxtaposé les deux équerres dans la bonne position, j'ai trouvé ça brillant . Même si ça annihile toutes les considérations sur la nécessité de la construction des arcs de cercles.<br />
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<br />Olivier Longuethttp://www.blogger.com/profile/17956431908495478881noreply@blogger.com0tag:blogger.com,1999:blog-3415252720574602648.post-63271240902503057762015-01-22T09:48:00.002+01:002015-01-22T09:48:28.716+01:00Un ancètre des mathématiques dynamiquesEn regardant les premiers essais de dessins animé sur une chaîne youtube , je suis tombé par hasard sur une pépite fascinante datant de 1911 ou 1912.
Elle est l'oeuvre d'un professeur allemand, Ludwig Münch, dont je n'ai pas trouvé d'autres traces par ailleurs . Il a réalisé de nombreux dessins animés didactiques, des folioscopes (flip-books ) montrant des propriétés géométriques, des démonstrations, ainsi que des recherches de lieux géométriques qui n'ont rien à envier à une animation sur geogebra, même si son travail a sans doute demandé beaucoup plus de travail de construction que quelques clics . Je trouve son intuition des mathématiques dynamiques très novatrice, pour une époque où le dessin animé n'était pas forcément très répandu.
Je vous mets en lien<a href="http://www.dailymotion.com/video/x1hra4_ludwig-munch-animated-geometry-1911_shortfilms" target="_blank"> le film </a>que j'ai trouvé sur le net .<br />
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<br />Olivier Longuethttp://www.blogger.com/profile/17956431908495478881noreply@blogger.com0