{"id":1383,"date":"2019-03-05T17:10:53","date_gmt":"2019-03-05T17:10:53","guid":{"rendered":"http:\/\/maths-simao.fr\/?p=1383"},"modified":"2019-04-11T09:31:53","modified_gmt":"2019-04-11T09:31:53","slug":"pavages-du-plan","status":"publish","type":"post","link":"https:\/\/maths-simao.fr\/?p=1383","title":{"rendered":"Pavages du plan"},"content":{"rendered":"\n<p>Au labo sciences, on a travaill\u00e9 pendant quelques s\u00e9ances sur le th\u00e8me des pavages du plan. Tout d&rsquo;abord on expliqu\u00e9 apr\u00e8s quelques notions sur les sym\u00e9tries, translations et rotations, qu&rsquo;il existait seulement 17 fa\u00e7ons de paver le plan \u00e0 partir d&rsquo;un motif et en utilisant ces transformations de base. On s&rsquo;est appuy\u00e9 sur le site de Th\u00e9r\u00e8se Eveillau et <a href=\"http:\/\/therese.eveilleau.pagesperso-orange.fr\/pages\/jeux_mat\/textes\/pavage_17_types.htm\">cet article<\/a> pour les visualiser.<\/p>\n\n\n\n<p>On s&rsquo;est ensuite occuper de retrouver les differents types de pavages sur des photos prises \u00e0 l&rsquo;Alhambra de Grenade.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" loading=\"lazy\" width=\"1024\" height=\"842\" src=\"https:\/\/maths-simao.fr\/wp-content\/uploads\/2019\/04\/alhambra-1024x842.jpg\" alt=\"\" class=\"wp-image-1409\" srcset=\"https:\/\/maths-simao.fr\/wp-content\/uploads\/2019\/04\/alhambra-1024x842.jpg 1024w, https:\/\/maths-simao.fr\/wp-content\/uploads\/2019\/04\/alhambra-150x123.jpg 150w, https:\/\/maths-simao.fr\/wp-content\/uploads\/2019\/04\/alhambra-300x247.jpg 300w, https:\/\/maths-simao.fr\/wp-content\/uploads\/2019\/04\/alhambra-768x632.jpg 768w, https:\/\/maths-simao.fr\/wp-content\/uploads\/2019\/04\/alhambra.jpg 1793w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><figcaption>Alc\u00f4ves ( Alhanias ) du patio des Myrtes<\/figcaption><\/figure>\n\n\n\n<p>  Un fois ces identifications faites, \u00e0 l&rsquo;aide du magnifique livre de Manuel Martinez Vella : \u00ab\u00a0L&rsquo;Alhambra avec une r\u00e8gle et un compas\u00a0\u00bb on s&rsquo;est attach\u00e9 \u00e0 reproduire ces motifs sous G\u00e9og\u00e9bra notamment la fameuse cocotte nasride.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" loading=\"lazy\" width=\"1024\" height=\"941\" src=\"https:\/\/maths-simao.fr\/wp-content\/uploads\/2019\/04\/cocotte_alhambra-1024x941.png\" alt=\"\" class=\"wp-image-1413\" srcset=\"https:\/\/maths-simao.fr\/wp-content\/uploads\/2019\/04\/cocotte_alhambra-1024x941.png 1024w, https:\/\/maths-simao.fr\/wp-content\/uploads\/2019\/04\/cocotte_alhambra-150x138.png 150w, https:\/\/maths-simao.fr\/wp-content\/uploads\/2019\/04\/cocotte_alhambra-300x276.png 300w, https:\/\/maths-simao.fr\/wp-content\/uploads\/2019\/04\/cocotte_alhambra-768x706.png 768w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><figcaption>Pajarita<br><\/figcaption><\/figure>\n\n\n\n<p>Une fois ce travail termin\u00e9 et apr\u00e8s export sous Tinkercad, on a imprim\u00e9 ces cocottes 3d pour faire un puzzle.<\/p>\n\n\n\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" width=\"540\" height=\"304\" src=\"https:\/\/www.youtube.com\/embed\/JXUlWLtHhqQ?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p>Voici un autre exemple de motif beaucoup plus complexe \u00e0 r\u00e9aliser.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/maths-simao.fr\/wp-content\/uploads\/2019\/04\/rosace_alhambre_2-1022x1024.png\" alt=\"\" class=\"wp-image-1420\" width=\"393\" height=\"393\" srcset=\"https:\/\/maths-simao.fr\/wp-content\/uploads\/2019\/04\/rosace_alhambre_2-1022x1024.png 1022w, https:\/\/maths-simao.fr\/wp-content\/uploads\/2019\/04\/rosace_alhambre_2-150x150.png 150w, https:\/\/maths-simao.fr\/wp-content\/uploads\/2019\/04\/rosace_alhambre_2-300x300.png 300w, https:\/\/maths-simao.fr\/wp-content\/uploads\/2019\/04\/rosace_alhambre_2-768x770.png 768w, https:\/\/maths-simao.fr\/wp-content\/uploads\/2019\/04\/rosace_alhambre_2.png 1506w\" sizes=\"(max-width: 393px) 100vw, 393px\" \/><\/figure><\/div>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" loading=\"lazy\" width=\"1015\" height=\"1024\" src=\"https:\/\/maths-simao.fr\/wp-content\/uploads\/2019\/04\/rosace_alhambre_4-1015x1024.png\" alt=\"\" class=\"wp-image-1421\" srcset=\"https:\/\/maths-simao.fr\/wp-content\/uploads\/2019\/04\/rosace_alhambre_4-1015x1024.png 1015w, https:\/\/maths-simao.fr\/wp-content\/uploads\/2019\/04\/rosace_alhambre_4-150x150.png 150w, https:\/\/maths-simao.fr\/wp-content\/uploads\/2019\/04\/rosace_alhambre_4-297x300.png 297w, https:\/\/maths-simao.fr\/wp-content\/uploads\/2019\/04\/rosace_alhambre_4-768x775.png 768w\" sizes=\"(max-width: 1015px) 100vw, 1015px\" \/><\/figure>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/maths-simao.fr\/wp-content\/uploads\/2019\/04\/IMG_20190403_112728-986x1024.jpg\" alt=\"\" class=\"wp-image-1385\" width=\"255\" height=\"265\" srcset=\"https:\/\/maths-simao.fr\/wp-content\/uploads\/2019\/04\/IMG_20190403_112728-986x1024.jpg 986w, https:\/\/maths-simao.fr\/wp-content\/uploads\/2019\/04\/IMG_20190403_112728-144x150.jpg 144w, https:\/\/maths-simao.fr\/wp-content\/uploads\/2019\/04\/IMG_20190403_112728-289x300.jpg 289w, https:\/\/maths-simao.fr\/wp-content\/uploads\/2019\/04\/IMG_20190403_112728-768x798.jpg 768w\" sizes=\"(max-width: 255px) 100vw, 255px\" \/><figcaption>Un motif plus complexe de l&rsquo;Alhambra<br><br><\/figcaption><\/figure><\/div>\n\n\n\n<p>Enfin pour terminer, apr\u00e8s visionnage des quelques jolies dessins d&rsquo;Escher, on a expliqu\u00e9 quelques r\u00e8gles pour r\u00e9aliser ses propres motifs. Ce qui a inspir\u00e9 notamment Basile qui m&rsquo;a remis le cours suivant un pavage cr\u00e9e sous G\u00e9og\u00e9bra.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/maths-simao.fr\/wp-content\/uploads\/2019\/04\/IMG_20190403_112822-1024x971.jpg\" alt=\"\" class=\"wp-image-1384\" width=\"257\" height=\"243\" srcset=\"https:\/\/maths-simao.fr\/wp-content\/uploads\/2019\/04\/IMG_20190403_112822-1024x971.jpg 1024w, https:\/\/maths-simao.fr\/wp-content\/uploads\/2019\/04\/IMG_20190403_112822-150x142.jpg 150w, https:\/\/maths-simao.fr\/wp-content\/uploads\/2019\/04\/IMG_20190403_112822-300x284.jpg 300w, https:\/\/maths-simao.fr\/wp-content\/uploads\/2019\/04\/IMG_20190403_112822-768x728.jpg 768w\" sizes=\"(max-width: 257px) 100vw, 257px\" \/><figcaption>Pavage cr\u00e9e par basile<\/figcaption><\/figure><\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Au labo sciences, on a travaill\u00e9 pendant quelques s\u00e9ances sur le th\u00e8me des pavages du plan. Tout d&rsquo;abord on expliqu\u00e9 apr\u00e8s quelques notions sur les sym\u00e9tries, translations et rotations, qu&rsquo;il existait seulement 17 fa\u00e7ons de paver le plan \u00e0 partir d&rsquo;un motif et en utilisant ces transformations de base. On s&rsquo;est appuy\u00e9 sur le site [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/maths-simao.fr\/index.php?rest_route=\/wp\/v2\/posts\/1383"}],"collection":[{"href":"https:\/\/maths-simao.fr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/maths-simao.fr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/maths-simao.fr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/maths-simao.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1383"}],"version-history":[{"count":14,"href":"https:\/\/maths-simao.fr\/index.php?rest_route=\/wp\/v2\/posts\/1383\/revisions"}],"predecessor-version":[{"id":1422,"href":"https:\/\/maths-simao.fr\/index.php?rest_route=\/wp\/v2\/posts\/1383\/revisions\/1422"}],"wp:attachment":[{"href":"https:\/\/maths-simao.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1383"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/maths-simao.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1383"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/maths-simao.fr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1383"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}