{"id":1786,"date":"2016-09-15T02:49:38","date_gmt":"2016-09-15T01:49:38","guid":{"rendered":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/?p=1786"},"modified":"2018-02-17T02:05:53","modified_gmt":"2018-02-17T01:05:53","slug":"section-dun-tetraedre","status":"publish","type":"post","link":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/section-dun-tetraedre\/","title":{"rendered":"Section d&#8217;un t\u00e9tra\u00e8dre"},"content":{"rendered":"<h1>Projet d&#8217;activit\u00e9 TICE<\/h1>\n<p>&nbsp;<\/p>\n<h2>\u00c9nonc\u00e9 :<img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-1799 alignright\" src=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2016\/09\/Section-dun-t\u00e9tra\u00e8dre-300x200.jpg\" alt=\"Section d'un t\u00e9tra\u00e8dre\" width=\"300\" height=\"200\" srcset=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2016\/09\/Section-dun-t\u00e9tra\u00e8dre-300x200.jpg 300w, https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2016\/09\/Section-dun-t\u00e9tra\u00e8dre.jpg 335w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/h2>\n<p>Dans le t\u00e9tra\u00e8dre ABCD, N est le milieu de [AD], L est le milieu de [AC].<\/p>\n<p>M \u00e9tant un point du segment [BC], le plan (MLN) coupe le segment [BD] en Q.<\/p>\n<p>On s\u2019int\u00e9resse d\u2019abord \u00e0 la nature de la section obtenue, puis \u00e0 la construction des patrons des deux solides ainsi d\u00e9finis dans le cas particulier d\u2019un t\u00e9tra\u00e8dre r\u00e9gulier.<\/p>\n<h2>Pr\u00e9requis<\/h2>\n<ul>\n<li>Utilisation basique de Geospace<\/li>\n<li>Parall\u00e9lisme dans l\u2019espace<\/li>\n<\/ul>\n<h2>Objectifs<\/h2>\n<ul>\n<li>Conjecturer la nature de la section d\u2019un t\u00e9tra\u00e8dre par un plan \u00e0 l\u2019aide de l\u2019outil informatique et d\u00e9montrer la conjecture.<\/li>\n<li>Construire \u00e0 la main les patrons de deux solides apr\u00e8s observation \u00e0 l\u2019aide de l\u2019outil informatique.<\/li>\n<\/ul>\n<h2>D\u00e9roulement de la s\u00e9quence<\/h2>\n<p>En salle informatique puis travail \u00e0 la maison.<\/p>\n<p>A partir d\u2019un fichier fourni par le professeur (section_tetraedre.g3w) les \u00e9l\u00e8ves compl\u00e8tent la figure afin d\u2019observer la nature de la section.<\/p>\n<p>Ils d\u00e9montrent les r\u00e9sultats conjectur\u00e9s.<br \/>\nles variations des volumes en fonction de h.<br \/>\nLes \u00e9l\u00e8ves cr\u00e9ent ensuite les deux solides, puis leurs patrons. Ils pourront visualiser le cas particulier gr\u00e2ce \u00e0 une commande existant dans le fichier.<br \/>\nA la maison ils r\u00e9alisent \u00e0 la main ces deux patrons dans le cas d\u2019un t\u00e9tra\u00e8dre r\u00e9gulier de 10 cm d\u2019ar\u00eate pour une position choisie de M autre que le milieu de [BC].<\/p>\n<p>Remarque :<br \/>\ndans le fichier section_tetraedre_corrige.g3w :<\/p>\n<p>&#8211; la touche M permet de placer le point M au milieu de [BC]<\/p>\n<p>&#8211; la touche T permet de montrer ou de cacher le t\u00e9tra\u00e8dre ABCD et ses sommets<\/p>\n<p>&#8211; la touche 1 permet de montrer l\u2019un ou l\u2019autre des deux solides et son patron (celui-ci se d\u00e9veloppe en utilisant les fl\u00e8ches du clavier)<\/p>\n<p>&#8211; la touche R permet d\u2019obtenir un t\u00e9tra\u00e8dre ABCD r\u00e9gulier.<\/p>\n<h2>Documents<\/h2>\n<p><a href=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2016\/09\/section_tetraedre.zip\">Figure g\u00e9ospace base Section d&#8217;un t\u00e9tra\u00e8dre<\/a> (en zip)<br \/>\n<a href=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2016\/09\/section_tetraedre_corrige.zip\">Figure g\u00e9ospace corrig\u00e9e Section d&#8217;un t\u00e9tra\u00e8dre<\/a>(en zip)<br \/>\n<a href=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2016\/09\/section_tetraedre_eleve_v2.pdf\">Document \u00e9l\u00e8ve Section d&#8217;un t\u00e9tra\u00e8dre<\/a>(en pdf )<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Projet d&#8217;activit\u00e9 TICE &nbsp; \u00c9nonc\u00e9 : Dans le t\u00e9tra\u00e8dre ABCD, N est le milieu de [AD], L est le milieu de [AC]. M \u00e9tant un point du segment [BC], le plan (MLN) coupe le segment [BD] en Q. On s\u2019int\u00e9resse d\u2019abord \u00e0 la nature de la section obtenue, puis \u00e0 la construction des patrons des &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/section-dun-tetraedre\/\">Lire la suite<\/a><\/p>\n","protected":false},"author":351,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"footnotes":""},"categories":[23,22,14],"tags":[],"class_list":["post-1786","post","type-post","status-publish","format-standard","hentry","category-seconde","category-lycee","category-numerique","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts\/1786","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/users\/351"}],"replies":[{"embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/comments?post=1786"}],"version-history":[{"count":4,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts\/1786\/revisions"}],"predecessor-version":[{"id":1800,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts\/1786\/revisions\/1800"}],"wp:attachment":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/media?parent=1786"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/categories?post=1786"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/tags?post=1786"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}