{"id":176,"date":"2008-06-19T13:50:20","date_gmt":"2008-06-19T11:50:20","guid":{"rendered":"http:\/\/wordpress.callac.online\/index.php\/patrons-depliables-de-solides-avec-xcas\/"},"modified":"2023-10-14T20:14:12","modified_gmt":"2023-10-14T18:14:12","slug":"patrons-depliables-de-solides-avec-xcas","status":"publish","type":"page","link":"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/geometrie-avec-xcas\/patrons-depliables-de-solides-avec-xcas\/","title":{"rendered":"Patrons d\u00e9pliables de solides avec Xcas"},"content":{"rendered":"

\nVoici quelques exemples de sections de solides faites avec Xcas.<\/p>\n

Dans chacun des cas, ouvrir une session geo3d et ins\u00e9rer les commandes correspondes.<\/p>\n

Le cube<\/h2>\n
\n\n(A:=point(0,0,0)),(B:=point(1,0,0)),(C:=point(1,1,0)),(D:=point(0,1,0)),affichage(polygone(A,B,C,D),rouge+rempli),affichage(polygone(A,B,C,D),noir) ;\nassume(a:=[1.57079632679,pi\/2,pi,pi\/100.0]) ;\n(E:=rotation(droite(D,A),a,B)),(F:=rotation(droite(D,A),a,C)),affichage(polygone(A,D,F,E),bleu+rempli),affichage(polygone(A,D,F,E),noir),(K:=rotation(droite(B,C),a,A)),(L:=rotation(droite(B,C),a,D)),affichage(polygone(B,C,L,K),bleu+rempli),affichage(polygone(B,C,L,K),noir) ;\nassume(b:=[1.57079632679,pi\/2,pi,pi\/100.0]) ;\n(G:=rotation(droite(A,B),b,D)),(H:=rotation(droite(A,B),b,C)),affichage(polygone(B,A,G,H),jaune+rempli),affichage(polygone(B,A,G,H),noir),(I:=rotation(droite(C,D),b,A)),(J:=rotation(droite(C,D),b,B)),affichage(polygone(C,D,I,J),jaune+rempli),affichage(polygone(C,D,I,J),noir) ;\nassume(c:=[1.88495562,pi\/2,pi,pi\/100.0]) ;\n(M:=rotation(droite(F,E),c,A)),(N:=rotation(droite(F,E),c,D)),affichage(polygone(E,F,N,M),rouge+rempli),affichage(polygone(E,F,N,M),noir) ;\n<\/plain>\n

\"patron-cube.jpg\"<\/p>\n

Le parall\u00e9l\u00e9pip\u00e8de<\/h2>\n
\n

\n(d:=5),(l:=3),(h:=1) ;\n(A:=point(0,0,0)),(B:=point(d,0,0)),(C:=point(d,l,0)),(D:=point(0,l,0)),affichage(polygone(A,B,C,D),rouge+rempli),affichage(polygone(A,B,C,D),noir) ;\nassume(a:=[1.57079632679,pi\/2,pi,pi\/100.0]) ;\n(E:=rotation(droite(D,A),a,point(h,0,0))),(F:=rotation(droite(D,A),a,point(h,l,0))),affichage(polygone(A,D,F,E),bleu+rempli),affichage(polygone(A,D,F,E),noir),(K:=rotation(droite(B,C),a,point(d-h,0,0))),(L:=rotation(droite(B,C),a,point(d-h,l,0))),affichage(polygone(B,C,L,K),bleu+rempli),affichage(polygone(B,C,L,K),noir) ;\nassume(b:=[1.57079632679,pi\/2,pi,pi\/100.0]) ;\n(G:=rotation(droite(A,B),b,point(0,h,0))),(H:=rotation(droite(A,B),b,point(d,h,0))),affichage(polygone(B,A,G,H),jaune+rempli),affichage(polygone(B,A,G,H),noir),(I:=rotation(droite(C,D),b,point(0,l-h,0))),(J:=rotation(droite(C,D),b,point(d,l-h,0))),affichage(polygone(C,D,I,J),jaune+rempli),affichage(polygone(C,D,I,J),noir) ;\nassume(c:=[1.88495562,pi\/2,pi,pi\/100.0]) ;\n(M:=rotation(droite(F,E),c,A)),(N:=rotation(droite(F,E),c,D)),(O:=translation((d-h)\/h*vecteur(E,M),M)),(P:=translation((d-h)\/h*vecteur(F,N),N)),affichage(polygone(E,F,P,O),rouge+rempli),affichage(polygone(E,F,P,O),noir) ;\n<\/plain>\n

\"patron-boite.jpg\"<\/p>\n

La pyramide<\/h2>\n
\n\n(A:=point(0,0,0)),(B:=point(2,0,0)),(C:=point(2,2,0)),(D:=point(0,2,0)),(S:=point(3,1,4)),(R:=isobarycentre(A,B,C,D)) ;\naffichage(polygone(A,B,C,D),bleu+rempli),affichage(polygone(A,B,C,D),noir) ;\n(O:=projection(plan(A,B,C),S)),(I:=projection(droite(A,B),O)),(J:=projection(droite(B,C),O)),(K:=projection(droite(C,D),O)),(L:=projection(droite(D,A),O)) ;\nassume(t:=[0.1,0,1,0.1]) ;\n(EE:=inter_unique(plan(I,S,O),parallele(R,droite(A,B)))),(FF:=inter_unique(plan(J,S,O),parallele(R,droite(B,C)))),(GG:=inter_unique(plan(K,S,O),parallele(R,droite(C,D)))),(HH:=inter_unique(plan(L,S,O),parallele(R,droite(D,A)))) ;\n(E:=rotation(droite(A,B),t*(pi-angle(I,EE,S)),S)),affichage(polygone(A,B,E),rouge+rempli),affichage(polygone(A,B,E),noir),(F:=rotation(droite(B,C),t*(pi-angle(J,FF,S)),S)),affichage(polygone(B,C,F),rouge+rempli),affichage(polygone(B,C,F),noir),(G:=rotation(droite(C,D),t*(pi-angle(K,GG,S)),S)),affichage(polygone(C,D,G),rouge+rempli),affichage(polygone(C,D,G),noir),(H:=rotation(droite(D,A),t*(pi-angle(L,HH,S)),S)),affichage(polygone(D,A,H),rouge+rempli),affichage(polygone(D,A,H),noir) ;\n<\/plain>\n

\"patron-pyramide.jpg\"<\/p>\n

Le t\u00e9tra\u00e8dre<\/h2>\n
\n\n(A:=point(0,0,0)),(B:=point(2,0,0)),(C:=point(1,3,0)),(S:=point(-2,1,4)),(R:=isobarycentre(A,B,C)) ;\naffichage(polygone(A,B,C),bleu+rempli),affichage(polygone(A,B,C),noir) ;\n(O:=projection(plan(A,B,C),S)),(I:=projection(droite(A,B),O)),(J:=projection(droite(B,C),O)),(K:=projection(droite(C,A),O)) ;\nassume(t:=[0.0,0,1,0.1]) ;\n(EE:=inter_unique(plan(I,S,O),parallele(R,droite(A,B)))),(FF:=inter_unique(plan(J,S,O),parallele(R,droite(B,C)))),(GG:=inter_unique(plan(K,S,O),parallele(R,droite(A,C)))) ;\n(E:=rotation(droite(A,B),t*(pi-angle(I,EE,S)),S)),affichage(polygone(A,B,E),rouge+rempli),affichage(polygone(A,B,E),noir),(F:=rotation(droite(B,C),t*(pi-angle(J,FF,S)),S)),affichage(polygone(B,C,F),rouge+rempli),affichage(polygone(B,C,F),noir),(G:=rotation(droite(C,A),t*(pi-angle(K,GG,S)),S)),affichage(polygone(A,C,G),rouge+rempli),affichage(polygone(A,C,G),noir) ;\n<\/plain>\n

\"patron-tetraedre.jpg\"<\/p>\n

<\/math><\/p>\n","protected":false},"excerpt":{"rendered":"

Voici quelques exemples de sections de solides faites avec Xcas. Dans chacun des cas, ouvrir une session geo3d et ins\u00e9rer les commandes correspondes. Le cube (A:=point(0,0,0)),(B:=point(1,0,0)),(C:=point(1,1,0)),(D:=point(0,1,0)),affichage(polygone(A,B,C,D),rouge+rempli),affichage(polygone(A,B,C,D),noir) ; assume(a:=[1.57079632679,pi\/2,pi,pi\/100.0]) ; (E:=rotation(droite(D,A),a,B)),(F:=rotation(droite(D,A),a,C)),affichage(polygone(A,D,F,E),bleu+rempli),affichage(polygone(A,D,F,E),noir),(K:=rotation(droite(B,C),a,A)),(L:=rotation(droite(B,C),a,D)),affichage(polygone(B,C,L,K),bleu+rempli),affichage(polygone(B,C,L,K),noir)…<\/p>\n","protected":false},"author":1,"featured_media":687,"parent":2230,"menu_order":3,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-176","page","type-page","status-publish","has-post-thumbnail","hentry"],"yoast_head":"\nPatrons d\u00e9pliables de solides avec Xcas - Maths & Num\u00e9rique<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/geometrie-avec-xcas\/patrons-depliables-de-solides-avec-xcas\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Patrons d\u00e9pliables de solides avec Xcas - Maths & Num\u00e9rique\" \/>\n<meta property=\"og:description\" content=\"Voici quelques exemples de sections de solides faites avec Xcas. Dans chacun des cas, ouvrir une session geo3d et ins\u00e9rer les commandes correspondes. Le cube (A:=point(0,0,0)),(B:=point(1,0,0)),(C:=point(1,1,0)),(D:=point(0,1,0)),affichage(polygone(A,B,C,D),rouge+rempli),affichage(polygone(A,B,C,D),noir) ; assume(a:=[1.57079632679,pi\/2,pi,pi\/100.0]) ; (E:=rotation(droite(D,A),a,B)),(F:=rotation(droite(D,A),a,C)),affichage(polygone(A,D,F,E),bleu+rempli),affichage(polygone(A,D,F,E),noir),(K:=rotation(droite(B,C),a,A)),(L:=rotation(droite(B,C),a,D)),affichage(polygone(B,C,L,K),bleu+rempli),affichage(polygone(B,C,L,K),noir)…\" \/>\n<meta property=\"og:url\" content=\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/geometrie-avec-xcas\/patrons-depliables-de-solides-avec-xcas\/\" \/>\n<meta property=\"og:site_name\" content=\"Maths & Num\u00e9rique\" \/>\n<meta property=\"article:modified_time\" content=\"2023-10-14T18:14:12+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/wordpress.callac.online\/wp-content\/uploads\/2008\/06\/jpg_patron-cube.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"574\" \/>\n\t<meta property=\"og:image:height\" content=\"574\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data1\" content=\"4 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/geometrie-avec-xcas\/patrons-depliables-de-solides-avec-xcas\/\",\"url\":\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/geometrie-avec-xcas\/patrons-depliables-de-solides-avec-xcas\/\",\"name\":\"Patrons d\u00e9pliables de solides avec Xcas - 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Dans chacun des cas, ouvrir une session geo3d et ins\u00e9rer les commandes correspondes. 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