{"id":88,"date":"2007-06-23T20:19:51","date_gmt":"2007-06-23T18:19:51","guid":{"rendered":"http:\/\/wordpress.callac.online\/index.php\/un-arbre-de-bernoulli-a-4-niveaux\/"},"modified":"2023-10-14T20:12:53","modified_gmt":"2023-10-14T18:12:53","slug":"un-arbre-de-bernoulli-a-4-niveaux","status":"publish","type":"page","link":"https:\/\/wordpress.callac.online\/index.php\/edition-mathematique\/metapost\/arbres-de-probabilite\/un-arbre-de-bernoulli-a-4-niveaux\/","title":{"rendered":"Un arbre de Bernoulli \u00e0 4 niveaux"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\" aligncenter size-full wp-image-593\" src=\"http:\/\/wordpress.callac.online\/wp-content\/uploads\/2007\/06\/jpg_bernoulli4.jpg\" alt=\"bernoulli4.jpg\" width=\"458\" height=\"582\" align=\"center\" srcset=\"https:\/\/wordpress.callac.online\/wp-content\/uploads\/2007\/06\/jpg_bernoulli4.jpg 458w, https:\/\/wordpress.callac.online\/wp-content\/uploads\/2007\/06\/jpg_bernoulli4-236x300.jpg 236w\" sizes=\"auto, (max-width: 458px) 100vw, 458px\" \/><\/p>\n<p>Voici son code :<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">input geometriesyr16.mp ;\n\n%%%%%%%%%%%%%%%%%%\n%%\n%%Ne pas oublier : export TEX=latex\n%%\n%%%%%%%%%%%%%%%%%\n\nvardef TEX primary s =\n  write \"verbatimtex\"   to \"mptextmp.mp\";\n  write \"%&amp;latex\" to  \"mptextmp.mp\";\n  write \"\\documentclass{article}\"  to \"mptextmp.mp\";\n  write \"\\usepackage{aeguill}\" to \"mptextmp.mp\";\n  write \"\\usepackage[frenchb]{babel}\" to \"mptextmp.mp\";\n  write \"\\usepackage{amsmath}\" to \"mptextmp.mp\";\n  write \"\\usepackage{amsfonts}\" to \"mptextmp.mp\";\n  write \"\\begin{document}\"  to \"mptextmp.mp\";\n  write \"etex\"    to \"mptextmp.mp\";\n  write \"btex \" &amp; s &amp; \" etex\" to \"mptextmp.mp\";\n  write EOF to \"mptextmp.mp\";\n  scantokens \"input mptextmp\"\nenddef;\n\n%------------------------------------------------------------------------\n% Arbre de Bernoulli \u00e0 quatre niveaux\n%------------------------------------------------------------------------\n\nu:=1cm;\nfigure (-8u,-17u,10u,8u);\npair S,T[],U[],V[],W[];\n\nnumeric dx,dh,cr;\ndx:=3;\ndh:=1;\ncr:=0.1;\n\nfor i:=1 upto 16:\n  W[i]:=(3*dx*u,-i*dh*u);\nendfor\n\nV[1]:= 0.5[W[1],W[2]] shifted(-dx*u,0);\nV[2]:= 0.5[W[3],W[4]] shifted(-dx*u,0);\nV[3]:= 0.5[W[5],W[6]] shifted(-dx*u,0);\nV[4]:= 0.5[W[7],W[8]] shifted(-dx*u,0);\nV[5]:= 0.5[W[9],W[10]] shifted(-dx*u,0);\nV[6]:= 0.5[W[11],W[12]] shifted(-dx*u,0);\nV[7]:= 0.5[W[13],W[14]] shifted(-dx*u,0);\nV[8]:= 0.5[W[15],W[16]] shifted(-dx*u,0);\n\n\nU[1]:= 0.5[V[1],V[2]] shifted(-dx*u,0);\nU[2]:= 0.5[V[3],V[4]] shifted(-dx*u,0);\nU[3]:= 0.5[V[5],V[6]] shifted(-dx*u,0);\nU[4]:= 0.5[V[7],V[8]] shifted(-dx*u,0);\n\nT[1]:= 0.5[U[1],U[2]] shifted(-dx*u,0);\nT[2]:= 0.5[U[3],U[4]] shifted(-dx*u,0);\n\nS:= 0.5[T[1],T[2]] shifted(-dx*u,0);\n\ndraw cr[S,T[1]]--(1-cr)[S,T[1]];\ndraw cr[S,T[2]]--(1-cr)[S,T[2]];\ndraw cr[T[1],U[1]]--(1-cr)[T[1],U[1]];\ndraw cr[T[1],U[2]]--(1-cr)[T[1],U[2]];\ndraw cr[T[2],U[3]]--(1-cr)[T[2],U[3]];\ndraw cr[T[2],U[4]]--(1-cr)[T[2],U[4]];\ndraw cr[U[1],V[1]]--(1-cr)[U[1],V[1]];\ndraw cr[U[1],V[2]]--(1-cr)[U[1],V[2]];\ndraw cr[U[2],V[3]]--(1-cr)[U[2],V[3]];\ndraw cr[U[2],V[4]]--(1-cr)[U[2],V[4]];\ndraw cr[U[3],V[5]]--(1-cr)[U[3],V[5]];\ndraw cr[U[3],V[6]]--(1-cr)[U[3],V[6]];\ndraw cr[U[4],V[7]]--(1-cr)[U[4],V[7]];\ndraw cr[U[4],V[8]]--(1-cr)[U[4],V[8]];\ndraw cr[V[1],W[1]]--(1-cr)[V[1],W[1]];\ndraw cr[V[1],W[2]]--(1-cr)[V[1],W[2]];\ndraw cr[V[2],W[3]]--(1-cr)[V[2],W[3]];\ndraw cr[V[2],W[4]]--(1-cr)[V[2],W[4]];\ndraw cr[V[3],W[5]]--(1-cr)[V[3],W[5]];\ndraw cr[V[3],W[6]]--(1-cr)[V[3],W[6]];\ndraw cr[V[4],W[7]]--(1-cr)[V[4],W[7]];\ndraw cr[V[4],W[8]]--(1-cr)[V[4],W[8]];\ndraw cr[V[5],W[9]]--(1-cr)[V[5],W[9]];\ndraw cr[V[5],W[10]]--(1-cr)[V[5],W[10]];\ndraw cr[V[6],W[11]]--(1-cr)[V[6],W[11]];\ndraw cr[V[6],W[12]]--(1-cr)[V[6],W[12]];\ndraw cr[V[7],W[13]]--(1-cr)[V[7],W[13]];\ndraw cr[V[7],W[14]]--(1-cr)[V[7],W[14]];\ndraw cr[V[8],W[15]]--(1-cr)[V[8],W[15]];\ndraw cr[V[8],W[16]]--(1-cr)[V[8],W[16]];\n\n\nstring a,na,pa,pna;\na:=\"$A$\";\nna:=\"$\\overline{A}$\";\npa:=\"$\\frac{1}{3}$\";\npna:=\"$\\frac{2}{3}$\";\n\n%----------- premier niveau\nlabel(TEX a,T[1]);\nlabel.ulft(TEX pa,0.6[S,T[1]]);\n\nlabel(TEX na,T[2]);\nlabel.llft(TEX pna,0.6[S,T[2]]);\n\n%----------- deuxi\u00e8me niveau sup\u00e9rieur\nlabel(TEX a,U[1]);\nlabel.ulft(TEX pa,0.6[T[1],U[1]]);\n\nlabel(TEX na,U[2]);\nlabel.llft(TEX pna,0.6[T[1],U[2]]);\n\n%----------- deuxi\u00e8me niveau inf\u00e9rieur\nlabel(TEX a,U[3]);\nlabel.ulft(TEX pa,0.6[T[2],U[3]]);\n\nlabel(TEX na,U[4]);\nlabel.llft(TEX pna,0.6[T[2],U[4]]);\n\n%----------- troisi\u00e8me niveau part 1\nlabel(TEX a,V[1]);\nlabel.ulft(TEX pa,0.6[U[1],V[1]]);\n\nlabel(TEX na,V[2]);\nlabel.llft(TEX pna,0.6[U[1],V[2]]);\n\n%----------- troisi\u00e8me niveau part 2\nlabel(TEX a,V[3]);\nlabel.ulft(TEX pa,0.6[U[2],V[3]]);\n\nlabel(TEX na,V[4]);\nlabel.llft(TEX pna,0.6[U[2],V[4]]);\n\n%----------- troisi\u00e8me niveau part 3\nlabel(TEX a,V[5]);\nlabel.ulft(TEX pa,0.6[U[3],V[5]]);\n\nlabel(TEX na,V[6]);\nlabel.llft(TEX pna,0.6[U[3],V[6]]);\n\n%----------- troisi\u00e8me niveau part 4\nlabel(TEX a,V[7]);\nlabel.ulft(TEX pa,0.6[U[4],V[7]]);\n\nlabel(TEX na,V[8]);\nlabel.llft(TEX pna,0.6[U[4],V[8]]);\n\n%----------- quatri\u00e8me niveau part 1\nlabel(TEX a,W[1]);\nlabel.ulft(TEX pa,0.6[V[1],W[1]]);\n\nlabel(TEX na,W[2]);\nlabel.llft(TEX pna,0.6[V[1],W[2]]);\n\n%----------- quatri\u00e8me niveau part 2\nlabel(TEX a,W[3]);\nlabel.ulft(TEX pa,0.6[V[2],W[3]]);\n\nlabel(TEX na,W[4]);\nlabel.llft(TEX pna,0.6[V[2],W[4]]);\n\n%----------- quatri\u00e8me niveau part 3\nlabel(TEX a,W[5]);\nlabel.ulft(TEX pa,0.6[V[3],W[5]]);\n\nlabel(TEX na,W[6]);\nlabel.llft(TEX pna,0.6[V[3],W[6]]);\n\n%----------- quatri\u00e8me niveau part 4\nlabel(TEX a,W[7]);\nlabel.ulft(TEX pa,0.6[V[4],W[7]]);\n\nlabel(TEX na,W[8]);\nlabel.llft(TEX pna,0.6[V[4],W[8]]);\n\n%----------- quatri\u00e8me niveau part 5\nlabel(TEX a,W[9]);\nlabel.ulft(TEX pa,0.6[V[5],W[9]]);\n\nlabel(TEX na,W[10]);\nlabel.llft(TEX pna,0.6[V[5],W[10]]);\n\n%----------- quatri\u00e8me niveau part 6\nlabel(TEX a,W[11]);\nlabel.ulft(TEX pa,0.6[V[6],W[11]]);\n\nlabel(TEX na,W[12]);\nlabel.llft(TEX pna,0.6[V[6],W[12]]);\n\n%----------- quatri\u00e8me niveau part 7\nlabel(TEX a,W[13]);\nlabel.ulft(TEX pa,0.6[V[7],W[13]]);\n\nlabel(TEX na,W[14]);\nlabel.llft(TEX pna,0.6[V[7],W[14]]);\n\n%----------- quatri\u00e8me niveau part 8\nlabel(TEX a,W[15]);\nlabel.ulft(TEX pa,0.6[V[8],W[15]]);\n\nlabel(TEX na,W[16]);\nlabel.llft(TEX pna,0.6[V[8],W[16]]);\n\nfin;\n %-----------------------------------------------------------------------\n\n\n%-----------------------------------------------------------------------\nend ;<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Voici son code : input geometriesyr16.mp ; %%%%%%%%%%%%%%%%%% %% %%Ne pas oublier : export TEX=latex %% %%%%%%%%%%%%%%%%% vardef TEX primary s = write \u00ab\u00a0verbatimtex\u00a0\u00bb to \u00ab\u00a0mptextmp.mp\u00a0\u00bb; write \u00ab\u00a0%&amp;latex\u00a0\u00bb to \u00ab\u00a0mptextmp.mp\u00a0\u00bb;&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":2410,"menu_order":6,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-88","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Un arbre de Bernoulli \u00e0 4 niveaux - Maths &amp; 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\/edition-mathematique\/metapost\/arbres-de-probabilite\/un-arbre-de-bernoulli-a-4-niveaux\/\" 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