{"id":553,"date":"2010-02-28T01:44:40","date_gmt":"2010-02-28T00:44:40","guid":{"rendered":"http:\/\/www.hyperbate.com\/whatever\/?p=553"},"modified":"2010-02-28T01:44:40","modified_gmt":"2010-02-28T00:44:40","slug":"maths-2-dessiner-la-fleur-du-tournesol","status":"publish","type":"post","link":"https:\/\/hyperbate.fr\/whatever\/2010\/02\/28\/maths-2-dessiner-la-fleur-du-tournesol\/","title":{"rendered":"Maths (2) dessiner la fleur du tournesol"},"content":{"rendered":"

En utilisant l’angle dit \u00ab\u00a0angle d’or\u00a0\u00bb (environ 137.5 degr\u00e9s ou\u00a02.3999 radians), on peut dessiner une spirale de Fermat selon un mod\u00e8le invent\u00e9 par H. Vogel, \u00e0 la mani\u00e8re des \u00e9tamines des tournesols, des \u00e9cailles des pommes de pin ou de diverses organisations naturelles.<\/span><\/span><\/p>\n

\"\"<\/p>\n

rayon = c * \u221an
\n\u03b8 = n * \u03c6<\/strong><\/p>\n

o\u00f9 c<\/strong> est une constante (si on change c<\/strong>, l’espacement qui s\u00e9pare les \u00e9l\u00e9ments de la spirale change), \u03c6<\/strong> est l’angle d’or\u00a0et n<\/strong> d\u00e9nombre chaque \u00e9l\u00e9ment de la spirale. Dans l’exemple qui suit (langage processing), n prend les valeurs successives de n<\/strong> sont 0, 1, 2, 3, 4, et ainsi de suite jusqu’\u00e0 1000 ; Le constante c<\/strong> a la valeur de 10 :<\/p>\n

float angledor=radians(137.5);<\/code>
\n <\/code>
\nvoid setup(){
\nsize(400,400);background(255);strokeWeight(7);smooth();
\nfloat x=200;float y=200;float constante=10;
\nfor(int a=0;a<1000;a++){
\nfloat r=constante*sqrt(a);
\nx+=cos(angledor*a)*r;y+=sin(angledor*a)*r;
\npoint(x,y);
\n}
\n} <\/code><\/p>\n

On pourrait \u00eatre encore plus pr\u00e9cis en calculant l’angle d’or \u00e0 la vol\u00e9e. Sa valeur est \u00e9gale \u00e0 (2*\u03a0)\/\u03c6+1<\/strong>. La valeur de \u03c6<\/strong>, le nombre d’or, est (1+\u221a5)\/2<\/strong>.
\n\u00c0 la place de float angledor=radians(137.5);<\/em> on pourra donc \u00e9crire :
\n<\/code><\/p>\n

<\/code><\/p>\n

<\/p>\n

float nombredor = (1+sqrt(5))\/2;<\/div>\n
float angledor = TWO_PI\/(1+nombredor);<\/div>\n

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

En utilisant l’angle dit \u00ab\u00a0angle d’or\u00a0\u00bb (environ 137.5 degr\u00e9s ou\u00a02.3999 radians), on peut dessiner une spirale de Fermat selon un mod\u00e8le invent\u00e9 par H. Vogel, \u00e0 la mani\u00e8re des \u00e9tamines des tournesols, des \u00e9cailles des pommes de pin ou de diverses organisations naturelles. rayon = c * \u221an \u03b8 = n * \u03c6 o\u00f9 c … Continuer la lecture de Maths (2) dessiner la fleur du tournesol<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,34],"tags":[],"class_list":["post-553","post","type-post","status-publish","format-standard","hentry","category-formes","category-processing"],"_links":{"self":[{"href":"https:\/\/hyperbate.fr\/whatever\/wp-json\/wp\/v2\/posts\/553","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hyperbate.fr\/whatever\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hyperbate.fr\/whatever\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hyperbate.fr\/whatever\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/hyperbate.fr\/whatever\/wp-json\/wp\/v2\/comments?post=553"}],"version-history":[{"count":0,"href":"https:\/\/hyperbate.fr\/whatever\/wp-json\/wp\/v2\/posts\/553\/revisions"}],"wp:attachment":[{"href":"https:\/\/hyperbate.fr\/whatever\/wp-json\/wp\/v2\/media?parent=553"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hyperbate.fr\/whatever\/wp-json\/wp\/v2\/categories?post=553"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hyperbate.fr\/whatever\/wp-json\/wp\/v2\/tags?post=553"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}