{"id":56558,"date":"2025-10-20T13:29:55","date_gmt":"2025-10-20T12:29:55","guid":{"rendered":"https:\/\/4.exstyle.fr\/le-blog-photo\/?p=56558"},"modified":"2025-10-20T13:42:33","modified_gmt":"2025-10-20T12:42:33","slug":"fr-d-et-mise-a-lechelle-24","status":"publish","type":"post","link":"https:\/\/4.exstyle.fr\/le-blog-photo\/fr-d-et-mise-a-lechelle-24\/","title":{"rendered":"FR -> D et mise \u00e0 l&rsquo;\u00e9chelle 24"},"content":{"rendered":"<p><!-- ------------------------------------------------------------\nUPdelta \u2014 \u00c9chelle 24 = 1 : un \u00ab mod\u00e8le dans le mod\u00e8le \u00bb pour traquer les cycles\nCollez ce bloc dans WordPress (HTML personnalis\u00e9). MathJax conseill\u00e9.\n------------------------------------------------------------- --><\/p>\n<article class=\"updelta-24\">\n<style>\n    .updelta-24 {font: 16px\/1.55 system-ui, -apple-system, Segoe UI, Roboto, Inter, Arial; color:#0b1222;}\n    .updelta-24 h1, .updelta-24 h2, .updelta-24 h3 {line-height:1.25; margin: 1.2em 0 .4em;}\n    .updelta-24 h1 {font-size: 1.8rem;}\n    .updelta-24 h2 {font-size: 1.35rem;}\n    .updelta-24 h3 {font-size: 1.1rem;}\n    .updelta-24 .note {color:#485572; font-size:.95em;}\n    .updelta-24 .box {background:#f7f9fd; border:1px solid #dfe7fb; border-radius:12px; padding:14px 16px; margin:12px 0;}\n    .updelta-24 .grid {display:grid; gap:10px;}\n    .updelta-24 table {width:100%; border-collapse:collapse; margin:.6em 0;}\n    .updelta-24 th, .updelta-24 td {border-bottom:1px solid #e9eef7; padding:8px 10px; text-align:left;}\n    .updelta-24 code {background:#f1f4fb; border:1px solid #e1e7f6; padding:2px 6px; border-radius:6px;}\n    .updelta-24 .tag {display:inline-block; padding:2px 8px; border-radius:999px; border:1px solid #e1e7f6; background:#f7f9fd; font-size:.85em; color:#465478; margin-right:6px;}\n    .updelta-24 .ok {color:#136f36; font-weight:600;}\n    .updelta-24 .warn {color:#b45309; font-weight:600;}\n    .updelta-24 .bad {color:#9b1c1c; font-weight:600;}\n    .updelta-24 .hr {height:1px; background:linear-gradient(90deg,#e9eef7,transparent); margin:18px 0;}\n  <\/style>\n<h1>UPdelta \u2014 \u00c9chelle <em>24 = 1<\/em> : un \u00ab mod\u00e8le dans le mod\u00e8le \u00bb pour comprendre l\u2019anti-cycle<\/h1>\n<p class=\"note\">Id\u00e9e cl\u00e9 : en divisant toutes les quantit\u00e9s par 24, chaque rang\u00e9e (distance <em>D<\/em>) devient le m\u00eame gabarit<br \/>\n  g\u00e9om\u00e9trique \u2014 un \u00ab ruban \u00bb constant \u2014 et toute la dynamique int\u00e9ress\u00e9e par les cycles se concentre alors sur la seule<br \/>\n  \u00e9volution de <em>D<\/em> et des valuations 2-adiques.<\/p>\n<div class=\"hr\"><\/div>\n<h2>1) Cadre UPdelta (rappels compacts)<\/h2>\n<p>Pour une distance enti\u00e8re <span>\\(D\\)<\/span>, on d\u00e9finit les cinq points de la rang\u00e9e :<\/p>\n<p>\n    <span>\\(r^-(D)=2D-1,\\quad Y^-(D)=3D-1,\\quad \\mathrm{med}(D)=3D,\\quad Y^+(D)=3D+1,\\quad r^+(D)=4D+1.\\)<\/span>\n  <\/p>\n<ul>\n<li>\u00c9tiquettes modulo 3 : <span>\\(Y^- \\equiv 2 \\pmod 3\\)<\/span>, <span>\\(Y^+ \\equiv 1 \\pmod 3\\)<\/span> pour tout <span>\\(D\\)<\/span>.<\/li>\n<li>Divisions (valuations) n\u00e9cessaires pour le lien <em>odd-only<\/em> :<br \/>\n      <span>\\(t_-(D)=1+\\nu_2(3D-1),\\quad t_+(D)=2+\\nu_2(3D+1).\\)<\/span><br \/>\n      <br \/><span class=\"tag\">D pair<\/span> <span class=\"ok\">exactement<\/span> \\(t_-{=}1,\\ t_+{=}2\\).<br \/>\n      <br \/><span class=\"tag\">D impair<\/span> on \u00ab paie \u00bb des divisions suppl\u00e9mentaires : \\(t_-{\\ge}2,\\ t_+{\\ge}3\\).\n    <\/li>\n<\/ul>\n<div class=\"box\">\n    <strong>Lemme de pli (normalisation locale).<\/strong><br \/>\n    <br \/>Pour tout \\(D\\), on a l\u2019identit\u00e9<br \/>\n    <span>\\[<br \/>\n      \\frac{3\\,r_+(D)-1}{2} \\;=\\; r_-(3D+1)<br \/>\n    \\]<\/span><br \/>\n    (donc tout segment \u00ab \\(+\\) avec \\(D\\) impair \u00bb se <em>plie<\/em> en un segment \u00ab \\(-\\) \u00bb \u00e0 la distance \\(3D{+}1\\)).\n  <\/div>\n<div class=\"hr\"><\/div>\n<h2>2) \u00c9chelle <em>24 = 1<\/em> : un gabarit g\u00e9om\u00e9trique universel<\/h2>\n<p>On travaille avec la quantit\u00e9 mise \u00e0 l\u2019\u00e9chelle \\(\\tilde x = x\/24\\). Alors :<\/p>\n<table>\n<thead>\n<tr>\n<th>Point<\/th>\n<th>Formule (entier)<\/th>\n<th>Position \u00e0 l\u2019\u00e9chelle<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\\(Y^\\pm\\)<\/td>\n<td>\\(3D \\pm 1\\)<\/td>\n<td>\\(\\displaystyle \\tilde Y^\\pm = \\frac{D}{8} \\pm \\frac{1}{24}\\)<\/td>\n<\/tr>\n<tr>\n<td>centre<\/td>\n<td>\\(3D\\)<\/td>\n<td>\\(\\displaystyle \\widetilde{\\mathrm{med}} = \\frac{D}{8}\\)<\/td>\n<\/tr>\n<tr>\n<td>\\(r^\\pm\\)<\/td>\n<td>\\(2D-1\\), \\(4D+1\\)<\/td>\n<td>\\(\\displaystyle \\tilde r^\\pm = \\frac{D}{6} \\pm \\frac{1}{24}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Cons\u00e9quences \u00ab micro \u00bb (ind\u00e9pendantes de \\(D\\)) :<\/p>\n<ul>\n<li><strong>Ruban constant<\/strong> : \\(\\tilde Y^+ &#8211; \\tilde Y^- = \\frac{1}{12}\\).<\/li>\n<li><strong>Centre commun<\/strong> : \\( \\widetilde{\\mathrm{med}} = D\/8\\).<\/li>\n<li><strong>Bras sym\u00e9triques<\/strong> : \\( \\tilde Y^- &#8211; \\tilde r^- = \\tilde r^+ &#8211; \\tilde Y^+ = \\frac{D}{24}\\).<\/li>\n<\/ul>\n<p class=\"note\">Autrement dit, le \u00ab mod\u00e8le local \u00bb d\u2019une ligne est identique pour toutes les distances : seule l\u2019<em>\u00e9chelle macro<\/em> (via \\(D\\)) s\u2019\u00e9tire.<\/p>\n<div class=\"hr\"><\/div>\n<h2>3) \u00ab Mod\u00e8le dans le mod\u00e8le \u00bb et r\u00e9duction du catalogue de cycles<\/h2>\n<h3>3.1 Forme normale des trajectoires<\/h3>\n<p>Gr\u00e2ce au lemme de pli, on peut supposer sans perte que toute trajectoire est \u00e9crite sous la forme normale :<\/p>\n<ul>\n<li>des pas \\(Y^-\\) pour n\u2019importe quel \\(D\\) ;<\/li>\n<li>des pas \\(Y^+\\) uniquement avec \\(D\\) <em>pair<\/em> (exactement 2 divisions).<\/li>\n<\/ul>\n<p>Au niveau \u00ab micro \u00bb, toutes les \u00e9tapes sont le m\u00eame ruban (largeur \\(1\/12\\)). Au niveau \u00ab macro \u00bb, le jeu se r\u00e9duit \u00e0 l\u2019\u00e9volution de \\(D\\) et aux surplus de division \\(e_\\pm=\\nu_2(3D\\pm1)\\).<\/p>\n<h3>3.2 Moyenne des divisions vs \\(\\log_2 3\\) (biais contractant)<\/h3>\n<p>Sur une boucle ferm\u00e9e (odd-only), la moyenne des divisions doit satisfaire <span>\\(\\bar t = \\log_2 3\\)<\/span> (sinon la taille d\u00e9rive). Or :<\/p>\n<ul>\n<li>\u00e0 \\(D\\) pair, la base minimale est \\(t_-{=}1\\), \\(t_+{=}2\\) ;<\/li>\n<li>\u00e0 \\(D\\) impair, on ajoute des divisions ( \\(e_\\pm \\ge 1\\) \u00ab en moyenne \u00bb sur de longues marches ).<\/li>\n<\/ul>\n<p>Conclusion : <em>par d\u00e9faut<\/em> \\(\\bar t > \\log_2 3\\) \u2014 la trajectoire contracte la taille \u2014, et il faudrait une corr\u00e9lation fine des \\(D\\) et des \\(e_\\pm\\) pour maintenir exactement \\(\\bar t=\\log_2 3\\). C\u2019est un frein structurel aux cycles non triviaux.<\/p>\n<h3>3.3 Monotonicit\u00e9s en \\(D\\) (ciseau)<\/h3>\n<p>Le pli remplace chaque \u00ab \\(+\\) impair \u00bb par \\(-\\) \u00e0 <span>\\(D&rsquo; = 3D + 1\\)<\/span> (strictement croissant). Revenir au \\(D\\) initial n\u00e9cessiterait des \u00e9tapes qui <em>abaissent<\/em> fortement \\(D\\).<br \/>\n  Mais ces \u00e9tapes co\u00efncident avec des valuations plus grandes, ce qui augmente encore la contraction (cf. \u00a73.2). Le cycle se heurte donc \u00e0 un <strong>ciseau<\/strong> : ou bien \\(D\\) ne se referme pas, ou bien la taille d\u00e9cro\u00eet.<\/p>\n<div class=\"hr\"><\/div>\n<h2>4) Guide de lecture du tableau (version pratique)<\/h2>\n<ul>\n<li>\u00c9tiquette <span class=\"tag\">mod 3<\/span> : <strong>toujours<\/strong> \\(Y^-\\equiv 2\\), \\(Y^+\\equiv 1\\).<\/li>\n<li>Compter les divisions \\(t_\\pm\\) :<br \/>\n      <span>\\(t_-(D)=1+\\nu_2(3D-1)\\)<\/span>,<br \/>\n      <span>\\(t_+(D)=2+\\nu_2(3D+1)\\)<\/span>.<br \/>\n      <br \/><span class=\"tag\">D pair<\/span> <span class=\"ok\">propre<\/span> : (1,2). <span class=\"tag\">D impair<\/span> <span class=\"warn\">surplus<\/span>.\n    <\/li>\n<li>Mise \u00e0 l\u2019\u00e9chelle <span class=\"tag\">24 = 1<\/span> : afficher les 5 points aux positions \\(\\frac{D}{8}\\pm\\frac{1}{24}\\) (liens) et \\(\\frac{D}{6}\\pm\\frac{1}{24}\\) (racines). Le ruban \\(Y^-{\\leftrightarrow}Y^+\\) est d\u2019embl\u00e9e visible et constant.<\/li>\n<\/ul>\n<div class=\"box\">\n    <strong>Attention<\/strong> : l\u2019\u00e9chelle \\(x \\mapsto x\/24\\) est une <em>normalisation visuelle\/m\u00e9trique<\/em>.<br \/>\n    On ne fait pas de calculs \u00ab mod 3 \u00bb <em>sur les valeurs d\u00e9j\u00e0 divis\u00e9es par 24<\/em> (puisque \\(24\\equiv 0 \\pmod 3\\)).<br \/>\n    Les r\u00e9sidus mod 3 se lisent sur les entiers d\u2019origine.\n  <\/div>\n<div class=\"hr\"><\/div>\n<h2>5) Deux exemples \u00e9clair<\/h2>\n<h3>Ex. A \u2014 \\(D=10\\) (pair, cas \u00ab propre \u00bb)<\/h3>\n<p>\\(r^-=19,\\ Y^-=29,\\ \\mathrm{med}=30,\\ Y^+=31,\\ r^+=41\\).<\/p>\n<ul>\n<li>mod 3 : \\(Y^- \\equiv 2\\), \\(Y^+ \\equiv 1\\).<\/li>\n<li>divisions : \\(t_-{=}1,\\ t_+{=}2\\).<\/li>\n<li>\u00e9chelle 24 = 1 : \\(\\tilde Y^\\pm = 10\/8 \\pm 1\/24\\), largeur \\(=1\/12\\); bras \\(= D\/24 = 10\/24\\).<\/li>\n<\/ul>\n<h3>Ex. B \u2014 \\(D=9\\) (impair, pli puis normalisation)<\/h3>\n<p>\\(r^-=17,\\ Y^-=26,\\ \\mathrm{med}=27,\\ Y^+=28,\\ r^+=37\\).<\/p>\n<ul>\n<li>divisions : \\(t_-= 1+\\nu_2(26)=2\\), \\(t_+=2+\\nu_2(28)=4\\) (surplus).<\/li>\n<li>Pli : \\(\\displaystyle \\frac{3r_+(9)-1}{2} = r_-(3\\cdot 9 + 1) = r_-(28) = 55\\) (on passe dans la branche \u00ab \u2212 \u00bb \u00e0 \\(D&rsquo;=28\\)).<\/li>\n<li>\u00c9chelle 24 = 1 : m\u00eame ruban (largeur \\(1\/12\\)), mais centre recul\u00e9 \\(D&rsquo;\/8=3.5\\) au lieu de \\(9\/8\\).<\/li>\n<\/ul>\n<div class=\"hr\"><\/div>\n<h2>6) Mise en \u0153uvre (check-list)<\/h2>\n<ol>\n<li><strong>Normaliser<\/strong> : remplacer chaque pas \u00ab \\(+\\) avec \\(D\\) impair \u00bb par \u00ab \\(-\\) avec \\(D&rsquo; = 3D+1\\) \u00bb.<\/li>\n<li><strong>Suivre \\(D\\)<\/strong> : travailler sur l\u2019automate des r\u00e9sidus de \\(D\\) (et l\u2019\u00e9tiquette de branche) plut\u00f4t que sur les valeurs.<\/li>\n<li><strong>Poids<\/strong> : utiliser \\(k = t &#8211; \\log_2 3\\) par transition. Sur un cycle, \\(\\sum k = 0\\) est n\u00e9cessaire ; en pratique on observe \\(\\sum k > 0\\) (biais contractant).<\/li>\n<li><strong>Visualiser<\/strong> : superposer plusieurs rang\u00e9es \u00e0 l\u2019\u00e9chelle 24 = 1. Un cycle exigerait de recoller exactement le m\u00eame ruban et la m\u00eame \u00e9chelle \\(D\/8\\) apr\u00e8s un nombre fini d\u2019\u00e9tapes \u2014 excellent diagnostic visuel.<\/li>\n<\/ol>\n<div class=\"hr\"><\/div>\n<h2>7) TL;DR<\/h2>\n<ul>\n<li>L\u2019\u00e9chelle <strong>24 = 1<\/strong> rend <em>identique<\/em> la micro-g\u00e9om\u00e9trie de chaque rang\u00e9e : ruban \\(Y^-{\\leftrightarrow}Y^+\\) de largeur fixe \\(1\/12\\), bras sym\u00e9triques.<\/li>\n<li>Le <strong>lemme de pli<\/strong> envoie \u00ab \\(+\\) impair \u00bb vers \u00ab \u2212 \u00bb \u00e0 \\(D&rsquo; = 3D+1\\) : on obtient une <strong>forme normale<\/strong> de toute trajectoire.<\/li>\n<li>Au macro-niveau, le probl\u00e8me des cycles se r\u00e9duit \u00e0 la suite des \\(D\\) et aux valuations \\(\\nu_2(3D\\pm 1)\\) ; la moyenne des divisions d\u00e9passe naturellement \\(\\log_2 3\\), ce qui <strong>contrarie<\/strong> les cycles non triviaux.<\/li>\n<\/ul>\n<p class=\"note\">Si tu veux, je peux ajouter \u00e0 la fin de l\u2019article un petit script SVG \u00ab light \u00bb (sans d\u00e9pendances) pour afficher automatiquement la ligne \\(D\\) et ses positions \u00e0 l\u2019\u00e9chelle \u2014 pratique pour des lecteurs non sp\u00e9cialistes.<\/p>\n<\/article>\n<p><!-- UPdelta \u2014 Bloc SVG \"light\" (WordPress-ready)\n     Collez ce bloc dans un Gutenberg \"HTML personnalis\u00e9\". Aucun framework requis. --><\/p>\n<div class=\"updelta-svg\" style=\"--bg:#0a0f22;--fg:#1f2a44;--txt:#0b1222;--grid:#dfe7fb;--tick:#c9d6f5;--root:#2563eb;--minus:#d97706;--plus:#10b981;--med:#94a3b8;--card:#f7f9fd;--line:#e9eef7;--muted:#485572; font:16px\/1.45 system-ui,Segoe UI,Roboto,Inter,Arial; color:var(--txt);\">\n<style>\n    .updelta-svg .card{max-width:900px;margin:10px auto;padding:14px;border:1px solid var(--line);border-radius:12px;background:var(--card)}\n    .updelta-svg .controls{display:flex;gap:10px;align-items:center;flex-wrap:wrap;margin-bottom:8px}\n    .updelta-svg input[type=number]{width:120px;padding:6px;border:1px solid var(--line);border-radius:8px;background:#fff}\n    .updelta-svg input[type=range]{width:360px}\n    .updelta-svg .badge{display:inline-block;padding:3px 8px;border:1px solid var(--line);border-radius:999px;background:#fff;color:var(--muted);font-size:.85em;margin-left:6px}\n    .updelta-svg svg{width:100%;height:180px;border:1px solid var(--line);border-radius:10px;background:#fff}\n    .updelta-svg .axis{stroke:var(--fg);stroke-width:1.5}\n    .updelta-svg .tick{stroke:var(--tick);stroke-width:1}\n    .updelta-svg .label{font-size:12px;fill:var(--muted)}\n    .updelta-svg .pt{stroke:#fff;stroke-width:1.5}\n    .updelta-svg .pt.root{fill:var(--root)}\n    .updelta-svg .pt.minus{fill:var(--minus)}\n    .updelta-svg .pt.plus{fill:var(--plus)}\n    .updelta-svg .pt.med{fill:var(--med)}\n    .updelta-svg table{width:100%;border-collapse:collapse;margin-top:10px}\n    .updelta-svg th,.updelta-svg td{padding:8px 10px;border-bottom:1px solid var(--line);text-align:left}\n    .updelta-svg th{color:var(--muted);font-weight:600;font-size:13px}\n    .updelta-svg code{background:#fff;border:1px solid var(--line);padding:1px 6px;border-radius:6px}\n  <\/style>\n<div class=\"card\">\n<div class=\"controls\">\n      <strong>D :<\/strong><br \/>\n      <input id=\"D_range\" type=\"range\" min=\"1\" max=\"200\" value=\"9\" \/><br \/>\n      <input id=\"D_num\" type=\"number\" min=\"1\" step=\"1\" value=\"9\" \/><br \/>\n      <span class=\"badge\" id=\"parite\">D impair<\/span><br \/>\n      <span class=\"badge\" id=\"tvals\">t\u2212=? \u00b7 t+=?<\/span>\n    <\/div>\n<p>    <svg id=\"updelta_svg\" viewBox=\"0 0 740 180\" role=\"img\" aria-label=\"UPdelta \u2014 \u00e9chelle 24=1 (SVG light)\"><\/svg><\/p>\n<table>\n<thead>\n<tr>\n<th>Point<\/th>\n<th>Valeur<\/th>\n<th>\u00c9chelle 24=1<\/th>\n<th>mod 3<\/th>\n<th>Divisions t<\/th>\n<\/tr>\n<\/thead>\n<tbody id=\"rows\"><\/tbody>\n<\/table><\/div>\n<p>  <script>(function(){\n    const svg = document.getElementById('updelta_svg');\n    const Dnum = document.getElementById('D_num');\n    const Drng = document.getElementById('D_range');\n    const rows = document.getElementById('rows');\n    const parite = document.getElementById('parite');\n    const tvals = document.getElementById('tvals');\n    const NS = 'http:\/\/www.w3.org\/2000\/svg';<\/p>\n<p>    function v2(n){let c=0;while(n%2===0){n\/=2;c++;}return c;}\n    function gcd(a,b){a=Math.abs(a);b=Math.abs(b);while(b){let t=b;b=a%b;a=t;}return a||1;}\n    function fracOver24(n){const d=24;const g=gcd(n,d);const nn=n\/g,dd=d\/g;return dd===1?String(nn):nn+'\/'+dd;}\n    function m3(x){let r=x%3;return r<0?r+3:r;}\n\n    function line(x1,y1,x2,y2,cls){const e=document.createElementNS(NS,'line');e.setAttribute('x1',x1);e.setAttribute('y1',y1);e.setAttribute('x2',x2);e.setAttribute('y2',y2);e.setAttribute('class',cls);svg.appendChild(e);}    \n    function circle(x,y,r,cls){const e=document.createElementNS(NS,'circle');e.setAttribute('cx',x);e.setAttribute('cy',y);e.setAttribute('r',r);e.setAttribute('class','pt '+cls);svg.appendChild(e);}    \n    function text(x,y,str,cls){const e=document.createElementNS(NS,'text');e.setAttribute('x',x);e.setAttribute('y',y);e.setAttribute('class',cls||'label');e.textContent=str;svg.appendChild(e);}    \n\n    function draw(D){\n      const r_ = 2*D-1, Ym=3*D-1, Md=3*D, Yp=3*D+1, rp=4*D+1;\n      const tminus = 1+v2(3*D-1), tplus=2+v2(3*D+1);\n      parite.textContent = (D%2===0? 'D pair':'D impair');\n      tvals.innerHTML = 't\u2212='+tminus+' \u00b7 t+='+tplus;\n\n      \/\/ Positions en unit\u00e9s 24=1 => extr\u00eames \u00e0 \u00b1(D+1)\/24 autour du centre\n      const cx=370, y=100, halfPx=300; \/\/ centre et demi-largeur cibles\n      const unitsHalf = (D+1)\/24; \/\/ r\u00b1 = centre \u00b1 unitsHalf\n      const pxPerUnit = halfPx \/ Math.max(unitsHalf, 1\/24); \/\/ \u00e9vite \/0\n      const pos = {\n        rMinus: cx - unitsHalf*pxPerUnit,\n        Yminus: cx - (1\/24)*pxPerUnit,\n        Med:    cx,\n        Yplus:  cx + (1\/24)*pxPerUnit,\n        rPlus:  cx + unitsHalf*pxPerUnit\n      };<\/p>\n<p>      \/\/ Clear & draw\n      svg.innerHTML='';\n      line(40,y,700,y,'axis');\n      line(pos.Med,y-8,pos.Med,y+8,'tick');\n      line(pos.Yminus,y-6,pos.Yminus,y+6,'tick');\n      line(pos.Yplus,y-6,pos.Yplus,y+6,'tick');\n      line(pos.rMinus,y-4,pos.rMinus,y+4,'tick');\n      line(pos.rPlus,y-4,pos.rPlus,y+4,'tick');\n      text(pos.Med-24,y-12,'centre D\/8','label');\n      text(pos.Yminus-14,y+22,'\u22121\/24','label');\n      text(pos.Yplus-14,y+22,'+1\/24','label');<\/p>\n<p>      circle(pos.rMinus,y,6,'root');\n      circle(pos.Yminus,y,6,'minus');\n      circle(pos.Med,y,5,'med');\n      circle(pos.Yplus,y,6,'plus');\n      circle(pos.rPlus,y,6,'root');<\/p>\n<p>      text(pos.rMinus-8,y-12,'r\u2212');\n      text(pos.Yminus-8,y-12,'Y\u2212');\n      text(pos.Med-10,y-12,'med');\n      text(pos.Yplus-8,y-12,'Y+');\n      text(pos.rPlus-8,y-12,'r+');<\/p>\n<p>      \/\/ Table\n      const data=[\n        {n:'r\u2212', val:r_,  sc:fracOver24(r_), mod:m3(r_), t:'\u2014'},\n        {n:'Y\u2212', val:Ym,  sc:fracOver24(Ym), mod:m3(Ym), t:tminus+' (\u22612)'},\n        {n:'med',val:Md,  sc:fracOver24(Md), mod:m3(Md), t:'\u2014'},\n        {n:'Y+', val:Yp,  sc:fracOver24(Yp), mod:m3(Yp), t:tplus+' (\u22611)'},\n        {n:'r+', val:rp,  sc:fracOver24(rp), mod:m3(rp), t:'\u2014'}\n      ];\n      rows.innerHTML = data.map(r=>`<\/p>\n<tr>\n<td><strong>${r.n}<\/strong><\/td>\n<td><code>${r.val}<\/code><\/td>\n<td><code>${r.sc}<\/code><\/td>\n<td>${r.mod}<\/td>\n<td>${r.t}<\/td>\n<\/tr>\n<p>`).join('');\n    }<\/p>\n<p>    function syncR(){ Dnum.value = Drng.value; draw(parseInt(Drng.value,10)); }\n    function syncN(){ const v=Math.max(1, parseInt(Dnum.value||'1',10)); Drng.value=v; draw(v); }<\/p>\n<p>    Drng.addEventListener('input', syncR);\n    Dnum.addEventListener('input', syncN);\n    draw(parseInt(Drng.value,10));\n  })();<\/script>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>UPdelta \u2014 \u00c9chelle 24 = 1 : un \u00ab mod\u00e8le dans le mod\u00e8le \u00bb pour comprendre l\u2019anti-cycle Id\u00e9e cl\u00e9 : en divisant toutes les quantit\u00e9s par 24, chaque rang\u00e9e (distance D) devient le m\u00eame gabarit g\u00e9om\u00e9trique \u2014 un \u00ab ruban \u00bb constant \u2014 et toute la dynamique int\u00e9ress\u00e9e par les cycles se concentre alors sur [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"saved_in_kubio":false,"footnotes":""},"categories":[1],"tags":[436],"class_list":["post-56558","post","type-post","status-publish","format-standard","hentry","category-non-classe","tag-math"],"_links":{"self":[{"href":"https:\/\/4.exstyle.fr\/le-blog-photo\/wp-json\/wp\/v2\/posts\/56558","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/4.exstyle.fr\/le-blog-photo\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/4.exstyle.fr\/le-blog-photo\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/4.exstyle.fr\/le-blog-photo\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/4.exstyle.fr\/le-blog-photo\/wp-json\/wp\/v2\/comments?post=56558"}],"version-history":[{"count":3,"href":"https:\/\/4.exstyle.fr\/le-blog-photo\/wp-json\/wp\/v2\/posts\/56558\/revisions"}],"predecessor-version":[{"id":56561,"href":"https:\/\/4.exstyle.fr\/le-blog-photo\/wp-json\/wp\/v2\/posts\/56558\/revisions\/56561"}],"wp:attachment":[{"href":"https:\/\/4.exstyle.fr\/le-blog-photo\/wp-json\/wp\/v2\/media?parent=56558"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/4.exstyle.fr\/le-blog-photo\/wp-json\/wp\/v2\/categories?post=56558"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/4.exstyle.fr\/le-blog-photo\/wp-json\/wp\/v2\/tags?post=56558"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}