Le nombre \u03c0 : 3,14159… mais jusqu’o\u00f9 ? \u2014 MathsVivantes<\/title>\n<link href=\"https:\/\/fonts.googleapis.com\/css2?family=Playfair+Display:ital,wght@0,400;0,700;1,400&family=Source+Serif+4:ital,wght@0,300;0,400;0,600;1,300;1,400&display=swap\" rel=\"stylesheet\">\n<style>\n :root {\n --noir: #0f0e0b;\n --creme: #f5f0e8;\n --cobalt: #0a1a4a;\n --cobalt-clair: #2a4aaa;\n --cobalt-pale: #eef0ff;\n --or: #c8a010;\n --or-clair: #f0d060;\n --rouge: #b03a2e;\n --gris: #6b6560;\n --gris-clair: #e8e2d8;\n }\n\n * { margin: 0; padding: 0; box-sizing: border-box; }\n\n body {\n background-color: var(--creme);\n color: var(--noir);\n font-family: 'Source Serif 4', Georgia, serif;\n font-weight: 300;\n line-height: 1.8;\n }\n\n .hero {\n background: #04091a;\n color: var(--creme);\n padding: 80px 40px 70px;\n position: relative;\n overflow: hidden;\n }\n .hero::before {\n content: \"\u03c0 \u03c0 \u03c0 \u03c0\";\n position: absolute;\n top: 10px; right: 30px;\n font-size: 8rem;\n opacity: 0.04;\n font-family: 'Playfair Display', serif;\n letter-spacing: 0.2em;\n }\n .hero-inner { max-width: 760px; margin: 0 auto; }\n\n .article-rubrique {\n display: inline-block;\n background: var(--cobalt-clair);\n color: white;\n font-size: 0.7rem;\n letter-spacing: 0.18em;\n text-transform: uppercase;\n padding: 4px 12px;\n margin-bottom: 24px;\n font-weight: 600;\n }\n\n .hero h1 {\n font-family: 'Playfair Display', serif;\n font-size: clamp(2rem, 5vw, 3.4rem);\n line-height: 1.2;\n margin-bottom: 24px;\n font-weight: 700;\n }\n .hero h1 em { color: var(--or-clair); font-style: italic; }\n\n .hero-intro {\n font-size: 1.15rem;\n opacity: 0.75;\n max-width: 600px;\n font-style: italic;\n border-left: 3px solid var(--cobalt-clair);\n padding-left: 20px;\n margin-bottom: 32px;\n }\n .meta { font-size: 0.8rem; opacity: 0.45; letter-spacing: 0.08em; text-transform: uppercase; }\n\n .article-body { max-width: 760px; margin: 0 auto; padding: 60px 40px 80px; }\n .article-body p { font-size: 1.05rem; margin-bottom: 1.6em; color: #2a2520; }\n\n h2 {\n font-family: 'Playfair Display', serif;\n font-size: 1.6rem;\n margin: 2.5em 0 0.8em;\n color: var(--noir);\n font-weight: 700;\n }\n h2::before { content: \"\u00a7 \"; color: var(--cobalt-clair); }\n\n h3 {\n font-family: 'Playfair Display', serif;\n font-size: 1.15rem;\n font-weight: 700;\n margin: 1.8em 0 0.6em;\n color: var(--cobalt);\n }\n\n .encadre {\n border: 1.5px solid var(--cobalt-clair);\n background: white;\n padding: 24px 28px;\n margin: 2em 0;\n position: relative;\n }\n .encadre-titre {\n position: absolute;\n top: -12px; left: 20px;\n background: white;\n padding: 0 8px;\n font-size: 0.72rem;\n letter-spacing: 0.15em;\n text-transform: uppercase;\n color: var(--cobalt-clair);\n font-weight: 600;\n }\n .encadre p { margin-bottom: 0.8em; font-size: 0.98rem; }\n .encadre p:last-child { margin-bottom: 0; }\n\n .encadre-histoire {\n background: #04091a;\n color: var(--creme);\n border: none;\n padding: 32px 36px;\n margin: 2.5em 0;\n }\n .encadre-histoire .encadre-titre { background: #04091a; color: var(--or-clair); }\n .encadre-histoire p { color: rgba(245,240,232,0.85); }\n\n .definition {\n background: var(--cobalt-pale);\n border-left: 4px solid var(--cobalt-clair);\n padding: 20px 24px;\n margin: 1.8em 0;\n font-style: italic;\n }\n .definition strong { font-style: normal; color: var(--cobalt); font-family: 'Playfair Display', serif; }\n\n \/* DIGITS DE PI *\/\n .pi-digits {\n background: #04091a;\n color: var(--creme);\n padding: 24px 28px;\n margin: 2em 0;\n font-family: 'Courier New', monospace;\n font-size: 0.95rem;\n line-height: 2;\n letter-spacing: 0.05em;\n overflow-x: auto;\n }\n .pi-digits .pi-sym {\n color: var(--or-clair);\n font-family: 'Playfair Display', serif;\n font-size: 1.4rem;\n font-weight: 700;\n }\n .pi-digits .d1 { color: #80b0ff; }\n .pi-digits .d2 { color: #80ffb0; }\n .pi-digits .d3 { color: #ffb080; }\n .pi-digits .d4 { color: #ff8080; }\n\n .schema-container {\n background: white;\n border: 1.5px solid var(--cobalt-clair);\n padding: 24px;\n margin: 2em 0;\n text-align: center;\n }\n .schema-titre {\n font-size: 0.72rem;\n letter-spacing: 0.15em;\n text-transform: uppercase;\n color: var(--cobalt-clair);\n font-weight: 600;\n margin-bottom: 16px;\n }\n\n .formule {\n text-align: center;\n font-size: 1.3rem;\n font-family: 'Playfair Display', serif;\n margin: 1.5em 0;\n color: var(--noir);\n padding: 16px;\n background: white;\n border-top: 2px solid var(--cobalt-clair);\n border-bottom: 2px solid var(--cobalt-clair);\n }\n\n .etape {\n background: white;\n border-left: 3px solid var(--cobalt-clair);\n padding: 12px 20px;\n margin: 0.6em 0;\n font-size: 0.97rem;\n }\n .etape-numero { font-family: 'Playfair Display', serif; font-weight: 700; color: var(--cobalt-clair); margin-right: 8px; }\n\n \/* TIMELINE *\/\n .timeline { margin: 2em 0; }\n .timeline-item {\n display: flex;\n gap: 20px;\n margin-bottom: 20px;\n align-items: flex-start;\n }\n .timeline-date {\n min-width: 110px;\n text-align: right;\n font-family: 'Playfair Display', serif;\n font-size: 0.9rem;\n font-weight: 700;\n color: var(--cobalt-clair);\n padding-top: 2px;\n }\n .timeline-dot {\n min-width: 12px;\n height: 12px;\n background: var(--cobalt-clair);\n border-radius: 50%;\n margin-top: 5px;\n flex-shrink: 0;\n }\n .timeline-content { font-size: 0.97rem; color: #2a2520; }\n .timeline-content strong { color: var(--cobalt); }\n\n .table-container { overflow-x: auto; margin: 2em 0; }\n table { width: 100%; border-collapse: collapse; background: white; font-size: 0.95rem; }\n th { background: var(--cobalt); color: white; padding: 12px 16px; text-align: center; font-family: 'Playfair Display', serif; font-weight: 400; }\n td { padding: 10px 16px; text-align: center; border-bottom: 1px solid var(--gris-clair); color: #2a2520; }\n tr:last-child td { border-bottom: none; }\n tr:nth-child(even) td { background: #f0f2ff; }\n\n .code-block {\n background: #04091a;\n color: #c0d0f0;\n padding: 24px 28px;\n margin: 2em 0;\n font-family: 'Courier New', monospace;\n font-size: 0.88rem;\n line-height: 1.7;\n overflow-x: auto;\n position: relative;\n }\n .code-label { position: absolute; top: 8px; right: 12px; font-size: 0.65rem; letter-spacing: 0.15em; text-transform: uppercase; color: var(--cobalt-clair); font-family: 'Source Serif 4', serif; }\n .code-comment { color: #4a5a8a; }\n .code-keyword { color: #80a0e0; }\n .code-string { color: var(--or-clair); }\n .code-number { color: #80e0b0; }\n .code-function { color: #a0c0ff; }\n\n .exercice {\n background: #04091a;\n color: var(--creme);\n padding: 36px 40px;\n margin: 3em 0;\n }\n .exercice h3 { color: var(--or-clair); font-style: normal; margin-top: 0; margin-bottom: 1em; font-size: 1.1rem; font-weight: 600; }\n .exercice p { color: rgba(245,240,232,0.82); font-size: 0.97rem; margin-bottom: 0.8em; }\n .exercice .correction { border-top: 1px solid rgba(42,74,170,0.4); margin-top: 1.5em; padding-top: 1.2em; }\n .exercice .correction-titre { font-size: 0.7rem; letter-spacing: 0.18em; text-transform: uppercase; color: var(--or-clair); margin-bottom: 0.8em; font-weight: 600; }\n\n blockquote {\n padding: 0 0 0 32px;\n margin: 2em 0;\n position: relative;\n font-style: italic;\n font-size: 1.12rem;\n color: #3a3530;\n }\n blockquote::before {\n content: \"\\201C\";\n position: absolute;\n left: 0; top: -10px;\n font-size: 3.5rem;\n color: var(--cobalt-clair);\n font-family: 'Playfair Display', serif;\n line-height: 1;\n }\n blockquote cite { display: block; font-size: 0.82rem; font-style: normal; letter-spacing: 0.1em; text-transform: uppercase; color: var(--gris); margin-top: 8px; }\n\n .conclusion { border-top: 2px solid var(--noir); margin-top: 3em; padding-top: 2em; }\n\n @media (max-width: 600px) {\n .hero { padding: 50px 20px 40px; }\n .article-body { padding: 40px 20px 60px; }\n .exercice { padding: 24px 20px; }\n .code-block { padding: 16px; font-size: 0.78rem; }\n .timeline-date { min-width: 80px; font-size: 0.8rem; }\n }\n<\/style>\n<\/head>\n<body>\n\n<div class=\"hero\">\n <div class=\"hero-inner\">\n <div class=\"article-rubrique\">Myst\u00e8res des maths \u00b7 Article #13<\/div>\n <h1>Le nombre <em>\u03c0<\/em> :<br>3,14159… mais jusqu’o\u00f9 ?<\/h1>\n <p class=\"hero-intro\">Tout le monde conna\u00eet \u03c0. Personne ne le comprend vraiment. Ce nombre bizarre qui se cache dans chaque cercle \u2014 des rondelles de gombo au march\u00e9 de Cotonou jusqu’aux orbites des plan\u00e8tes \u2014 est l’un des myst\u00e8res les plus profonds et les plus anciens de toute l’humanit\u00e9.<\/p>\n <div class=\"meta\">Par Odilon AKOWANOU \u00b7 MathsVivantes \u00b7 Lecture : 11 min<\/div>\n <\/div>\n<\/div>\n\n<article class=\"article-body\">\n\n <p>\n Prends n’importe quel objet rond autour de toi \u2014 un couvercle de casserole, un pneu de z\u00e9midjan, une assiette, la bouche d’un puits. Mesure sa circonf\u00e9rence (le tour). Mesure son diam\u00e8tre (la largeur). Divise l’un par l’autre. Tu obtiendras toujours, quoi qu’il arrive, le m\u00eame nombre :\n <\/p>\n\n <div class=\"formule\">\u03c0 \u2248 3,14159265358979…<\/div>\n\n <p>\n Toujours. Pour n’importe quel cercle. Partout dans l’univers. C’est vertigineux. Ce nombre \u2014 qu’on appelle pi et qu’on \u00e9crit \u03c0 \u2014 est l’une des constantes les plus fondamentales de la nature. Et ses d\u00e9cimales ne s’arr\u00eatent jamais.\n <\/p>\n\n <h2>\u03c0 : la d\u00e9finition simple<\/h2>\n\n <div class=\"definition\">\n <strong>\u03c0 (pi) :<\/strong> Le rapport constant entre la circonf\u00e9rence d’un cercle et son diam\u00e8tre. Pour tout cercle, quelle que soit sa taille : C \/ d = \u03c0. Ce nombre est universel, irrationnel et transcendant.\n <\/div>\n\n <div class=\"schema-container\">\n <div class=\"schema-titre\">\u2b55 \u03c0 = Circonf\u00e9rence \u00f7 Diam\u00e8tre \u2014 toujours, partout<\/div>\n <svg width=\"100%\" viewBox=\"0 0 520 220\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\">\n <rect width=\"520\" height=\"220\" fill=\"white\"\/>\n\n \n <circle cx=\"90\" cy=\"110\" r=\"50\" fill=\"none\" stroke=\"#2a4aaa\" stroke-width=\"2.5\"\/>\n <line x1=\"40\" y1=\"110\" x2=\"140\" y2=\"110\" stroke=\"#b03a2e\" stroke-width=\"2\" stroke-dasharray=\"4,3\"\/>\n <text x=\"90\" y=\"172\" font-size=\"11\" fill=\"#b03a2e\" text-anchor=\"middle\">d = 100mm<\/text>\n <text x=\"90\" y=\"186\" font-size=\"11\" fill=\"#2a4aaa\" text-anchor=\"middle\">C = 314mm<\/text>\n <text x=\"90\" y=\"205\" font-size=\"12\" fill=\"#c8a010\" text-anchor=\"middle\" font-weight=\"bold\">314\/100 = \u03c0<\/text>\n\n \n <circle cx=\"270\" cy=\"110\" r=\"75\" fill=\"none\" stroke=\"#2a4aaa\" stroke-width=\"2.5\"\/>\n <line x1=\"195\" y1=\"110\" x2=\"345\" y2=\"110\" stroke=\"#b03a2e\" stroke-width=\"2\" stroke-dasharray=\"4,3\"\/>\n <text x=\"270\" y=\"197\" font-size=\"11\" fill=\"#b03a2e\" text-anchor=\"middle\">d = 150mm<\/text>\n <text x=\"270\" y=\"211\" font-size=\"11\" fill=\"#2a4aaa\" text-anchor=\"middle\">C = 471mm<\/text>\n\n \n <circle cx=\"450\" cy=\"110\" r=\"55\" fill=\"none\" stroke=\"#2a4aaa\" stroke-width=\"2.5\"\/>\n <line x1=\"395\" y1=\"110\" x2=\"505\" y2=\"110\" stroke=\"#b03a2e\" stroke-width=\"2\" stroke-dasharray=\"4,3\"\/>\n <text x=\"450\" y=\"177\" font-size=\"11\" fill=\"#b03a2e\" text-anchor=\"middle\">d = 110mm<\/text>\n <text x=\"450\" y=\"191\" font-size=\"11\" fill=\"#2a4aaa\" text-anchor=\"middle\">C = 346mm<\/text>\n\n \n <text x=\"260\" y=\"30\" font-size=\"14\" fill=\"#2a4aaa\" text-anchor=\"middle\" font-family=\"Playfair Display, serif\" font-weight=\"700\">Tailles diff\u00e9rentes \u2014 m\u00eame rapport !<\/text>\n <text x=\"260\" y=\"50\" font-size=\"13\" fill=\"#c8a010\" text-anchor=\"middle\" font-family=\"Playfair Display, serif\">C\/d = \u03c0 \u2248 3,14159… toujours<\/text>\n\n \n <text x=\"270\" y=\"103\" font-size=\"10\" fill=\"#b03a2e\" text-anchor=\"middle\">diam\u00e8tre<\/text>\n <\/svg>\n <\/div>\n\n <h2>Ses premi\u00e8res d\u00e9cimales<\/h2>\n\n <p>\n Voici les 100 premi\u00e8res d\u00e9cimales de \u03c0. Observe-les. Cherches-y un motif, une r\u00e9p\u00e9tition, une logique. Tu n’en trouveras aucune \u2014 parce qu’il n’y en a pas.\n <\/p>\n\n <div class=\"pi-digits\">\n <span class=\"pi-sym\">\u03c0<\/span> = 3.<span class=\"d1\">14159 26535<\/span> <span class=\"d2\">89793 23846<\/span> <span class=\"d3\">26433 83279<\/span> <span class=\"d4\">50288 41971<\/span><br>\n <span class=\"d1\">69399 37510<\/span> <span class=\"d2\">58209 74944<\/span> <span class=\"d3\">59230 78164<\/span> <span class=\"d4\">06286 20899<\/span><br>\n <span class=\"d1\">86280 34825<\/span> <span class=\"d2\">34211 70679<\/span><br>\n <br>\n <span style=\"color:rgba(245,240,232,0.4); font-size:0.8rem;\">… et \u00e7a continue \u00e0 l’infini, sans jamais se r\u00e9p\u00e9ter.<\/span>\n <\/div>\n\n <h2>L’histoire de \u03c0 : 4 000 ans de traque<\/h2>\n\n <div class=\"timeline\">\n <div class=\"timeline-item\">\n <div class=\"timeline-date\">~1650 av. J.-C.<\/div>\n <div class=\"timeline-dot\"><\/div>\n <div class=\"timeline-content\"><strong>\u00c9gypte ancienne (Afrique !)<\/strong> \u2014 Le papyrus Rhind, r\u00e9dig\u00e9 par le scribe Ahm\u00e8s, utilise une approximation de \u03c0 \u2248 3,16. C’est l’une des premi\u00e8res traces \u00e9crites de ce nombre. L’Afrique \u00e9tait l\u00e0 d\u00e8s le d\u00e9but.<\/div>\n <\/div>\n <div class=\"timeline-item\">\n <div class=\"timeline-date\">~250 av. J.-C.<\/div>\n <div class=\"timeline-dot\"><\/div>\n <div class=\"timeline-content\"><strong>Archim\u00e8de de Syracuse<\/strong> \u2014 Il encadre \u03c0 entre 223\/71 et 22\/7 en inscrivant et circonscrivant des polygones \u00e0 96 c\u00f4t\u00e9s dans un cercle. Premi\u00e8re m\u00e9thode rigoureuse.<\/div>\n <\/div>\n <div class=\"timeline-item\">\n <div class=\"timeline-date\">~500 ap. J.-C.<\/div>\n <div class=\"timeline-dot\"><\/div>\n <div class=\"timeline-content\"><strong>Aryabhata (Inde)<\/strong> \u2014 Calcule \u03c0 \u2248 3,1416 avec une pr\u00e9cision remarquable pour l’\u00e9poque.<\/div>\n <\/div>\n <div class=\"timeline-item\">\n <div class=\"timeline-date\">1706<\/div>\n <div class=\"timeline-dot\"><\/div>\n <div class=\"timeline-content\"><strong>William Jones<\/strong> \u2014 Utilise pour la premi\u00e8re fois la lettre grecque <strong>\u03c0<\/strong> pour d\u00e9signer ce rapport. Leonhard Euler popularisera cette notation.<\/div>\n <\/div>\n <div class=\"timeline-item\">\n <div class=\"timeline-date\">1761<\/div>\n <div class=\"timeline-dot\"><\/div>\n <div class=\"timeline-content\"><strong>Johann Lambert<\/strong> \u2014 D\u00e9montre que \u03c0 est <strong>irrationnel<\/strong> : il ne peut pas s’\u00e9crire comme fraction p\/q.<\/div>\n <\/div>\n <div class=\"timeline-item\">\n <div class=\"timeline-date\">1882<\/div>\n <div class=\"timeline-dot\"><\/div>\n <div class=\"timeline-content\"><strong>Ferdinand von Lindemann<\/strong> \u2014 D\u00e9montre que \u03c0 est <strong>transcendant<\/strong> \u2014 il ne satisfait aucune \u00e9quation alg\u00e9brique \u00e0 coefficients entiers. La quadrature du cercle est impossible \u00e0 jamais.<\/div>\n <\/div>\n <div class=\"timeline-item\">\n <div class=\"timeline-date\">2024<\/div>\n <div class=\"timeline-dot\"><\/div>\n <div class=\"timeline-content\"><strong>Record actuel<\/strong> \u2014 \u03c0 est connu \u00e0 plus de <strong>105 000 milliards de d\u00e9cimales<\/strong>. Calcul\u00e9 par des supercalculateurs. Et toujours sans motif r\u00e9p\u00e9titif visible.<\/div>\n <\/div>\n <\/div>\n\n <h2>Pourquoi \u03c0 est irrationnel \u2014 l’intuition<\/h2>\n\n <p>\n Un nombre rationnel s’\u00e9crit comme fraction : 1\/2, 3\/4, 22\/7… Sa repr\u00e9sentation d\u00e9cimale finit ou se r\u00e9p\u00e8te : 1\/3 = 0,333333…, 1\/7 = 0,142857142857…\n <\/p>\n\n <p>\n \u03c0, lui, ne se r\u00e9p\u00e8te jamais. Ses d\u00e9cimales sont ap\u00e9riodiques \u2014 elles ne forment aucun motif qui se r\u00e9p\u00e8te, aussi loin qu’on aille. Ce n’est pas un hasard ni un manque de calcul : c’est une propri\u00e9t\u00e9 math\u00e9matique profonde, <em>d\u00e9montr\u00e9e<\/em>.\n <\/p>\n\n <div class=\"encadre\">\n <span class=\"encadre-titre\">\ud83d\udca1 Intuition de l’irrationalit\u00e9<\/span>\n <p>Un cercle \u00ab\u00a0parfait\u00a0\u00bb est une forme g\u00e9om\u00e9trique id\u00e9ale \u2014 sans angle, sans rupture, infiniment lisse. Mesurer sa circonf\u00e9rence avec des unit\u00e9s enti\u00e8res, c’est essayer de capturer quelque chose de continu avec des mots discrets. Il y a une incompatibilit\u00e9 fondamentale entre la rondeur parfaite du cercle et les fractions faites d’entiers.<\/p>\n <p>C’est cette incompatibilit\u00e9 qui se manifeste dans les d\u00e9cimales infinies de \u03c0.<\/p>\n <\/div>\n\n <h2>Comment calculer \u03c0 \u2014 trois m\u00e9thodes fascinantes<\/h2>\n\n <h3>M\u00e9thode 1 \u2014 Archim\u00e8de : les polygones<\/h3>\n\n <p>\n Archim\u00e8de a encadr\u00e9 \u03c0 en inscrivant un polygone \u00e0 l’int\u00e9rieur d’un cercle et en en circonscrivant un autre \u00e0 l’ext\u00e9rieur. Plus on augmente le nombre de c\u00f4t\u00e9s, plus les deux polygones se rapprochent du cercle, et plus l’encadrement de \u03c0 devient pr\u00e9cis.\n <\/p>\n\n <div class=\"etape\"><span class=\"etape-numero\">6 c\u00f4t\u00e9s<\/span> 3 < \u03c0 < 3,464<\/div>\n <div class=\"etape\"><span class=\"etape-numero\">12 c\u00f4t\u00e9s<\/span> 3,105 < \u03c0 < 3,215<\/div>\n <div class=\"etape\"><span class=\"etape-numero\">96 c\u00f4t\u00e9s<\/span> 3,1408 < \u03c0 < 3,1429 (Archim\u00e8de)<\/div>\n <div class=\"etape\"><span class=\"etape-numero\">\u221e c\u00f4t\u00e9s<\/span> \u03c0 = 3,14159265… (limite exacte)<\/div>\n\n <h3>M\u00e9thode 2 \u2014 La s\u00e9rie de Leibniz<\/h3>\n\n <p>\n Au XVIIe si\u00e8cle, Leibniz d\u00e9couvre une formule stup\u00e9fiante : \u03c0 peut s’exprimer comme une somme infinie de fractions simples !\n <\/p>\n\n <div class=\"formule\">\u03c0\/4 = 1 \u2212 1\/3 + 1\/5 \u2212 1\/7 + 1\/9 \u2212 1\/11 + …<\/div>\n\n <p>\n Elle converge tr\u00e8s lentement \u2014 il faut des millions de termes pour avoir 6 d\u00e9cimales exactes. Mais la beaut\u00e9 de la formule est saisissante : les nombres impairs 1, 3, 5, 7, 9… cachent \u03c0 en eux.\n <\/p>\n\n <h3>M\u00e9thode 3 \u2014 Monte Carlo : le hasard calcule \u03c0<\/h3>\n\n <p>\n Voici la m\u00e9thode la plus \u00e9tonnante : on peut calculer \u03c0 en lan\u00e7ant des points au hasard ! Si on lance des points al\u00e9atoires dans un carr\u00e9 de c\u00f4t\u00e9 1, la proportion de points qui tombent dans le quart de cercle inscrit converge vers \u03c0\/4.\n <\/p>\n\n <div class=\"schema-container\">\n <div class=\"schema-titre\">\ud83c\udfb2 M\u00e9thode Monte Carlo \u2014 le hasard approche \u03c0<\/div>\n <svg width=\"100%\" viewBox=\"0 0 360 300\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\">\n <rect width=\"360\" height=\"300\" fill=\"white\"\/>\n\n \n <rect x=\"80\" y=\"40\" width=\"200\" height=\"200\" fill=\"#f8f5ef\" stroke=\"#2a4aaa\" stroke-width=\"2\"\/>\n \n <path d=\"M 80,240 A 200,200 0 0,1 280,40\" fill=\"#eef0ff\" stroke=\"#2a4aaa\" stroke-width=\"2\"\/>\n\n \n <circle cx=\"130\" cy=\"80\" r=\"4\" fill=\"#2a4aaa\" opacity=\"0.8\"\/>\n <circle cx=\"160\" cy=\"100\" r=\"4\" fill=\"#2a4aaa\" opacity=\"0.8\"\/>\n <circle cx=\"110\" cy=\"140\" r=\"4\" fill=\"#2a4aaa\" opacity=\"0.8\"\/>\n <circle cx=\"180\" cy=\"70\" r=\"4\" fill=\"#2a4aaa\" opacity=\"0.8\"\/>\n <circle cx=\"140\" cy=\"160\" r=\"4\" fill=\"#2a4aaa\" opacity=\"0.8\"\/>\n <circle cx=\"200\" cy=\"110\" r=\"4\" fill=\"#2a4aaa\" opacity=\"0.8\"\/>\n <circle cx=\"120\" cy=\"110\" r=\"4\" fill=\"#2a4aaa\" opacity=\"0.8\"\/>\n <circle cx=\"170\" cy=\"140\" r=\"4\" fill=\"#2a4aaa\" opacity=\"0.8\"\/>\n <circle cx=\"150\" cy=\"200\" r=\"4\" fill=\"#2a4aaa\" opacity=\"0.8\"\/>\n <circle cx=\"220\" cy=\"150\" r=\"4\" fill=\"#2a4aaa\" opacity=\"0.8\"\/>\n <circle cx=\"100\" cy=\"180\" r=\"4\" fill=\"#2a4aaa\" opacity=\"0.8\"\/>\n <circle cx=\"240\" cy=\"130\" r=\"4\" fill=\"#2a4aaa\" opacity=\"0.8\"\/>\n\n \n <circle cx=\"250\" cy=\"60\" r=\"4\" fill=\"#b03a2e\" opacity=\"0.8\"\/>\n <circle cx=\"260\" cy=\"180\" r=\"4\" fill=\"#b03a2e\" opacity=\"0.8\"\/>\n <circle cx=\"270\" cy=\"210\" r=\"4\" fill=\"#b03a2e\" opacity=\"0.8\"\/>\n <circle cx=\"240\" cy=\"220\" r=\"4\" fill=\"#b03a2e\" opacity=\"0.8\"\/>\n\n \n <circle cx=\"100\" cy=\"268\" r=\"5\" fill=\"#2a4aaa\"\/>\n <text x=\"112\" y=\"272\" font-size=\"11\" fill=\"#6b6560\">Dans le cercle (12)<\/text>\n <circle cx=\"220\" cy=\"268\" r=\"5\" fill=\"#b03a2e\"\/>\n <text x=\"232\" y=\"272\" font-size=\"11\" fill=\"#6b6560\">Hors (4)<\/text>\n\n \n <text x=\"180\" y=\"292\" font-size=\"11\" fill=\"#2a4aaa\" text-anchor=\"middle\" font-family=\"Playfair Display, serif\">\u03c0 \u2248 4 \u00d7 12\/16 = 3,0<\/text>\n <\/svg>\n <\/div>\n\n <p>\n Plus on lance de points, plus l’approximation est pr\u00e9cise. Avec 10 millions de points, on obtient \u03c0 avec 3-4 d\u00e9cimales exactes. C’est la magie de la m\u00e9thode Monte Carlo \u2014 et c’est aussi la base de nombreux algorithmes en data science et en finance.\n <\/p>\n\n <h2>\u03c0 dans les formules \u2014 il est partout<\/h2>\n\n <p>\n Ce qui rend \u03c0 encore plus myst\u00e9rieux, c’est qu’il appara\u00eet dans des formules qui n’ont apparemment rien \u00e0 voir avec les cercles :\n <\/p>\n\n <div class=\"table-container\">\n <table>\n <tr>\n <th>Formule<\/th>\n <th>Domaine<\/th>\n <th>Pourquoi c’est surprenant<\/th>\n <\/tr>\n <tr>\n <td style=\"font-family:'Playfair Display',serif;\">C = 2\u03c0r<\/td>\n <td>G\u00e9om\u00e9trie<\/td>\n <td>Normal \u2014 c’est la d\u00e9finition<\/td>\n <\/tr>\n <tr>\n <td style=\"font-family:'Playfair Display',serif;\">A = \u03c0r\u00b2<\/td>\n <td>G\u00e9om\u00e9trie<\/td>\n <td>Aire du cercle<\/td>\n <\/tr>\n <tr>\n <td style=\"font-family:'Playfair Display',serif;\">e\u2071\u1d56\u2071 + 1 = 0<\/td>\n <td>Analyse complexe<\/td>\n <td>\ud83d\ude31 \u03c0, e, i, 1 et 0 dans une seule formule !<\/td>\n <\/tr>\n <tr>\n <td style=\"font-family:'Playfair Display',serif;\">\u222b\u208b\u221e\u207a\u221e e\u207b\u02e3\u00b2 dx = \u221a\u03c0<\/td>\n <td>Probabilit\u00e9s<\/td>\n <td>\u03c0 dans la loi normale \u2014 sans cercle en vue !<\/td>\n <\/tr>\n <tr>\n <td style=\"font-family:'Playfair Display',serif;\">1\/1\u00b2 + 1\/2\u00b2 + 1\/3\u00b2 + … = \u03c0\u00b2\/6<\/td>\n <td>S\u00e9ries<\/td>\n <td>Les carr\u00e9s des entiers cachent \u03c0 !<\/td>\n <\/tr>\n <tr>\n <td style=\"font-family:'Playfair Display',serif;\">T = 2\u03c0\u221a(L\/g)<\/td>\n <td>Physique (pendule)<\/td>\n <td>La p\u00e9riode d’un pendule contient \u03c0<\/td>\n <\/tr>\n <\/table>\n <\/div>\n\n <div class=\"encadre-histoire encadre\">\n <span class=\"encadre-titre\">\ud83d\ude31 La formule la plus belle des maths<\/span>\n <p>\n La formule <strong>e\u2071\u1d56\u2071 + 1 = 0<\/strong> \u2014 appel\u00e9e identit\u00e9 d’Euler \u2014 est r\u00e9guli\u00e8rement \u00e9lue \u00ab\u00a0plus belle formule math\u00e9matique\u00a0\u00bb par les math\u00e9maticiens du monde entier.\n <\/p>\n <p>\n Elle r\u00e9unit en une seule \u00e9quation les cinq nombres les plus importants des math\u00e9matiques : <strong>e<\/strong> (la constante de la croissance naturelle), <strong>i<\/strong> (le nombre imaginaire, racine de \u22121), <strong>\u03c0<\/strong> (notre h\u00e9ros du jour), <strong>1<\/strong> (l’unit\u00e9 multiplicative) et <strong>0<\/strong> (l’unit\u00e9 additive).\n <\/p>\n <p>\n Ce n’est pas une co\u00efncidence. C’est la signature d’une unit\u00e9 profonde qui traverse toutes les math\u00e9matiques. Et \u03c0 est au c\u0153ur de tout \u00e7a.\n <\/p>\n <\/div>\n\n <h2>Le code Python : calculons \u03c0 nous-m\u00eames<\/h2>\n\n <div class=\"code-block\">\n <span class=\"code-label\">Python<\/span>\n<span class=\"code-comment\"># Trois fa\u00e7ons de calculer \u03c0 en Python<\/span>\n<span class=\"code-keyword\">import<\/span> random\n<span class=\"code-keyword\">import<\/span> math\n\n<span class=\"code-comment\"># — M\u00e9thode 1 : S\u00e9rie de Leibniz —<\/span>\n<span class=\"code-keyword\">def<\/span> <span class=\"code-function\">pi_leibniz<\/span>(n_termes):\n <span class=\"code-string\">\u00ab\u00a0\u00a0\u00bb\u00a0\u00bb\u03c0\/4 = 1 – 1\/3 + 1\/5 – 1\/7 + …\u00a0\u00bb\u00a0\u00bb\u00a0\u00bb<\/span>\n resultat = <span class=\"code-number\">0<\/span>\n signe = <span class=\"code-number\">1<\/span>\n <span class=\"code-keyword\">for<\/span> k <span class=\"code-keyword\">in<\/span> <span class=\"code-function\">range<\/span>(n_termes):\n resultat += signe \/ (<span class=\"code-number\">2<\/span>*k + <span class=\"code-number\">1<\/span>)\n signe *= –<span class=\"code-number\">1<\/span>\n <span class=\"code-keyword\">return<\/span> <span class=\"code-number\">4<\/span> * resultat\n\n<span class=\"code-comment\"># — M\u00e9thode 2 : Monte Carlo —<\/span>\n<span class=\"code-keyword\">def<\/span> <span class=\"code-function\">pi_monte_carlo<\/span>(n_points):\n <span class=\"code-string\">\u00ab\u00a0\u00a0\u00bb\u00a0\u00bbLance n points al\u00e9atoires, compte ceux dans le quart de cercle\u00a0\u00bb\u00a0\u00bb\u00a0\u00bb<\/span>\n dans_cercle = <span class=\"code-number\">0<\/span>\n <span class=\"code-keyword\">for<\/span> _ <span class=\"code-keyword\">in<\/span> <span class=\"code-function\">range<\/span>(n_points):\n x = random.<span class=\"code-function\">uniform<\/span>(<span class=\"code-number\">0<\/span>, <span class=\"code-number\">1<\/span>)\n y = random.<span class=\"code-function\">uniform<\/span>(<span class=\"code-number\">0<\/span>, <span class=\"code-number\">1<\/span>)\n <span class=\"code-keyword\">if<\/span> x**<span class=\"code-number\">2<\/span> + y**<span class=\"code-number\">2<\/span> <= <span class=\"code-number\">1<\/span>:\n dans_cercle += <span class=\"code-number\">1<\/span>\n <span class=\"code-keyword\">return<\/span> <span class=\"code-number\">4<\/span> * dans_cercle \/ n_points\n\n<span class=\"code-comment\"># — M\u00e9thode 3 : Formule de Nilakantha (converge vite !) —<\/span>\n<span class=\"code-keyword\">def<\/span> <span class=\"code-function\">pi_nilakantha<\/span>(n_termes):\n <span class=\"code-string\">\u00ab\u00a0\u00a0\u00bb\u00a0\u00bb\u03c0 = 3 + 4\/(2\u00d73\u00d74) – 4\/(4\u00d75\u00d76) + 4\/(6\u00d77\u00d78) – …\u00a0\u00bb\u00a0\u00bb\u00a0\u00bb<\/span>\n resultat = <span class=\"code-number\">3.0<\/span>\n signe = <span class=\"code-number\">1<\/span>\n <span class=\"code-keyword\">for<\/span> k <span class=\"code-keyword\">in<\/span> <span class=\"code-function\">range<\/span>(<span class=\"code-number\">1<\/span>, n_termes + <span class=\"code-number\">1<\/span>):\n n = <span class=\"code-number\">2<\/span> * k\n resultat += signe * <span class=\"code-number\">4<\/span> \/ (n * (n+<span class=\"code-number\">1<\/span>) * (n+<span class=\"code-number\">2<\/span>))\n signe *= –<span class=\"code-number\">1<\/span>\n <span class=\"code-keyword\">return<\/span> resultat\n\n<span class=\"code-comment\"># — Comparaison —<\/span>\n<span class=\"code-function\">print<\/span>(<span class=\"code-string\">f\u00a0\u00bb\u03c0 r\u00e9el = {math.pi:.10f}\u00a0\u00bb<\/span>)\n<span class=\"code-function\">print<\/span>(<span class=\"code-string\">f\u00a0\u00bbLeibniz (10 000 termes) = {pi_leibniz(10000):.10f}\u00a0\u00bb<\/span>)\n<span class=\"code-function\">print<\/span>(<span class=\"code-string\">f\u00a0\u00bbMonte Carlo (1M points) = {pi_monte_carlo(1000000):.10f}\u00a0\u00bb<\/span>)\n<span class=\"code-function\">print<\/span>(<span class=\"code-string\">f\u00a0\u00bbNilakantha (100 termes) = {pi_nilakantha(100):.10f}\u00a0\u00bb<\/span>)\n\n<span class=\"code-comment\"># Convergence de Monte Carlo selon le nombre de points<\/span>\n<span class=\"code-function\">print<\/span>(<span class=\"code-string\">\u00ab\u00a0\\nConvergence Monte Carlo :\u00a0\u00bb<\/span>)\n<span class=\"code-keyword\">for<\/span> n <span class=\"code-keyword\">in<\/span> [<span class=\"code-number\">100<\/span>, <span class=\"code-number\">1000<\/span>, <span class=\"code-number\">10000<\/span>, <span class=\"code-number\">100000<\/span>, <span class=\"code-number\">1000000<\/span>]:\n approx = <span class=\"code-function\">pi_monte_carlo<\/span>(n)\n erreur = <span class=\"code-function\">abs<\/span>(approx – math.pi)\n <span class=\"code-function\">print<\/span>(<span class=\"code-string\">f\u00a0\u00bb n={n:8d} \u2192 \u03c0 \u2248 {approx:.6f} | erreur = {erreur:.6f}\u00a0\u00bb<\/span>)\n <\/div>\n\n <blockquote>\n \u03c0 est comme l’horizon \u2014 plus tu t’en approches, plus tu r\u00e9alises qu’il s’\u00e9tend \u00e0 l’infini. Et pourtant, tu l’utilises chaque fois que tu traces un cercle.\n <cite>\u2014 M\u00e9ditation math\u00e9matique<\/cite>\n <\/blockquote>\n\n \n <div class=\"exercice\">\n <h3>\u270f\ufe0f Exercice corrig\u00e9 \u2014 du primaire au lyc\u00e9e<\/h3>\n <p><strong>Niveau primaire\/6\u00e8me :<\/strong> Le grand bassin rond du quartier Agla \u00e0 Cotonou a un diam\u00e8tre de 14 m\u00e8tres. Calcule sa circonf\u00e9rence. (Utilise \u03c0 \u2248 22\/7)<\/p>\n <p><strong>Niveau 4\u00e8me\/3\u00e8me :<\/strong> Une roue de z\u00e9midjan a un rayon de 28 cm. Combien de tours fait-elle pour parcourir 1 km ? (\u03c0 \u2248 3,14)<\/p>\n <p><strong>Niveau lyc\u00e9e :<\/strong> En utilisant les 4 premiers termes de la s\u00e9rie de Leibniz, calcule une approximation de \u03c0. Quelle est l’erreur relative par rapport \u00e0 \u03c0 \u2248 3,14159 ?<\/p>\n\n <div class=\"correction\">\n <div class=\"correction-titre\">\u25b8 Correction<\/div>\n <p><strong>Niveau primaire\/6\u00e8me :<\/strong><\/p>\n <p>C = \u03c0 \u00d7 d = (22\/7) \u00d7 14 = 22 \u00d7 2 = <strong>44 m\u00e8tres<\/strong><\/p>\n\n <p><strong>Niveau 4\u00e8me\/3\u00e8me :<\/strong><\/p>\n <p>Circonf\u00e9rence d’une roue = 2\u03c0r = 2 \u00d7 3,14 \u00d7 0,28 = <strong>1,7584 m<\/strong><\/p>\n <p>1 km = 1000 m<\/p>\n <p>Nombre de tours = 1000 \/ 1,7584 \u2248 <strong>568,7 tours<\/strong><\/p>\n\n <p><strong>Niveau lyc\u00e9e :<\/strong><\/p>\n <p>S\u00e9rie de Leibniz : \u03c0\/4 = 1 \u2212 1\/3 + 1\/5 \u2212 1\/7 + …<\/p>\n <p>4 termes : \u03c0\/4 \u2248 1 \u2212 0,333 + 0,200 \u2212 0,143 = 0,724<\/p>\n <p>\u03c0 \u2248 4 \u00d7 0,724 = <strong>2,896<\/strong><\/p>\n <p>Erreur relative = |2,896 \u2212 3,14159| \/ 3,14159 \u2248 <strong>7,8%<\/strong><\/p>\n <p>\u2192 La s\u00e9rie de Leibniz converge tr\u00e8s lentement. Il faut des milliers de termes pour avoir 3 d\u00e9cimales exactes ! \u2705<\/p>\n <\/div>\n <\/div>\n\n <div class=\"conclusion\">\n <h2>Ce qu’on retient<\/h2>\n <p>\n \u03c0 est partout \u2014 dans les cercles, les ondes, les probabilit\u00e9s, les pendules, les nombres complexes. Il est irrationnel, transcendant, et ses d\u00e9cimales n’ont aucun motif connu. On le conna\u00eet \u00e0 plus de 100 000 milliards de chiffres et on n’en a toujours pas vu la fin. Et pourtant, pour construire une maison ronde, une citerne ou un puits \u00e0 Cotonou, \u03c0 \u2248 3,14 suffit amplement.\n <\/p>\n <p>\n C’est \u00e7a la beaut\u00e9 de \u03c0 : il est \u00e0 la fois infiniment myst\u00e9rieux et imm\u00e9diatement utile. Un pied dans l’abstraction pure, un autre dans la r\u00e9alit\u00e9 quotidienne. Exactement comme les math\u00e9matiques elles-m\u00eames.\n <\/p>\n <p>\n Dans le prochain article, nous plongerons dans <strong>les tontines b\u00e9ninoises \u2014 un mod\u00e8le math\u00e9matique parfait<\/strong>. Int\u00e9r\u00eats compos\u00e9s, valeur temporelle de l’argent, th\u00e9orie des jeux \u2014 tout \u00e7a se cache dans cette pratique que nos mamans connaissent depuis toujours.\n <\/p>\n <\/div>\n\n<\/article>\n\n<\/body>\n<\/html>\n","protected":false},"excerpt":{"rendered":"<p>Le nombre \u03c0 : 3,14159… mais jusqu’o\u00f9 ? \u2014 MathsVivantes Myst\u00e8res des maths \u00b7 Article #13 Le nombre \u03c0 :3,14159… […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_uag_custom_page_level_css":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[8],"tags":[],"class_list":["post-132","post","type-post","status-publish","format-standard","hentry","category-fondements"],"yoast_head":"\n<title>Le nombre Pi - AfrikIntelligent<\/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:\/\/vmi3217629.contaboserver.net\/?p=132\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Le nombre Pi - AfrikIntelligent\" \/>\n<meta property=\"og:description\" content=\"Le nombre \u03c0 : 3,14159… mais jusqu’o\u00f9 ? \u2014 MathsVivantes Myst\u00e8res des maths \u00b7 Article #13 Le nombre \u03c0 :3,14159… […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/vmi3217629.contaboserver.net\/?p=132\" \/>\n<meta property=\"og:site_name\" content=\"AfrikIntelligent\" \/>\n<meta property=\"article:published_time\" content=\"2026-04-29T06:00:38+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-04-29T06:00:39+00:00\" \/>\n<meta name=\"author\" content=\"Odilon\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u00c9crit par\" \/>\n\t<meta name=\"twitter:data1\" content=\"Odilon\" \/>\n\t<meta name=\"twitter:label2\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data2\" content=\"9 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=132#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=132\"},\"author\":{\"name\":\"Odilon\",\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/#\\\/schema\\\/person\\\/a3da39574d729b6b3ff7514ccc055923\"},\"headline\":\"Le nombre Pi\",\"datePublished\":\"2026-04-29T06:00:38+00:00\",\"dateModified\":\"2026-04-29T06:00:39+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=132\"},\"wordCount\":1153,\"commentCount\":0,\"articleSection\":[\"Fondements\"],\"inLanguage\":\"fr-FR\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=132#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=132\",\"url\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=132\",\"name\":\"Le nombre Pi - AfrikIntelligent\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/#website\"},\"datePublished\":\"2026-04-29T06:00:38+00:00\",\"dateModified\":\"2026-04-29T06:00:39+00:00\",\"author\":{\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/#\\\/schema\\\/person\\\/a3da39574d729b6b3ff7514ccc055923\"},\"breadcrumb\":{\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=132#breadcrumb\"},\"inLanguage\":\"fr-FR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=132\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=132#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Accueil\",\"item\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Le nombre Pi\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/#website\",\"url\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/\",\"name\":\"AfrikIntelligent\",\"description\":\"Append autrement\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"fr-FR\"},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/#\\\/schema\\\/person\\\/a3da39574d729b6b3ff7514ccc055923\",\"name\":\"Odilon\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"fr-FR\",\"@id\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/57bcd6a76fa395ae5e994943b66ccd3dd7e71cd0b1b77b351986e88c27801523?s=96&d=mm&r=g\",\"url\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/57bcd6a76fa395ae5e994943b66ccd3dd7e71cd0b1b77b351986e88c27801523?s=96&d=mm&r=g\",\"contentUrl\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/57bcd6a76fa395ae5e994943b66ccd3dd7e71cd0b1b77b351986e88c27801523?s=96&d=mm&r=g\",\"caption\":\"Odilon\"},\"sameAs\":[\"https:\\\/\\\/vmi3217629.contaboserver.net\"],\"url\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?author=1\"}]}<\/script>\n","yoast_head_json":{"title":"Le nombre Pi - AfrikIntelligent","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/vmi3217629.contaboserver.net\/?p=132","og_locale":"fr_FR","og_type":"article","og_title":"Le nombre Pi - AfrikIntelligent","og_description":"Le nombre \u03c0 : 3,14159… mais jusqu’o\u00f9 ? \u2014 MathsVivantes Myst\u00e8res des maths \u00b7 Article #13 Le nombre \u03c0 :3,14159… […]","og_url":"https:\/\/vmi3217629.contaboserver.net\/?p=132","og_site_name":"AfrikIntelligent","article_published_time":"2026-04-29T06:00:38+00:00","article_modified_time":"2026-04-29T06:00:39+00:00","author":"Odilon","twitter_card":"summary_large_image","twitter_misc":{"\u00c9crit par":"Odilon","Dur\u00e9e de lecture estim\u00e9e":"9 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/vmi3217629.contaboserver.net\/?p=132#article","isPartOf":{"@id":"https:\/\/vmi3217629.contaboserver.net\/?p=132"},"author":{"name":"Odilon","@id":"https:\/\/vmi3217629.contaboserver.net\/#\/schema\/person\/a3da39574d729b6b3ff7514ccc055923"},"headline":"Le nombre Pi","datePublished":"2026-04-29T06:00:38+00:00","dateModified":"2026-04-29T06:00:39+00:00","mainEntityOfPage":{"@id":"https:\/\/vmi3217629.contaboserver.net\/?p=132"},"wordCount":1153,"commentCount":0,"articleSection":["Fondements"],"inLanguage":"fr-FR","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/vmi3217629.contaboserver.net\/?p=132#respond"]}]},{"@type":"WebPage","@id":"https:\/\/vmi3217629.contaboserver.net\/?p=132","url":"https:\/\/vmi3217629.contaboserver.net\/?p=132","name":"Le nombre Pi - AfrikIntelligent","isPartOf":{"@id":"https:\/\/vmi3217629.contaboserver.net\/#website"},"datePublished":"2026-04-29T06:00:38+00:00","dateModified":"2026-04-29T06:00:39+00:00","author":{"@id":"https:\/\/vmi3217629.contaboserver.net\/#\/schema\/person\/a3da39574d729b6b3ff7514ccc055923"},"breadcrumb":{"@id":"https:\/\/vmi3217629.contaboserver.net\/?p=132#breadcrumb"},"inLanguage":"fr-FR","potentialAction":[{"@type":"ReadAction","target":["https:\/\/vmi3217629.contaboserver.net\/?p=132"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/vmi3217629.contaboserver.net\/?p=132#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Accueil","item":"https:\/\/vmi3217629.contaboserver.net\/"},{"@type":"ListItem","position":2,"name":"Le nombre Pi"}]},{"@type":"WebSite","@id":"https:\/\/vmi3217629.contaboserver.net\/#website","url":"https:\/\/vmi3217629.contaboserver.net\/","name":"AfrikIntelligent","description":"Append autrement","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/vmi3217629.contaboserver.net\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"fr-FR"},{"@type":"Person","@id":"https:\/\/vmi3217629.contaboserver.net\/#\/schema\/person\/a3da39574d729b6b3ff7514ccc055923","name":"Odilon","image":{"@type":"ImageObject","inLanguage":"fr-FR","@id":"https:\/\/secure.gravatar.com\/avatar\/57bcd6a76fa395ae5e994943b66ccd3dd7e71cd0b1b77b351986e88c27801523?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/57bcd6a76fa395ae5e994943b66ccd3dd7e71cd0b1b77b351986e88c27801523?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/57bcd6a76fa395ae5e994943b66ccd3dd7e71cd0b1b77b351986e88c27801523?s=96&d=mm&r=g","caption":"Odilon"},"sameAs":["https:\/\/vmi3217629.contaboserver.net"],"url":"https:\/\/vmi3217629.contaboserver.net\/?author=1"}]}},"uagb_featured_image_src":{"full":false,"thumbnail":false,"medium":false,"medium_large":false,"large":false,"1536x1536":false,"2048x2048":false},"uagb_author_info":{"display_name":"Odilon","author_link":"https:\/\/vmi3217629.contaboserver.net\/?author=1"},"uagb_comment_info":0,"uagb_excerpt":"Le nombre \u03c0 : 3,14159… mais jusqu’o\u00f9 ? \u2014 MathsVivantes Myst\u00e8res des maths \u00b7 Article #13 Le nombre \u03c0 :3,14159… […]","_links":{"self":[{"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=\/wp\/v2\/posts\/132","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=132"}],"version-history":[{"count":1,"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=\/wp\/v2\/posts\/132\/revisions"}],"predecessor-version":[{"id":133,"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=\/wp\/v2\/posts\/132\/revisions\/133"}],"wp:attachment":[{"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=132"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=132"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=132"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}

{"id":132,"date":"2026-04-29T07:00:38","date_gmt":"2026-04-29T06:00:38","guid":{"rendered":"https:\/\/vmi3217629.contaboserver.net\/?p=132"},"modified":"2026-04-29T07:00:39","modified_gmt":"2026-04-29T06:00:39","slug":"le-nombre-pi","status":"publish","type":"post","link":"https:\/\/vmi3217629.contaboserver.net\/?p=132","title":{"rendered":"Le nombre Pi"},"content":{"rendered":"\n\n\n\n\n\nLe nombre \u03c0 : 3,14159… mais jusqu’o\u00f9 ? \u2014 MathsVivantes<\/title>\n<link href=\"https:\/\/fonts.googleapis.com\/css2?family=Playfair+Display:ital,wght@0,400;0,700;1,400&family=Source+Serif+4:ital,wght@0,300;0,400;0,600;1,300;1,400&display=swap\" rel=\"stylesheet\">\n<style>\n :root {\n --noir: #0f0e0b;\n --creme: #f5f0e8;\n --cobalt: #0a1a4a;\n --cobalt-clair: #2a4aaa;\n --cobalt-pale: #eef0ff;\n --or: #c8a010;\n --or-clair: #f0d060;\n --rouge: #b03a2e;\n --gris: #6b6560;\n --gris-clair: #e8e2d8;\n }\n\n * { margin: 0; padding: 0; box-sizing: border-box; }\n\n body {\n background-color: var(--creme);\n color: var(--noir);\n font-family: 'Source Serif 4', Georgia, serif;\n font-weight: 300;\n line-height: 1.8;\n }\n\n .hero {\n background: #04091a;\n color: var(--creme);\n padding: 80px 40px 70px;\n position: relative;\n overflow: hidden;\n }\n .hero::before {\n content: \"\u03c0 \u03c0 \u03c0 \u03c0\";\n position: absolute;\n top: 10px; right: 30px;\n font-size: 8rem;\n opacity: 0.04;\n font-family: 'Playfair Display', serif;\n letter-spacing: 0.2em;\n }\n .hero-inner { max-width: 760px; margin: 0 auto; }\n\n .article-rubrique {\n display: inline-block;\n background: var(--cobalt-clair);\n color: white;\n font-size: 0.7rem;\n letter-spacing: 0.18em;\n text-transform: uppercase;\n padding: 4px 12px;\n margin-bottom: 24px;\n font-weight: 600;\n }\n\n .hero h1 {\n font-family: 'Playfair Display', serif;\n font-size: clamp(2rem, 5vw, 3.4rem);\n line-height: 1.2;\n margin-bottom: 24px;\n font-weight: 700;\n }\n .hero h1 em { color: var(--or-clair); font-style: italic; }\n\n .hero-intro {\n font-size: 1.15rem;\n opacity: 0.75;\n max-width: 600px;\n font-style: italic;\n border-left: 3px solid var(--cobalt-clair);\n padding-left: 20px;\n margin-bottom: 32px;\n }\n .meta { font-size: 0.8rem; opacity: 0.45; letter-spacing: 0.08em; text-transform: uppercase; }\n\n .article-body { max-width: 760px; margin: 0 auto; padding: 60px 40px 80px; }\n .article-body p { font-size: 1.05rem; margin-bottom: 1.6em; color: #2a2520; }\n\n h2 {\n font-family: 'Playfair Display', serif;\n font-size: 1.6rem;\n margin: 2.5em 0 0.8em;\n color: var(--noir);\n font-weight: 700;\n }\n h2::before { content: \"\u00a7 \"; color: var(--cobalt-clair); }\n\n h3 {\n font-family: 'Playfair Display', serif;\n font-size: 1.15rem;\n font-weight: 700;\n margin: 1.8em 0 0.6em;\n color: var(--cobalt);\n }\n\n .encadre {\n border: 1.5px solid var(--cobalt-clair);\n background: white;\n padding: 24px 28px;\n margin: 2em 0;\n position: relative;\n }\n .encadre-titre {\n position: absolute;\n top: -12px; left: 20px;\n background: white;\n padding: 0 8px;\n font-size: 0.72rem;\n letter-spacing: 0.15em;\n text-transform: uppercase;\n color: var(--cobalt-clair);\n font-weight: 600;\n }\n .encadre p { margin-bottom: 0.8em; font-size: 0.98rem; }\n .encadre p:last-child { margin-bottom: 0; }\n\n .encadre-histoire {\n background: #04091a;\n color: var(--creme);\n border: none;\n padding: 32px 36px;\n margin: 2.5em 0;\n }\n .encadre-histoire .encadre-titre { background: #04091a; color: var(--or-clair); }\n .encadre-histoire p { color: rgba(245,240,232,0.85); }\n\n .definition {\n background: var(--cobalt-pale);\n border-left: 4px solid var(--cobalt-clair);\n padding: 20px 24px;\n margin: 1.8em 0;\n font-style: italic;\n }\n .definition strong { font-style: normal; color: var(--cobalt); font-family: 'Playfair Display', serif; }\n\n \/* DIGITS DE PI *\/\n .pi-digits {\n background: #04091a;\n color: var(--creme);\n padding: 24px 28px;\n margin: 2em 0;\n font-family: 'Courier New', monospace;\n font-size: 0.95rem;\n line-height: 2;\n letter-spacing: 0.05em;\n overflow-x: auto;\n }\n .pi-digits .pi-sym {\n color: var(--or-clair);\n font-family: 'Playfair Display', serif;\n font-size: 1.4rem;\n font-weight: 700;\n }\n .pi-digits .d1 { color: #80b0ff; }\n .pi-digits .d2 { color: #80ffb0; }\n .pi-digits .d3 { color: #ffb080; }\n .pi-digits .d4 { color: #ff8080; }\n\n .schema-container {\n background: white;\n border: 1.5px solid var(--cobalt-clair);\n padding: 24px;\n margin: 2em 0;\n text-align: center;\n }\n .schema-titre {\n font-size: 0.72rem;\n letter-spacing: 0.15em;\n text-transform: uppercase;\n color: var(--cobalt-clair);\n font-weight: 600;\n margin-bottom: 16px;\n }\n\n .formule {\n text-align: center;\n font-size: 1.3rem;\n font-family: 'Playfair Display', serif;\n margin: 1.5em 0;\n color: var(--noir);\n padding: 16px;\n background: white;\n border-top: 2px solid var(--cobalt-clair);\n border-bottom: 2px solid var(--cobalt-clair);\n }\n\n .etape {\n background: white;\n border-left: 3px solid var(--cobalt-clair);\n padding: 12px 20px;\n margin: 0.6em 0;\n font-size: 0.97rem;\n }\n .etape-numero { font-family: 'Playfair Display', serif; font-weight: 700; color: var(--cobalt-clair); margin-right: 8px; }\n\n \/* TIMELINE *\/\n .timeline { margin: 2em 0; }\n .timeline-item {\n display: flex;\n gap: 20px;\n margin-bottom: 20px;\n align-items: flex-start;\n }\n .timeline-date {\n min-width: 110px;\n text-align: right;\n font-family: 'Playfair Display', serif;\n font-size: 0.9rem;\n font-weight: 700;\n color: var(--cobalt-clair);\n padding-top: 2px;\n }\n .timeline-dot {\n min-width: 12px;\n height: 12px;\n background: var(--cobalt-clair);\n border-radius: 50%;\n margin-top: 5px;\n flex-shrink: 0;\n }\n .timeline-content { font-size: 0.97rem; color: #2a2520; }\n .timeline-content strong { color: var(--cobalt); }\n\n .table-container { overflow-x: auto; margin: 2em 0; }\n table { width: 100%; border-collapse: collapse; background: white; font-size: 0.95rem; }\n th { background: var(--cobalt); color: white; padding: 12px 16px; text-align: center; font-family: 'Playfair Display', serif; font-weight: 400; }\n td { padding: 10px 16px; text-align: center; border-bottom: 1px solid var(--gris-clair); color: #2a2520; }\n tr:last-child td { border-bottom: none; }\n tr:nth-child(even) td { background: #f0f2ff; }\n\n .code-block {\n background: #04091a;\n color: #c0d0f0;\n padding: 24px 28px;\n margin: 2em 0;\n font-family: 'Courier New', monospace;\n font-size: 0.88rem;\n line-height: 1.7;\n overflow-x: auto;\n position: relative;\n }\n .code-label { position: absolute; top: 8px; right: 12px; font-size: 0.65rem; letter-spacing: 0.15em; text-transform: uppercase; color: var(--cobalt-clair); font-family: 'Source Serif 4', serif; }\n .code-comment { color: #4a5a8a; }\n .code-keyword { color: #80a0e0; }\n .code-string { color: var(--or-clair); }\n .code-number { color: #80e0b0; }\n .code-function { color: #a0c0ff; }\n\n .exercice {\n background: #04091a;\n color: var(--creme);\n padding: 36px 40px;\n margin: 3em 0;\n }\n .exercice h3 { color: var(--or-clair); font-style: normal; margin-top: 0; margin-bottom: 1em; font-size: 1.1rem; font-weight: 600; }\n .exercice p { color: rgba(245,240,232,0.82); font-size: 0.97rem; margin-bottom: 0.8em; }\n .exercice .correction { border-top: 1px solid rgba(42,74,170,0.4); margin-top: 1.5em; padding-top: 1.2em; }\n .exercice .correction-titre { font-size: 0.7rem; letter-spacing: 0.18em; text-transform: uppercase; color: var(--or-clair); margin-bottom: 0.8em; font-weight: 600; }\n\n blockquote {\n padding: 0 0 0 32px;\n margin: 2em 0;\n position: relative;\n font-style: italic;\n font-size: 1.12rem;\n color: #3a3530;\n }\n blockquote::before {\n content: \"\\201C\";\n position: absolute;\n left: 0; top: -10px;\n font-size: 3.5rem;\n color: var(--cobalt-clair);\n font-family: 'Playfair Display', serif;\n line-height: 1;\n }\n blockquote cite { display: block; font-size: 0.82rem; font-style: normal; letter-spacing: 0.1em; text-transform: uppercase; color: var(--gris); margin-top: 8px; }\n\n .conclusion { border-top: 2px solid var(--noir); margin-top: 3em; padding-top: 2em; }\n\n @media (max-width: 600px) {\n .hero { padding: 50px 20px 40px; }\n .article-body { padding: 40px 20px 60px; }\n .exercice { padding: 24px 20px; }\n .code-block { padding: 16px; font-size: 0.78rem; }\n .timeline-date { min-width: 80px; font-size: 0.8rem; }\n }\n<\/style>\n<\/head>\n<body>\n\n<div class=\"hero\">\n <div class=\"hero-inner\">\n <div class=\"article-rubrique\">Myst\u00e8res des maths \u00b7 Article #13<\/div>\n <h1>Le nombre <em>\u03c0<\/em> :<br>3,14159… mais jusqu’o\u00f9 ?<\/h1>\n <p class=\"hero-intro\">Tout le monde conna\u00eet \u03c0. Personne ne le comprend vraiment. Ce nombre bizarre qui se cache dans chaque cercle \u2014 des rondelles de gombo au march\u00e9 de Cotonou jusqu’aux orbites des plan\u00e8tes \u2014 est l’un des myst\u00e8res les plus profonds et les plus anciens de toute l’humanit\u00e9.<\/p>\n <div class=\"meta\">Par Odilon AKOWANOU \u00b7 MathsVivantes \u00b7 Lecture : 11 min<\/div>\n <\/div>\n<\/div>\n\n<article class=\"article-body\">\n\n <p>\n Prends n’importe quel objet rond autour de toi \u2014 un couvercle de casserole, un pneu de z\u00e9midjan, une assiette, la bouche d’un puits. Mesure sa circonf\u00e9rence (le tour). Mesure son diam\u00e8tre (la largeur). Divise l’un par l’autre. Tu obtiendras toujours, quoi qu’il arrive, le m\u00eame nombre :\n <\/p>\n\n <div class=\"formule\">\u03c0 \u2248 3,14159265358979…<\/div>\n\n <p>\n Toujours. Pour n’importe quel cercle. Partout dans l’univers. C’est vertigineux. Ce nombre \u2014 qu’on appelle pi et qu’on \u00e9crit \u03c0 \u2014 est l’une des constantes les plus fondamentales de la nature. Et ses d\u00e9cimales ne s’arr\u00eatent jamais.\n <\/p>\n\n <h2>\u03c0 : la d\u00e9finition simple<\/h2>\n\n <div class=\"definition\">\n <strong>\u03c0 (pi) :<\/strong> Le rapport constant entre la circonf\u00e9rence d’un cercle et son diam\u00e8tre. Pour tout cercle, quelle que soit sa taille : C \/ d = \u03c0. Ce nombre est universel, irrationnel et transcendant.\n <\/div>\n\n <div class=\"schema-container\">\n <div class=\"schema-titre\">\u2b55 \u03c0 = Circonf\u00e9rence \u00f7 Diam\u00e8tre \u2014 toujours, partout<\/div>\n <svg width=\"100%\" viewBox=\"0 0 520 220\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\">\n <rect width=\"520\" height=\"220\" fill=\"white\"\/>\n\n \n <circle cx=\"90\" cy=\"110\" r=\"50\" fill=\"none\" stroke=\"#2a4aaa\" stroke-width=\"2.5\"\/>\n <line x1=\"40\" y1=\"110\" x2=\"140\" y2=\"110\" stroke=\"#b03a2e\" stroke-width=\"2\" stroke-dasharray=\"4,3\"\/>\n <text x=\"90\" y=\"172\" font-size=\"11\" fill=\"#b03a2e\" text-anchor=\"middle\">d = 100mm<\/text>\n <text x=\"90\" y=\"186\" font-size=\"11\" fill=\"#2a4aaa\" text-anchor=\"middle\">C = 314mm<\/text>\n <text x=\"90\" y=\"205\" font-size=\"12\" fill=\"#c8a010\" text-anchor=\"middle\" font-weight=\"bold\">314\/100 = \u03c0<\/text>\n\n \n <circle cx=\"270\" cy=\"110\" r=\"75\" fill=\"none\" stroke=\"#2a4aaa\" stroke-width=\"2.5\"\/>\n <line x1=\"195\" y1=\"110\" x2=\"345\" y2=\"110\" stroke=\"#b03a2e\" stroke-width=\"2\" stroke-dasharray=\"4,3\"\/>\n <text x=\"270\" y=\"197\" font-size=\"11\" fill=\"#b03a2e\" text-anchor=\"middle\">d = 150mm<\/text>\n <text x=\"270\" y=\"211\" font-size=\"11\" fill=\"#2a4aaa\" text-anchor=\"middle\">C = 471mm<\/text>\n\n \n <circle cx=\"450\" cy=\"110\" r=\"55\" fill=\"none\" stroke=\"#2a4aaa\" stroke-width=\"2.5\"\/>\n <line x1=\"395\" y1=\"110\" x2=\"505\" y2=\"110\" stroke=\"#b03a2e\" stroke-width=\"2\" stroke-dasharray=\"4,3\"\/>\n <text x=\"450\" y=\"177\" font-size=\"11\" fill=\"#b03a2e\" text-anchor=\"middle\">d = 110mm<\/text>\n <text x=\"450\" y=\"191\" font-size=\"11\" fill=\"#2a4aaa\" text-anchor=\"middle\">C = 346mm<\/text>\n\n \n <text x=\"260\" y=\"30\" font-size=\"14\" fill=\"#2a4aaa\" text-anchor=\"middle\" font-family=\"Playfair Display, serif\" font-weight=\"700\">Tailles diff\u00e9rentes \u2014 m\u00eame rapport !<\/text>\n <text x=\"260\" y=\"50\" font-size=\"13\" fill=\"#c8a010\" text-anchor=\"middle\" font-family=\"Playfair Display, serif\">C\/d = \u03c0 \u2248 3,14159… toujours<\/text>\n\n \n <text x=\"270\" y=\"103\" font-size=\"10\" fill=\"#b03a2e\" text-anchor=\"middle\">diam\u00e8tre<\/text>\n <\/svg>\n <\/div>\n\n <h2>Ses premi\u00e8res d\u00e9cimales<\/h2>\n\n <p>\n Voici les 100 premi\u00e8res d\u00e9cimales de \u03c0. Observe-les. Cherches-y un motif, une r\u00e9p\u00e9tition, une logique. Tu n’en trouveras aucune \u2014 parce qu’il n’y en a pas.\n <\/p>\n\n <div class=\"pi-digits\">\n <span class=\"pi-sym\">\u03c0<\/span> = 3.<span class=\"d1\">14159 26535<\/span> <span class=\"d2\">89793 23846<\/span> <span class=\"d3\">26433 83279<\/span> <span class=\"d4\">50288 41971<\/span><br>\n <span class=\"d1\">69399 37510<\/span> <span class=\"d2\">58209 74944<\/span> <span class=\"d3\">59230 78164<\/span> <span class=\"d4\">06286 20899<\/span><br>\n <span class=\"d1\">86280 34825<\/span> <span class=\"d2\">34211 70679<\/span><br>\n <br>\n <span style=\"color:rgba(245,240,232,0.4); font-size:0.8rem;\">… et \u00e7a continue \u00e0 l’infini, sans jamais se r\u00e9p\u00e9ter.<\/span>\n <\/div>\n\n <h2>L’histoire de \u03c0 : 4 000 ans de traque<\/h2>\n\n <div class=\"timeline\">\n <div class=\"timeline-item\">\n <div class=\"timeline-date\">~1650 av. J.-C.<\/div>\n <div class=\"timeline-dot\"><\/div>\n <div class=\"timeline-content\"><strong>\u00c9gypte ancienne (Afrique !)<\/strong> \u2014 Le papyrus Rhind, r\u00e9dig\u00e9 par le scribe Ahm\u00e8s, utilise une approximation de \u03c0 \u2248 3,16. C’est l’une des premi\u00e8res traces \u00e9crites de ce nombre. L’Afrique \u00e9tait l\u00e0 d\u00e8s le d\u00e9but.<\/div>\n <\/div>\n <div class=\"timeline-item\">\n <div class=\"timeline-date\">~250 av. J.-C.<\/div>\n <div class=\"timeline-dot\"><\/div>\n <div class=\"timeline-content\"><strong>Archim\u00e8de de Syracuse<\/strong> \u2014 Il encadre \u03c0 entre 223\/71 et 22\/7 en inscrivant et circonscrivant des polygones \u00e0 96 c\u00f4t\u00e9s dans un cercle. Premi\u00e8re m\u00e9thode rigoureuse.<\/div>\n <\/div>\n <div class=\"timeline-item\">\n <div class=\"timeline-date\">~500 ap. J.-C.<\/div>\n <div class=\"timeline-dot\"><\/div>\n <div class=\"timeline-content\"><strong>Aryabhata (Inde)<\/strong> \u2014 Calcule \u03c0 \u2248 3,1416 avec une pr\u00e9cision remarquable pour l’\u00e9poque.<\/div>\n <\/div>\n <div class=\"timeline-item\">\n <div class=\"timeline-date\">1706<\/div>\n <div class=\"timeline-dot\"><\/div>\n <div class=\"timeline-content\"><strong>William Jones<\/strong> \u2014 Utilise pour la premi\u00e8re fois la lettre grecque <strong>\u03c0<\/strong> pour d\u00e9signer ce rapport. Leonhard Euler popularisera cette notation.<\/div>\n <\/div>\n <div class=\"timeline-item\">\n <div class=\"timeline-date\">1761<\/div>\n <div class=\"timeline-dot\"><\/div>\n <div class=\"timeline-content\"><strong>Johann Lambert<\/strong> \u2014 D\u00e9montre que \u03c0 est <strong>irrationnel<\/strong> : il ne peut pas s’\u00e9crire comme fraction p\/q.<\/div>\n <\/div>\n <div class=\"timeline-item\">\n <div class=\"timeline-date\">1882<\/div>\n <div class=\"timeline-dot\"><\/div>\n <div class=\"timeline-content\"><strong>Ferdinand von Lindemann<\/strong> \u2014 D\u00e9montre que \u03c0 est <strong>transcendant<\/strong> \u2014 il ne satisfait aucune \u00e9quation alg\u00e9brique \u00e0 coefficients entiers. La quadrature du cercle est impossible \u00e0 jamais.<\/div>\n <\/div>\n <div class=\"timeline-item\">\n <div class=\"timeline-date\">2024<\/div>\n <div class=\"timeline-dot\"><\/div>\n <div class=\"timeline-content\"><strong>Record actuel<\/strong> \u2014 \u03c0 est connu \u00e0 plus de <strong>105 000 milliards de d\u00e9cimales<\/strong>. Calcul\u00e9 par des supercalculateurs. Et toujours sans motif r\u00e9p\u00e9titif visible.<\/div>\n <\/div>\n <\/div>\n\n <h2>Pourquoi \u03c0 est irrationnel \u2014 l’intuition<\/h2>\n\n <p>\n Un nombre rationnel s’\u00e9crit comme fraction : 1\/2, 3\/4, 22\/7… Sa repr\u00e9sentation d\u00e9cimale finit ou se r\u00e9p\u00e8te : 1\/3 = 0,333333…, 1\/7 = 0,142857142857…\n <\/p>\n\n <p>\n \u03c0, lui, ne se r\u00e9p\u00e8te jamais. Ses d\u00e9cimales sont ap\u00e9riodiques \u2014 elles ne forment aucun motif qui se r\u00e9p\u00e8te, aussi loin qu’on aille. Ce n’est pas un hasard ni un manque de calcul : c’est une propri\u00e9t\u00e9 math\u00e9matique profonde, <em>d\u00e9montr\u00e9e<\/em>.\n <\/p>\n\n <div class=\"encadre\">\n <span class=\"encadre-titre\">\ud83d\udca1 Intuition de l’irrationalit\u00e9<\/span>\n <p>Un cercle \u00ab\u00a0parfait\u00a0\u00bb est une forme g\u00e9om\u00e9trique id\u00e9ale \u2014 sans angle, sans rupture, infiniment lisse. Mesurer sa circonf\u00e9rence avec des unit\u00e9s enti\u00e8res, c’est essayer de capturer quelque chose de continu avec des mots discrets. Il y a une incompatibilit\u00e9 fondamentale entre la rondeur parfaite du cercle et les fractions faites d’entiers.<\/p>\n <p>C’est cette incompatibilit\u00e9 qui se manifeste dans les d\u00e9cimales infinies de \u03c0.<\/p>\n <\/div>\n\n <h2>Comment calculer \u03c0 \u2014 trois m\u00e9thodes fascinantes<\/h2>\n\n <h3>M\u00e9thode 1 \u2014 Archim\u00e8de : les polygones<\/h3>\n\n <p>\n Archim\u00e8de a encadr\u00e9 \u03c0 en inscrivant un polygone \u00e0 l’int\u00e9rieur d’un cercle et en en circonscrivant un autre \u00e0 l’ext\u00e9rieur. Plus on augmente le nombre de c\u00f4t\u00e9s, plus les deux polygones se rapprochent du cercle, et plus l’encadrement de \u03c0 devient pr\u00e9cis.\n <\/p>\n\n <div class=\"etape\"><span class=\"etape-numero\">6 c\u00f4t\u00e9s<\/span> 3 < \u03c0 < 3,464<\/div>\n <div class=\"etape\"><span class=\"etape-numero\">12 c\u00f4t\u00e9s<\/span> 3,105 < \u03c0 < 3,215<\/div>\n <div class=\"etape\"><span class=\"etape-numero\">96 c\u00f4t\u00e9s<\/span> 3,1408 < \u03c0 < 3,1429 (Archim\u00e8de)<\/div>\n <div class=\"etape\"><span class=\"etape-numero\">\u221e c\u00f4t\u00e9s<\/span> \u03c0 = 3,14159265… (limite exacte)<\/div>\n\n <h3>M\u00e9thode 2 \u2014 La s\u00e9rie de Leibniz<\/h3>\n\n <p>\n Au XVIIe si\u00e8cle, Leibniz d\u00e9couvre une formule stup\u00e9fiante : \u03c0 peut s’exprimer comme une somme infinie de fractions simples !\n <\/p>\n\n <div class=\"formule\">\u03c0\/4 = 1 \u2212 1\/3 + 1\/5 \u2212 1\/7 + 1\/9 \u2212 1\/11 + …<\/div>\n\n <p>\n Elle converge tr\u00e8s lentement \u2014 il faut des millions de termes pour avoir 6 d\u00e9cimales exactes. Mais la beaut\u00e9 de la formule est saisissante : les nombres impairs 1, 3, 5, 7, 9… cachent \u03c0 en eux.\n <\/p>\n\n <h3>M\u00e9thode 3 \u2014 Monte Carlo : le hasard calcule \u03c0<\/h3>\n\n <p>\n Voici la m\u00e9thode la plus \u00e9tonnante : on peut calculer \u03c0 en lan\u00e7ant des points au hasard ! Si on lance des points al\u00e9atoires dans un carr\u00e9 de c\u00f4t\u00e9 1, la proportion de points qui tombent dans le quart de cercle inscrit converge vers \u03c0\/4.\n <\/p>\n\n <div class=\"schema-container\">\n <div class=\"schema-titre\">\ud83c\udfb2 M\u00e9thode Monte Carlo \u2014 le hasard approche \u03c0<\/div>\n <svg width=\"100%\" viewBox=\"0 0 360 300\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\">\n <rect width=\"360\" height=\"300\" fill=\"white\"\/>\n\n \n <rect x=\"80\" y=\"40\" width=\"200\" height=\"200\" fill=\"#f8f5ef\" stroke=\"#2a4aaa\" stroke-width=\"2\"\/>\n \n <path d=\"M 80,240 A 200,200 0 0,1 280,40\" fill=\"#eef0ff\" stroke=\"#2a4aaa\" stroke-width=\"2\"\/>\n\n \n <circle cx=\"130\" cy=\"80\" r=\"4\" fill=\"#2a4aaa\" opacity=\"0.8\"\/>\n <circle cx=\"160\" cy=\"100\" r=\"4\" fill=\"#2a4aaa\" opacity=\"0.8\"\/>\n <circle cx=\"110\" cy=\"140\" r=\"4\" fill=\"#2a4aaa\" opacity=\"0.8\"\/>\n <circle cx=\"180\" cy=\"70\" r=\"4\" fill=\"#2a4aaa\" opacity=\"0.8\"\/>\n <circle cx=\"140\" cy=\"160\" r=\"4\" fill=\"#2a4aaa\" opacity=\"0.8\"\/>\n <circle cx=\"200\" cy=\"110\" r=\"4\" fill=\"#2a4aaa\" opacity=\"0.8\"\/>\n <circle cx=\"120\" cy=\"110\" r=\"4\" fill=\"#2a4aaa\" opacity=\"0.8\"\/>\n <circle cx=\"170\" cy=\"140\" r=\"4\" fill=\"#2a4aaa\" opacity=\"0.8\"\/>\n <circle cx=\"150\" cy=\"200\" r=\"4\" fill=\"#2a4aaa\" opacity=\"0.8\"\/>\n <circle cx=\"220\" cy=\"150\" r=\"4\" fill=\"#2a4aaa\" opacity=\"0.8\"\/>\n <circle cx=\"100\" cy=\"180\" r=\"4\" fill=\"#2a4aaa\" opacity=\"0.8\"\/>\n <circle cx=\"240\" cy=\"130\" r=\"4\" fill=\"#2a4aaa\" opacity=\"0.8\"\/>\n\n \n <circle cx=\"250\" cy=\"60\" r=\"4\" fill=\"#b03a2e\" opacity=\"0.8\"\/>\n <circle cx=\"260\" cy=\"180\" r=\"4\" fill=\"#b03a2e\" opacity=\"0.8\"\/>\n <circle cx=\"270\" cy=\"210\" r=\"4\" fill=\"#b03a2e\" opacity=\"0.8\"\/>\n <circle cx=\"240\" cy=\"220\" r=\"4\" fill=\"#b03a2e\" opacity=\"0.8\"\/>\n\n \n <circle cx=\"100\" cy=\"268\" r=\"5\" fill=\"#2a4aaa\"\/>\n <text x=\"112\" y=\"272\" font-size=\"11\" fill=\"#6b6560\">Dans le cercle (12)<\/text>\n <circle cx=\"220\" cy=\"268\" r=\"5\" fill=\"#b03a2e\"\/>\n <text x=\"232\" y=\"272\" font-size=\"11\" fill=\"#6b6560\">Hors (4)<\/text>\n\n \n <text x=\"180\" y=\"292\" font-size=\"11\" fill=\"#2a4aaa\" text-anchor=\"middle\" font-family=\"Playfair Display, serif\">\u03c0 \u2248 4 \u00d7 12\/16 = 3,0<\/text>\n <\/svg>\n <\/div>\n\n <p>\n Plus on lance de points, plus l’approximation est pr\u00e9cise. Avec 10 millions de points, on obtient \u03c0 avec 3-4 d\u00e9cimales exactes. C’est la magie de la m\u00e9thode Monte Carlo \u2014 et c’est aussi la base de nombreux algorithmes en data science et en finance.\n <\/p>\n\n <h2>\u03c0 dans les formules \u2014 il est partout<\/h2>\n\n <p>\n Ce qui rend \u03c0 encore plus myst\u00e9rieux, c’est qu’il appara\u00eet dans des formules qui n’ont apparemment rien \u00e0 voir avec les cercles :\n <\/p>\n\n <div class=\"table-container\">\n <table>\n <tr>\n <th>Formule<\/th>\n <th>Domaine<\/th>\n <th>Pourquoi c’est surprenant<\/th>\n <\/tr>\n <tr>\n <td style=\"font-family:'Playfair Display',serif;\">C = 2\u03c0r<\/td>\n <td>G\u00e9om\u00e9trie<\/td>\n <td>Normal \u2014 c’est la d\u00e9finition<\/td>\n <\/tr>\n <tr>\n <td style=\"font-family:'Playfair Display',serif;\">A = \u03c0r\u00b2<\/td>\n <td>G\u00e9om\u00e9trie<\/td>\n <td>Aire du cercle<\/td>\n <\/tr>\n <tr>\n <td style=\"font-family:'Playfair Display',serif;\">e\u2071\u1d56\u2071 + 1 = 0<\/td>\n <td>Analyse complexe<\/td>\n <td>\ud83d\ude31 \u03c0, e, i, 1 et 0 dans une seule formule !<\/td>\n <\/tr>\n <tr>\n <td style=\"font-family:'Playfair Display',serif;\">\u222b\u208b\u221e\u207a\u221e e\u207b\u02e3\u00b2 dx = \u221a\u03c0<\/td>\n <td>Probabilit\u00e9s<\/td>\n <td>\u03c0 dans la loi normale \u2014 sans cercle en vue !<\/td>\n <\/tr>\n <tr>\n <td style=\"font-family:'Playfair Display',serif;\">1\/1\u00b2 + 1\/2\u00b2 + 1\/3\u00b2 + … = \u03c0\u00b2\/6<\/td>\n <td>S\u00e9ries<\/td>\n <td>Les carr\u00e9s des entiers cachent \u03c0 !<\/td>\n <\/tr>\n <tr>\n <td style=\"font-family:'Playfair Display',serif;\">T = 2\u03c0\u221a(L\/g)<\/td>\n <td>Physique (pendule)<\/td>\n <td>La p\u00e9riode d’un pendule contient \u03c0<\/td>\n <\/tr>\n <\/table>\n <\/div>\n\n <div class=\"encadre-histoire encadre\">\n <span class=\"encadre-titre\">\ud83d\ude31 La formule la plus belle des maths<\/span>\n <p>\n La formule <strong>e\u2071\u1d56\u2071 + 1 = 0<\/strong> \u2014 appel\u00e9e identit\u00e9 d’Euler \u2014 est r\u00e9guli\u00e8rement \u00e9lue \u00ab\u00a0plus belle formule math\u00e9matique\u00a0\u00bb par les math\u00e9maticiens du monde entier.\n <\/p>\n <p>\n Elle r\u00e9unit en une seule \u00e9quation les cinq nombres les plus importants des math\u00e9matiques : <strong>e<\/strong> (la constante de la croissance naturelle), <strong>i<\/strong> (le nombre imaginaire, racine de \u22121), <strong>\u03c0<\/strong> (notre h\u00e9ros du jour), <strong>1<\/strong> (l’unit\u00e9 multiplicative) et <strong>0<\/strong> (l’unit\u00e9 additive).\n <\/p>\n <p>\n Ce n’est pas une co\u00efncidence. C’est la signature d’une unit\u00e9 profonde qui traverse toutes les math\u00e9matiques. Et \u03c0 est au c\u0153ur de tout \u00e7a.\n <\/p>\n <\/div>\n\n <h2>Le code Python : calculons \u03c0 nous-m\u00eames<\/h2>\n\n <div class=\"code-block\">\n <span class=\"code-label\">Python<\/span>\n<span class=\"code-comment\"># Trois fa\u00e7ons de calculer \u03c0 en Python<\/span>\n<span class=\"code-keyword\">import<\/span> random\n<span class=\"code-keyword\">import<\/span> math\n\n<span class=\"code-comment\"># — M\u00e9thode 1 : S\u00e9rie de Leibniz —<\/span>\n<span class=\"code-keyword\">def<\/span> <span class=\"code-function\">pi_leibniz<\/span>(n_termes):\n <span class=\"code-string\">\u00ab\u00a0\u00a0\u00bb\u00a0\u00bb\u03c0\/4 = 1 – 1\/3 + 1\/5 – 1\/7 + …\u00a0\u00bb\u00a0\u00bb\u00a0\u00bb<\/span>\n resultat = <span class=\"code-number\">0<\/span>\n signe = <span class=\"code-number\">1<\/span>\n <span class=\"code-keyword\">for<\/span> k <span class=\"code-keyword\">in<\/span> <span class=\"code-function\">range<\/span>(n_termes):\n resultat += signe \/ (<span class=\"code-number\">2<\/span>*k + <span class=\"code-number\">1<\/span>)\n signe *= –<span class=\"code-number\">1<\/span>\n <span class=\"code-keyword\">return<\/span> <span class=\"code-number\">4<\/span> * resultat\n\n<span class=\"code-comment\"># — M\u00e9thode 2 : Monte Carlo —<\/span>\n<span class=\"code-keyword\">def<\/span> <span class=\"code-function\">pi_monte_carlo<\/span>(n_points):\n <span class=\"code-string\">\u00ab\u00a0\u00a0\u00bb\u00a0\u00bbLance n points al\u00e9atoires, compte ceux dans le quart de cercle\u00a0\u00bb\u00a0\u00bb\u00a0\u00bb<\/span>\n dans_cercle = <span class=\"code-number\">0<\/span>\n <span class=\"code-keyword\">for<\/span> _ <span class=\"code-keyword\">in<\/span> <span class=\"code-function\">range<\/span>(n_points):\n x = random.<span class=\"code-function\">uniform<\/span>(<span class=\"code-number\">0<\/span>, <span class=\"code-number\">1<\/span>)\n y = random.<span class=\"code-function\">uniform<\/span>(<span class=\"code-number\">0<\/span>, <span class=\"code-number\">1<\/span>)\n <span class=\"code-keyword\">if<\/span> x**<span class=\"code-number\">2<\/span> + y**<span class=\"code-number\">2<\/span> <= <span class=\"code-number\">1<\/span>:\n dans_cercle += <span class=\"code-number\">1<\/span>\n <span class=\"code-keyword\">return<\/span> <span class=\"code-number\">4<\/span> * dans_cercle \/ n_points\n\n<span class=\"code-comment\"># — M\u00e9thode 3 : Formule de Nilakantha (converge vite !) —<\/span>\n<span class=\"code-keyword\">def<\/span> <span class=\"code-function\">pi_nilakantha<\/span>(n_termes):\n <span class=\"code-string\">\u00ab\u00a0\u00a0\u00bb\u00a0\u00bb\u03c0 = 3 + 4\/(2\u00d73\u00d74) – 4\/(4\u00d75\u00d76) + 4\/(6\u00d77\u00d78) – …\u00a0\u00bb\u00a0\u00bb\u00a0\u00bb<\/span>\n resultat = <span class=\"code-number\">3.0<\/span>\n signe = <span class=\"code-number\">1<\/span>\n <span class=\"code-keyword\">for<\/span> k <span class=\"code-keyword\">in<\/span> <span class=\"code-function\">range<\/span>(<span class=\"code-number\">1<\/span>, n_termes + <span class=\"code-number\">1<\/span>):\n n = <span class=\"code-number\">2<\/span> * k\n resultat += signe * <span class=\"code-number\">4<\/span> \/ (n * (n+<span class=\"code-number\">1<\/span>) * (n+<span class=\"code-number\">2<\/span>))\n signe *= –<span class=\"code-number\">1<\/span>\n <span class=\"code-keyword\">return<\/span> resultat\n\n<span class=\"code-comment\"># — Comparaison —<\/span>\n<span class=\"code-function\">print<\/span>(<span class=\"code-string\">f\u00a0\u00bb\u03c0 r\u00e9el = {math.pi:.10f}\u00a0\u00bb<\/span>)\n<span class=\"code-function\">print<\/span>(<span class=\"code-string\">f\u00a0\u00bbLeibniz (10 000 termes) = {pi_leibniz(10000):.10f}\u00a0\u00bb<\/span>)\n<span class=\"code-function\">print<\/span>(<span class=\"code-string\">f\u00a0\u00bbMonte Carlo (1M points) = {pi_monte_carlo(1000000):.10f}\u00a0\u00bb<\/span>)\n<span class=\"code-function\">print<\/span>(<span class=\"code-string\">f\u00a0\u00bbNilakantha (100 termes) = {pi_nilakantha(100):.10f}\u00a0\u00bb<\/span>)\n\n<span class=\"code-comment\"># Convergence de Monte Carlo selon le nombre de points<\/span>\n<span class=\"code-function\">print<\/span>(<span class=\"code-string\">\u00ab\u00a0\\nConvergence Monte Carlo :\u00a0\u00bb<\/span>)\n<span class=\"code-keyword\">for<\/span> n <span class=\"code-keyword\">in<\/span> [<span class=\"code-number\">100<\/span>, <span class=\"code-number\">1000<\/span>, <span class=\"code-number\">10000<\/span>, <span class=\"code-number\">100000<\/span>, <span class=\"code-number\">1000000<\/span>]:\n approx = <span class=\"code-function\">pi_monte_carlo<\/span>(n)\n erreur = <span class=\"code-function\">abs<\/span>(approx – math.pi)\n <span class=\"code-function\">print<\/span>(<span class=\"code-string\">f\u00a0\u00bb n={n:8d} \u2192 \u03c0 \u2248 {approx:.6f} | erreur = {erreur:.6f}\u00a0\u00bb<\/span>)\n <\/div>\n\n <blockquote>\n \u03c0 est comme l’horizon \u2014 plus tu t’en approches, plus tu r\u00e9alises qu’il s’\u00e9tend \u00e0 l’infini. Et pourtant, tu l’utilises chaque fois que tu traces un cercle.\n <cite>\u2014 M\u00e9ditation math\u00e9matique<\/cite>\n <\/blockquote>\n\n \n <div class=\"exercice\">\n <h3>\u270f\ufe0f Exercice corrig\u00e9 \u2014 du primaire au lyc\u00e9e<\/h3>\n <p><strong>Niveau primaire\/6\u00e8me :<\/strong> Le grand bassin rond du quartier Agla \u00e0 Cotonou a un diam\u00e8tre de 14 m\u00e8tres. Calcule sa circonf\u00e9rence. (Utilise \u03c0 \u2248 22\/7)<\/p>\n <p><strong>Niveau 4\u00e8me\/3\u00e8me :<\/strong> Une roue de z\u00e9midjan a un rayon de 28 cm. Combien de tours fait-elle pour parcourir 1 km ? (\u03c0 \u2248 3,14)<\/p>\n <p><strong>Niveau lyc\u00e9e :<\/strong> En utilisant les 4 premiers termes de la s\u00e9rie de Leibniz, calcule une approximation de \u03c0. Quelle est l’erreur relative par rapport \u00e0 \u03c0 \u2248 3,14159 ?<\/p>\n\n <div class=\"correction\">\n <div class=\"correction-titre\">\u25b8 Correction<\/div>\n <p><strong>Niveau primaire\/6\u00e8me :<\/strong><\/p>\n <p>C = \u03c0 \u00d7 d = (22\/7) \u00d7 14 = 22 \u00d7 2 = <strong>44 m\u00e8tres<\/strong><\/p>\n\n <p><strong>Niveau 4\u00e8me\/3\u00e8me :<\/strong><\/p>\n <p>Circonf\u00e9rence d’une roue = 2\u03c0r = 2 \u00d7 3,14 \u00d7 0,28 = <strong>1,7584 m<\/strong><\/p>\n <p>1 km = 1000 m<\/p>\n <p>Nombre de tours = 1000 \/ 1,7584 \u2248 <strong>568,7 tours<\/strong><\/p>\n\n <p><strong>Niveau lyc\u00e9e :<\/strong><\/p>\n <p>S\u00e9rie de Leibniz : \u03c0\/4 = 1 \u2212 1\/3 + 1\/5 \u2212 1\/7 + …<\/p>\n <p>4 termes : \u03c0\/4 \u2248 1 \u2212 0,333 + 0,200 \u2212 0,143 = 0,724<\/p>\n <p>\u03c0 \u2248 4 \u00d7 0,724 = <strong>2,896<\/strong><\/p>\n <p>Erreur relative = |2,896 \u2212 3,14159| \/ 3,14159 \u2248 <strong>7,8%<\/strong><\/p>\n <p>\u2192 La s\u00e9rie de Leibniz converge tr\u00e8s lentement. Il faut des milliers de termes pour avoir 3 d\u00e9cimales exactes ! \u2705<\/p>\n <\/div>\n <\/div>\n\n <div class=\"conclusion\">\n <h2>Ce qu’on retient<\/h2>\n <p>\n \u03c0 est partout \u2014 dans les cercles, les ondes, les probabilit\u00e9s, les pendules, les nombres complexes. Il est irrationnel, transcendant, et ses d\u00e9cimales n’ont aucun motif connu. On le conna\u00eet \u00e0 plus de 100 000 milliards de chiffres et on n’en a toujours pas vu la fin. Et pourtant, pour construire une maison ronde, une citerne ou un puits \u00e0 Cotonou, \u03c0 \u2248 3,14 suffit amplement.\n <\/p>\n <p>\n C’est \u00e7a la beaut\u00e9 de \u03c0 : il est \u00e0 la fois infiniment myst\u00e9rieux et imm\u00e9diatement utile. Un pied dans l’abstraction pure, un autre dans la r\u00e9alit\u00e9 quotidienne. Exactement comme les math\u00e9matiques elles-m\u00eames.\n <\/p>\n <p>\n Dans le prochain article, nous plongerons dans <strong>les tontines b\u00e9ninoises \u2014 un mod\u00e8le math\u00e9matique parfait<\/strong>. Int\u00e9r\u00eats compos\u00e9s, valeur temporelle de l’argent, th\u00e9orie des jeux \u2014 tout \u00e7a se cache dans cette pratique que nos mamans connaissent depuis toujours.\n <\/p>\n <\/div>\n\n<\/article>\n\n<\/body>\n<\/html>\n","protected":false},"excerpt":{"rendered":"<p>Le nombre \u03c0 : 3,14159… mais jusqu’o\u00f9 ? \u2014 MathsVivantes Myst\u00e8res des maths \u00b7 Article #13 Le nombre \u03c0 :3,14159… […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_uag_custom_page_level_css":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[8],"tags":[],"class_list":["post-132","post","type-post","status-publish","format-standard","hentry","category-fondements"],"yoast_head":"\n<title>Le nombre Pi - AfrikIntelligent<\/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:\/\/vmi3217629.contaboserver.net\/?p=132\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Le nombre Pi - AfrikIntelligent\" \/>\n<meta property=\"og:description\" content=\"Le nombre \u03c0 : 3,14159… mais jusqu’o\u00f9 ? \u2014 MathsVivantes Myst\u00e8res des maths \u00b7 Article #13 Le nombre \u03c0 :3,14159… […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/vmi3217629.contaboserver.net\/?p=132\" \/>\n<meta property=\"og:site_name\" content=\"AfrikIntelligent\" \/>\n<meta property=\"article:published_time\" content=\"2026-04-29T06:00:38+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-04-29T06:00:39+00:00\" \/>\n<meta name=\"author\" content=\"Odilon\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u00c9crit par\" \/>\n\t<meta name=\"twitter:data1\" content=\"Odilon\" \/>\n\t<meta name=\"twitter:label2\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data2\" content=\"9 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=132#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=132\"},\"author\":{\"name\":\"Odilon\",\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/#\\\/schema\\\/person\\\/a3da39574d729b6b3ff7514ccc055923\"},\"headline\":\"Le nombre Pi\",\"datePublished\":\"2026-04-29T06:00:38+00:00\",\"dateModified\":\"2026-04-29T06:00:39+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=132\"},\"wordCount\":1153,\"commentCount\":0,\"articleSection\":[\"Fondements\"],\"inLanguage\":\"fr-FR\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=132#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=132\",\"url\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=132\",\"name\":\"Le nombre Pi - AfrikIntelligent\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/#website\"},\"datePublished\":\"2026-04-29T06:00:38+00:00\",\"dateModified\":\"2026-04-29T06:00:39+00:00\",\"author\":{\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/#\\\/schema\\\/person\\\/a3da39574d729b6b3ff7514ccc055923\"},\"breadcrumb\":{\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=132#breadcrumb\"},\"inLanguage\":\"fr-FR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=132\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=132#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Accueil\",\"item\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Le nombre Pi\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/#website\",\"url\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/\",\"name\":\"AfrikIntelligent\",\"description\":\"Append autrement\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"fr-FR\"},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/#\\\/schema\\\/person\\\/a3da39574d729b6b3ff7514ccc055923\",\"name\":\"Odilon\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"fr-FR\",\"@id\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/57bcd6a76fa395ae5e994943b66ccd3dd7e71cd0b1b77b351986e88c27801523?s=96&d=mm&r=g\",\"url\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/57bcd6a76fa395ae5e994943b66ccd3dd7e71cd0b1b77b351986e88c27801523?s=96&d=mm&r=g\",\"contentUrl\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/57bcd6a76fa395ae5e994943b66ccd3dd7e71cd0b1b77b351986e88c27801523?s=96&d=mm&r=g\",\"caption\":\"Odilon\"},\"sameAs\":[\"https:\\\/\\\/vmi3217629.contaboserver.net\"],\"url\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?author=1\"}]}<\/script>\n","yoast_head_json":{"title":"Le nombre Pi - AfrikIntelligent","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/vmi3217629.contaboserver.net\/?p=132","og_locale":"fr_FR","og_type":"article","og_title":"Le nombre Pi - AfrikIntelligent","og_description":"Le nombre \u03c0 : 3,14159… mais jusqu’o\u00f9 ? \u2014 MathsVivantes Myst\u00e8res des maths \u00b7 Article #13 Le nombre \u03c0 :3,14159… […]","og_url":"https:\/\/vmi3217629.contaboserver.net\/?p=132","og_site_name":"AfrikIntelligent","article_published_time":"2026-04-29T06:00:38+00:00","article_modified_time":"2026-04-29T06:00:39+00:00","author":"Odilon","twitter_card":"summary_large_image","twitter_misc":{"\u00c9crit par":"Odilon","Dur\u00e9e de lecture estim\u00e9e":"9 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/vmi3217629.contaboserver.net\/?p=132#article","isPartOf":{"@id":"https:\/\/vmi3217629.contaboserver.net\/?p=132"},"author":{"name":"Odilon","@id":"https:\/\/vmi3217629.contaboserver.net\/#\/schema\/person\/a3da39574d729b6b3ff7514ccc055923"},"headline":"Le nombre Pi","datePublished":"2026-04-29T06:00:38+00:00","dateModified":"2026-04-29T06:00:39+00:00","mainEntityOfPage":{"@id":"https:\/\/vmi3217629.contaboserver.net\/?p=132"},"wordCount":1153,"commentCount":0,"articleSection":["Fondements"],"inLanguage":"fr-FR","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/vmi3217629.contaboserver.net\/?p=132#respond"]}]},{"@type":"WebPage","@id":"https:\/\/vmi3217629.contaboserver.net\/?p=132","url":"https:\/\/vmi3217629.contaboserver.net\/?p=132","name":"Le nombre Pi - AfrikIntelligent","isPartOf":{"@id":"https:\/\/vmi3217629.contaboserver.net\/#website"},"datePublished":"2026-04-29T06:00:38+00:00","dateModified":"2026-04-29T06:00:39+00:00","author":{"@id":"https:\/\/vmi3217629.contaboserver.net\/#\/schema\/person\/a3da39574d729b6b3ff7514ccc055923"},"breadcrumb":{"@id":"https:\/\/vmi3217629.contaboserver.net\/?p=132#breadcrumb"},"inLanguage":"fr-FR","potentialAction":[{"@type":"ReadAction","target":["https:\/\/vmi3217629.contaboserver.net\/?p=132"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/vmi3217629.contaboserver.net\/?p=132#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Accueil","item":"https:\/\/vmi3217629.contaboserver.net\/"},{"@type":"ListItem","position":2,"name":"Le nombre Pi"}]},{"@type":"WebSite","@id":"https:\/\/vmi3217629.contaboserver.net\/#website","url":"https:\/\/vmi3217629.contaboserver.net\/","name":"AfrikIntelligent","description":"Append autrement","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/vmi3217629.contaboserver.net\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"fr-FR"},{"@type":"Person","@id":"https:\/\/vmi3217629.contaboserver.net\/#\/schema\/person\/a3da39574d729b6b3ff7514ccc055923","name":"Odilon","image":{"@type":"ImageObject","inLanguage":"fr-FR","@id":"https:\/\/secure.gravatar.com\/avatar\/57bcd6a76fa395ae5e994943b66ccd3dd7e71cd0b1b77b351986e88c27801523?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/57bcd6a76fa395ae5e994943b66ccd3dd7e71cd0b1b77b351986e88c27801523?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/57bcd6a76fa395ae5e994943b66ccd3dd7e71cd0b1b77b351986e88c27801523?s=96&d=mm&r=g","caption":"Odilon"},"sameAs":["https:\/\/vmi3217629.contaboserver.net"],"url":"https:\/\/vmi3217629.contaboserver.net\/?author=1"}]}},"uagb_featured_image_src":{"full":false,"thumbnail":false,"medium":false,"medium_large":false,"large":false,"1536x1536":false,"2048x2048":false},"uagb_author_info":{"display_name":"Odilon","author_link":"https:\/\/vmi3217629.contaboserver.net\/?author=1"},"uagb_comment_info":0,"uagb_excerpt":"Le nombre \u03c0 : 3,14159… mais jusqu’o\u00f9 ? \u2014 MathsVivantes Myst\u00e8res des maths \u00b7 Article #13 Le nombre \u03c0 :3,14159… […]","_links":{"self":[{"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=\/wp\/v2\/posts\/132","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=132"}],"version-history":[{"count":1,"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=\/wp\/v2\/posts\/132\/revisions"}],"predecessor-version":[{"id":133,"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=\/wp\/v2\/posts\/132\/revisions\/133"}],"wp:attachment":[{"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=132"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=132"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=132"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}