{"id":9942,"date":"2024-07-04T17:47:55","date_gmt":"2024-07-04T15:47:55","guid":{"rendered":"https:\/\/www.mathweb.fr\/euclide\/?p=9942"},"modified":"2024-07-04T17:47:58","modified_gmt":"2024-07-04T15:47:58","slug":"un-triangle-de-pascal-colore-en-python","status":"publish","type":"post","link":"https:\/\/www.mathweb.fr\/euclide\/2024\/07\/04\/un-triangle-de-pascal-colore-en-python\/","title":{"rendered":"Un triangle de Pascal color\u00e9 en Python"},"content":{"rendered":"\n<p class=\"is-style-Paragraph-paragraph wp-block-paragraph\">Faire un triangle de Pascal color\u00e9 en Python est un bon moyen de s&#8217;occuper alors que les vacances sont l\u00e0. Je vais vous pr\u00e9senter plusieurs designs, mon pr\u00e9f\u00e9r\u00e9 allant au dernier.<\/p>\n\n\n\n<!--more-->\n\n\n\n<p class=\"is-style-Paragraph-paragraph wp-block-paragraph\">Alors oui, je sais, j&#8217;avais d\u00e9j\u00e0 propos\u00e9 une m\u00e9thode pour construire le triangle de Pascal dans <a href=\"https:\/\/www.mathweb.fr\/euclide\/2019\/05\/26\/triangle-de-pascal-construit-avec-python-et-latex\/\" target=\"_blank\" rel=\"noreferrer noopener\">ce post<\/a>. Mais j&#8217;avais envie d&#8217;explorer de nouvelles contr\u00e9es informatiques. Je ne voulais pas passer par \\(\\LaTeX\\).<\/p>\n\n\n\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_84 counter-hierarchy ez-toc-counter ez-toc-white ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Au menu sur cette page...<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.mathweb.fr\/euclide\/2024\/07\/04\/un-triangle-de-pascal-colore-en-python\/#Un_triangle_de_Pascal_colore_en_Python_les_premices\" >Un triangle de Pascal color\u00e9 en Python: les pr\u00e9mices<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.mathweb.fr\/euclide\/2024\/07\/04\/un-triangle-de-pascal-colore-en-python\/#Un_triangle_de_Pascal_colore_en_Python_les_differentes_propositions\" >Un triangle de Pascal color\u00e9 en Python: les diff\u00e9rentes propositions<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.mathweb.fr\/euclide\/2024\/07\/04\/un-triangle-de-pascal-colore-en-python\/#Un_triangle_de_Pascal_colore_en_Python_script_1\" >Un triangle de Pascal color\u00e9 en Python: script 1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.mathweb.fr\/euclide\/2024\/07\/04\/un-triangle-de-pascal-colore-en-python\/#Script_2_cases_carrees_triangle_aligne_a_gauche\" >Script 2: cases carr\u00e9es, triangle align\u00e9 \u00e0 gauche<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.mathweb.fr\/euclide\/2024\/07\/04\/un-triangle-de-pascal-colore-en-python\/#Script_3_cases_carrees_triangle_centre\" >Script 3: cases carr\u00e9es, triangle centr\u00e9<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.mathweb.fr\/euclide\/2024\/07\/04\/un-triangle-de-pascal-colore-en-python\/#Script_4_cases_avec_coins_arrondis_cases_qui_se_chevauchent\" >Script 4: cases avec coins arrondis, cases qui se chevauchent<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.mathweb.fr\/euclide\/2024\/07\/04\/un-triangle-de-pascal-colore-en-python\/#Script_5_cases_a_coins_arrondis_nombres_qui_sadaptent\" >Script 5: cases \u00e0 coins arrondis, nombres qui s&#8217;adaptent<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Un_triangle_de_Pascal_colore_en_Python_les_premices\"><\/span>Un triangle de Pascal color\u00e9 en Python: les pr\u00e9mices<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"is-style-Paragraph-paragraph wp-block-paragraph\">Faire un triangle de Pascal en Python, c&#8217;est pas trop compliqu\u00e9. Mais rendre le r\u00e9sultat attrayant, joli, et donc en mode graphique, c&#8217;est mieux&#8230; Il y a plusieurs techniques: <\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>pygame (pas g\u00e9nial \u00e0 mon go\u00fbt), <\/li>\n\n\n\n<li>tkinter (beurk! pour si peu ?)<\/li>\n\n\n\n<li>via \\(\\LaTeX\\) et TiKZ (mouais&#8230; mais bon! je veux \u00e9viter justement!)<\/li>\n\n\n\n<li>matplotlib&#8230; Ouais!<\/li>\n<\/ul>\n\n\n\n<p class=\"is-style-Paragraph-paragraph wp-block-paragraph\">On va partir sur matplotlib!<\/p>\n\n\n\n<p class=\"is-style-Paragraph-paragraph wp-block-paragraph\">Le cahier des charges est simple:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>un triangle de Pascal centr\u00e9 ou pas<\/li>\n\n\n\n<li>des couleurs de fond pour chaque &#8220;cases&#8221;<\/li>\n\n\n\n<li>des couleurs en fonction de la position du nombre par rapport au centre des lignes<\/li>\n\n\n\n<li>une sauvegarde en haute d\u00e9finition de l&#8217;image.<\/li>\n<\/ul>\n\n\n\n<p class=\"is-style-Paragraph-paragraph wp-block-paragraph\">Je pr\u00e9cise que je ne vais pas d\u00e9finir ce qu&#8217;est le triangle de Pascal: z&#8217;avez cas regarder sur <a href=\"https:\/\/fr.wikipedia.org\/wiki\/Triangle_de_Pascal\" target=\"_blank\" rel=\"noreferrer noopener\">wikipedia<\/a>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Un_triangle_de_Pascal_colore_en_Python_les_differentes_propositions\"><\/span>Un triangle de Pascal color\u00e9 en Python: les diff\u00e9rentes propositions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Je vais vous pr\u00e9senter six scripts.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Un_triangle_de_Pascal_colore_en_Python_script_1\"><\/span>Un triangle de Pascal color\u00e9 en Python: script 1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">import numpy as np\nimport matplotlib.pyplot as plt\nimport matplotlib.colors as mcolors\n\ndef pascal_triangle(n):\n    \"\"\"Generate the first n rows of Pascal's triangle.\"\"\"\n    triangle = np.zeros((n, n), dtype=int)\n    for i in range(n):\n        triangle[i, 0] = 1\n        for j in range(1, i + 1):\n            triangle[i, j] = triangle[i - 1, j - 1] + triangle[i - 1, j]\n    return triangle\n\ndef plot_pascal_triangle(n):\n    \"\"\"Plot the first n rows of Pascal's triangle with color.\"\"\"\n    triangle = pascal_triangle(n)\n    \n    fig, ax = plt.subplots(figsize=(10, 10))\n    ax.axis('off')\n\n    # Define a color map\n    colors = plt.cm.viridis(np.linspace(0, 1, n))\n    \n    for i in range(n):\n        for j in range(i + 1):\n            x = i\n            y = -i \/ 2 + j\n            color = colors[i]\n            intensity = 1 - abs(j - i \/ 2) \/ (i \/ 2 + 1)\n            ax.text(y, -x, triangle[i, j], ha='center', va='center',\n                    bbox=dict(facecolor=color * intensity, edgecolor='none', boxstyle='round,pad=0.3'))\n    \n    plt.xlim(-n\/2, n\/2)\n    plt.ylim(-n, 1)\n    plt.gca().set_aspect('equal', adjustable='box')\n    plt.savefig('triangle_de_pascal.png', dpi=300, bbox_inches='tight')\n    plt.show()\n\nplot_pascal_triangle(10)<\/pre>\n\n\n<div class=\"wp-block-image\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;6a1bcb5e562b7&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"6a1bcb5e562b7\" class=\"aligncenter size-medium wp-lightbox-container\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"295\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on--pointerdown=\"actions.preloadImage\" data-wp-on--pointerenter=\"actions.preloadImageWithDelay\" data-wp-on--pointerleave=\"actions.cancelPreload\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2024\/07\/image-300x295.png\" alt=\"triangle de Pascal color\u00e9 en Python\" class=\"wp-image-9943\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2024\/07\/image-300x295.png 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2024\/07\/image-600x590.png 600w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2024\/07\/image.png 674w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\tdata-wp-bind--aria-label=\"state.thisImage.triggerButtonAriaLabel\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.thisImage.buttonRight\"\n\t\t\tdata-wp-style--top=\"state.thisImage.buttonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n<\/div>\n\n\n<p class=\"is-style-Paragraph-paragraph wp-block-paragraph\">Bon, clairement, c&#8217;est joli mais pas ouf&#8230; On peut am\u00e9liorer!<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Script_2_cases_carrees_triangle_aligne_a_gauche\"><\/span>Script 2: cases carr\u00e9es, triangle align\u00e9 \u00e0 gauche<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">import numpy as np\nimport matplotlib.pyplot as plt\n\ndef pascal_triangle(n):\n    \"\"\"Generate the first n rows of Pascal's triangle.\"\"\"\n    triangle = np.zeros((n, n), dtype=int)\n    for i in range(n):\n        triangle[i, 0] = 1\n        for j in range(1, i + 1):\n            triangle[i, j] = triangle[i - 1, j - 1] + triangle[i - 1, j]\n    return triangle\n\ndef plot_pascal_triangle(n):\n    \"\"\"Plot the first n rows of Pascal's triangle with color.\"\"\"\n    triangle = pascal_triangle(n)\n    \n    fig, ax = plt.subplots(figsize=(10, 10))\n    ax.axis('off')\n\n    # Define a color map\n    colors = plt.cm.viridis(np.linspace(0, 1, n))\n    \n    max_width = max([len(str(triangle[i, j])) for i in range(n) for j in range(i + 1)])\n    \n    for i in range(n):\n        for j in range(i + 1):\n            x = j\n            y = -i\n            color = colors[i]\n            intensity = 1 - abs(j - i \/ 2) \/ (i \/ 2 + 1)\n            rect = plt.Rectangle((x - 0.5, y - 0.5), 1, 1, facecolor=color * intensity, edgecolor='none')\n            ax.add_patch(rect)\n            ax.text(x, y, triangle[i, j], ha='center', va='center', fontsize=10)\n\n    plt.xlim(-0.5, n - 0.5)\n    plt.ylim(-n, 0.5)\n    plt.gca().set_aspect('equal', adjustable='box')\n    plt.savefig('triangle_de_pascal.png', dpi=300, bbox_inches='tight')\n    plt.show()\n\nplot_pascal_triangle(10)<\/pre>\n\n\n<div class=\"wp-block-image\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;6a1bcb5e56980&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"6a1bcb5e56980\" class=\"aligncenter size-medium wp-lightbox-container\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"298\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on--pointerdown=\"actions.preloadImage\" data-wp-on--pointerenter=\"actions.preloadImageWithDelay\" data-wp-on--pointerleave=\"actions.cancelPreload\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2024\/07\/image-1-300x298.png\" alt=\"\" class=\"wp-image-9944\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2024\/07\/image-1-300x298.png 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2024\/07\/image-1-160x160.png 160w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2024\/07\/image-1-600x596.png 600w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2024\/07\/image-1-150x150.png 150w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2024\/07\/image-1.png 747w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\tdata-wp-bind--aria-label=\"state.thisImage.triggerButtonAriaLabel\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.thisImage.buttonRight\"\n\t\t\tdata-wp-style--top=\"state.thisImage.buttonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n<\/div>\n\n\n<p class=\"is-style-Paragraph-paragraph wp-block-paragraph\">Cela commence \u00e0 avoir de la gueule&#8230; Mais j&#8217;aime bien quand c&#8217;est centr\u00e9!<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Script_3_cases_carrees_triangle_centre\"><\/span>Script 3: cases carr\u00e9es, triangle centr\u00e9<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">import numpy as np\nimport matplotlib.pyplot as plt\n\ndef pascal_triangle(n):\n    \"\"\"Generate the first n rows of Pascal's triangle.\"\"\"\n    triangle = np.zeros((n, n), dtype=int)\n    for i in range(n):\n        triangle[i, 0] = 1\n        for j in range(1, i + 1):\n            triangle[i, j] = triangle[i - 1, j - 1] + triangle[i - 1, j]\n    return triangle\n\ndef plot_pascal_triangle(n):\n    \"\"\"Plot the first n rows of Pascal's triangle with color.\"\"\"\n    triangle = pascal_triangle(n)\n    \n    fig, ax = plt.subplots(figsize=(10, 10))\n    ax.axis('off')\n\n    # Define a color map\n    colors = plt.cm.viridis(np.linspace(0, 1, n))\n    \n    for i in range(n):\n        for j in range(i + 1):\n            x = j - i \/ 2\n            y = -i\n            color = colors[i]\n            intensity = 1 - abs(j - i \/ 2) \/ (i \/ 2 + 1)\n            rect = plt.Rectangle((x - 0.5, y - 0.5), 1, 1, facecolor=color * intensity, edgecolor='none')\n            ax.add_patch(rect)\n            ax.text(x, y, triangle[i, j], ha='center', va='center', fontsize=10)\n\n    plt.xlim(-n\/2 - 0.5, n\/2 + 0.5)\n    plt.ylim(-n, 0.5)\n    plt.gca().set_aspect('equal', adjustable='box')\n    plt.savefig('triangle_de_pascal.png', dpi=300, bbox_inches='tight')\n    plt.show()\n\nplot_pascal_triangle(10)<\/pre>\n\n\n<div class=\"wp-block-image\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;6a1bcb5e5705b&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"6a1bcb5e5705b\" class=\"aligncenter size-medium wp-lightbox-container\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"294\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on--pointerdown=\"actions.preloadImage\" data-wp-on--pointerenter=\"actions.preloadImageWithDelay\" data-wp-on--pointerleave=\"actions.cancelPreload\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2024\/07\/image-2-300x294.png\" alt=\"\" class=\"wp-image-9945\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2024\/07\/image-2-300x294.png 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2024\/07\/image-2-600x588.png 600w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2024\/07\/image-2.png 733w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\tdata-wp-bind--aria-label=\"state.thisImage.triggerButtonAriaLabel\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.thisImage.buttonRight\"\n\t\t\tdata-wp-style--top=\"state.thisImage.buttonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n<\/div>\n\n\n<p class=\"is-style-Paragraph-paragraph wp-block-paragraph\">Voil\u00e0! C&#8217;est centr\u00e9, mais peut-\u00eatre trop &#8220;carr\u00e9&#8221; ! Non ?<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Script_4_cases_avec_coins_arrondis_cases_qui_se_chevauchent\"><\/span>Script 4: cases avec coins arrondis, cases qui se chevauchent<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">import numpy as np\nimport matplotlib.pyplot as plt\nfrom matplotlib.patches import FancyBboxPatch\n\ndef pascal_triangle(n):\n    \"\"\"Generate the first n rows of Pascal's triangle.\"\"\"\n    triangle = np.zeros((n, n), dtype=int)\n    for i in range(n):\n        triangle[i, 0] = 1\n        for j in range(1, i + 1):\n            triangle[i, j] = triangle[i - 1, j - 1] + triangle[i - 1, j]\n    return triangle\n\ndef plot_pascal_triangle(n):\n    \"\"\"Plot the first n rows of Pascal's triangle with color.\"\"\"\n    triangle = pascal_triangle(n)\n    \n    fig, ax = plt.subplots(figsize=(10, 10))\n    ax.axis('off')\n\n    # Define a color map\n    colors = plt.cm.viridis(np.linspace(0, 1, n))\n    \n    for i in range(n):\n        for j in range(i + 1):\n            x = j - i \/ 2\n            y = -i\n            color = colors[i]\n            intensity = 1 - abs(j - i \/ 2) \/ (i \/ 2 + 1)\n            rect = FancyBboxPatch((x - 0.5, y - 0.5), 1, 1,\n                                  boxstyle=\"round,pad=0.1,rounding_size=0.2\",\n                                  facecolor=color * intensity, edgecolor='none')\n            ax.add_patch(rect)\n            ax.text(x, y, triangle[i, j], ha='center', va='center', fontsize=10, color='white')\n\n    plt.xlim(-n\/2 - 0.5, n\/2 + 0.5)\n    plt.ylim(-n, 0.5)\n    plt.gca().set_aspect('equal', adjustable='box')\n    plt.savefig('triangle_de_pascal.png', dpi=300, bbox_inches='tight')\n    plt.show()\n\nplot_pascal_triangle(10)<\/pre>\n\n\n<div class=\"wp-block-image\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;6a1bcb5e576d1&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"6a1bcb5e576d1\" class=\"aligncenter size-medium wp-lightbox-container\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"292\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on--pointerdown=\"actions.preloadImage\" data-wp-on--pointerenter=\"actions.preloadImageWithDelay\" data-wp-on--pointerleave=\"actions.cancelPreload\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2024\/07\/image-3-300x292.png\" alt=\"\" class=\"wp-image-9946\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2024\/07\/image-3-300x292.png 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2024\/07\/image-3-600x584.png 600w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2024\/07\/image-3.png 744w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\tdata-wp-bind--aria-label=\"state.thisImage.triggerButtonAriaLabel\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.thisImage.buttonRight\"\n\t\t\tdata-wp-style--top=\"state.thisImage.buttonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Script_5_cases_a_coins_arrondis_nombres_qui_sadaptent\"><\/span>Script 5: cases \u00e0 coins arrondis, nombres qui s&#8217;adaptent<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">import numpy as np\nimport matplotlib.pyplot as plt\nfrom matplotlib.patches import FancyBboxPatch\n\ndef pascal_triangle(n):\n    \"\"\"Generate the first n rows of Pascal's triangle.\"\"\"\n    triangle = np.zeros((n, n), dtype=int)\n    for i in range(n):\n        triangle[i, 0] = 1\n        for j in range(1, i + 1):\n            triangle[i, j] = triangle[i - 1, j - 1] + triangle[i - 1, j]\n    return triangle\n\ndef plot_pascal_triangle(n):\n    \"\"\"Plot the first n rows of Pascal's triangle with color.\"\"\"\n    triangle = pascal_triangle(n)\n    \n    fig, ax = plt.subplots(figsize=(10, 10))\n    ax.axis('off')\n\n    # Define a color map\n    colors = plt.cm.viridis(np.linspace(0, 1, n))\n\n    box_width = 0.8\n    box_height = 0.8\n    rounding_size = 0.1\n\n    base_fontsize = 12  # Max font size\n\n    for i in range(n):\n        for j in range(i + 1):\n            x = j - i \/ 2\n            y = -i\n            color = colors[i]\n            intensity = 1 - abs(j - i \/ 2) \/ (i \/ 2 + 1)\n            rect = FancyBboxPatch((x - box_width \/ 2, y - box_height \/ 2), box_width, box_height,\n                                  boxstyle=f\"round,pad=0.1,rounding_size={rounding_size}\",\n                                  facecolor=color * intensity, edgecolor='none')\n            ax.add_patch(rect)\n            \n            # Adjust font size based on number length\n            number_str = str(triangle[i, j])\n            fontsize = min(base_fontsize, box_width * 30 \/ len(number_str))\n            ax.text(x, y, number_str, ha='center', va='center', fontsize=fontsize, color='white')\n\n    plt.xlim(-n\/2 - 1, n\/2 + 1)\n    plt.ylim(-n, 1)\n    plt.gca().set_aspect('equal', adjustable='box')\n    plt.savefig('triangle_de_pascal.png', dpi=300, bbox_inches='tight')\n    plt.show()\n\nplot_pascal_triangle(10)<\/pre>\n\n\n<div class=\"wp-block-image\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;6a1bcb5e57b30&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"6a1bcb5e57b30\" class=\"aligncenter size-medium wp-lightbox-container\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"294\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on--pointerdown=\"actions.preloadImage\" data-wp-on--pointerenter=\"actions.preloadImageWithDelay\" data-wp-on--pointerleave=\"actions.cancelPreload\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2024\/07\/image-4-300x294.png\" alt=\"triangle de Pascal color\u00e9 en Python\" class=\"wp-image-9947\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2024\/07\/image-4-300x294.png 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2024\/07\/image-4-600x588.png 600w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2024\/07\/image-4.png 668w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\tdata-wp-bind--aria-label=\"state.thisImage.triggerButtonAriaLabel\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.thisImage.buttonRight\"\n\t\t\tdata-wp-style--top=\"state.thisImage.buttonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n<\/div>\n\n\n<p class=\"is-style-Paragraph-paragraph wp-block-paragraph\">L&#8217;avantage de ce dernier code est que la taille des nombres s&#8217;adapte. Voici ce que donne l&#8217;image lorsque n = 30:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-medium\"><a href=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2024\/07\/triangle_de_pascal.png\" data-fancybox=\"gallery\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"291\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2024\/07\/triangle_de_pascal-300x291.png\" alt=\"triangle de Pascal color\u00e9 en Python\" class=\"wp-image-9949\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2024\/07\/triangle_de_pascal-300x291.png 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2024\/07\/triangle_de_pascal-600x582.png 600w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2024\/07\/triangle_de_pascal-1024x993.png 1024w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2024\/07\/triangle_de_pascal-768x744.png 768w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2024\/07\/triangle_de_pascal-1536x1489.png 1536w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2024\/07\/triangle_de_pascal-2048x1985.png 2048w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/figure>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>Faire un triangle de Pascal color\u00e9 en Python est un bon moyen de s&#8217;occuper alors que les vacances sont l\u00e0. Je vais vous pr\u00e9senter plusieurs designs, mon pr\u00e9f\u00e9r\u00e9 allant au dernier.<\/p>\n","protected":false},"author":1,"featured_media":9950,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6,5],"tags":[135,110],"class_list":["post-9942","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematiques","category-python","tag-matplotlib","tag-triangle-de-pascal"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.7 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Un triangle de Pascal color\u00e9 en Python - Mathweb.fr<\/title>\n<meta name=\"description\" content=\"Faire un triangle de Pascal color\u00e9 en Python est un bon moyen de s&#039;occuper alors que les vacances sont l\u00e0.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.mathweb.fr\/euclide\/2024\/07\/04\/un-triangle-de-pascal-colore-en-python\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Un triangle de Pascal color\u00e9 en Python - 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