{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 1 À propos du calcul de $\\pi$\n", "## 1.1 En demandant à la lib maths\n", "Mon ordinateur m'indique que $pi$ vaut *approximativement*" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3.141592653589793\n" ] } ], "source": [ "from math import *\n", "print(pi)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1.2 En utilisant la méthode des aiguilles de Buffon\n", "Mais calculé avec la **méthode** des [aiguilles de Buffon](https://fr.wikipedia.org/wiki/Aiguille_de_Buffon), on obtiendrait comme **approximation**:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3.128911138923655" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "np.random.seed(seed=42)\n", "N = 10000\n", "x = np.random.uniform(size=N, low=0, high=1)\n", "theta = np.random.uniform(size=N, low=0, high=pi/2)\n", "2/(sum((x+np.sin(theta))>1)/N)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1.3 Avec un argument \"fréquentiel\" de surface\n", "Sinon, une méthode plus simple à comprendre et ne faisant pas intervenir d'appel à la fonction sinus se base sur le fait que si $X \\sim \\mathcal{U}(0,1)$ et $Y \\sim \\mathcal{U}(0,1)$ alors $P[X^2+Y^2 \\leq 1] = \\pi/4$ (voir [méthode de Monte Carlo sur Wikipédia](https://fr.wikipedia.org/wiki/M%C3%A9thode_de_Monte-Carlo#D%C3%A9termination_de_la_valeur_de_%CF%80)). Le code suivant illustre ce fait:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "\n", "np.random.seed(seed=42)\n", "N = 1000\n", "x = np.random.uniform(size=N, low=0, high=1)\n", "y = np.random.uniform(size=N, low=0, high=1)\n", "\n", "accept = (x*x+y*y) <= 1\n", "reject = np.logical_not(accept)\n", "\n", "fig, ax = plt.subplots(1)\n", "ax.scatter(x[accept], y[accept], c='b', alpha=0.2, edgecolor=None)\n", "ax.scatter(x[reject], y[reject], c='r', alpha=0.2, edgecolor=None)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Il est alors aisé d'obtenir une approximation (pas terrible) de $\\pi$ en ocmptant combien de fois, en moyenne, $X^2+Y^2$ est inférieur à 1:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3.112" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "4*np.mean(accept)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.4" } }, "nbformat": 4, "nbformat_minor": 2 }