{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# À propos du calcul de $\\pi$\n", "\n", "## En demandant à lib maths\n", "\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": [ "## En utilisant la methode des aiguilles de Buffon\n", "\n", "Mais calculé en utilisant la **méthode** des [aiguilles de Buffon](https://fr.wikipedia.org/wiki/Aiguille_de_Buffon) , on obtiendrai 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": [ "# Avec un argument fréquentiel de surface\n", "\n", "Sinon, une méthode plus simple à comprendre et ne faisant pas appel à la fonction sinus se base sur le fait que si $X \\sim U(0,1)$ et $Y\\sim U(0,1)$ alors $p[X^2+Y^2 \\leq 1]=\\pi/4$ (voir la [méthode de MonteCarlo 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": { "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", "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='r', alpha=0.2, edgecolor=None)\n", "ax.scatter(x[reject], y[reject], c='b', alpha=0.2, edgecolor=None)\n", "ax.set_aspect('equal')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Il est alors aisé d'obtenir une approximation (pas terrible) de $\\pi$ en comptant 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)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Hola Chicos\n" ] } ], "source": [] } ], "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 }