{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# toy_notbook_fr " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "March 28, 2019" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## À propos du calcul de $\\pi$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### En démandant à la lib maths " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Mon ordinateur m'indique de $\\pi$ 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 méthode des aiguilles de Buffon" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "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": [ "3.144654088050314" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "np.random.seed(seed=42)\n", "N = 1000\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" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "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 $X \\sim U(0,1)$ et $Y \\sim U(0,1)$ alors $P[X^2 + Y^2] = \\pi/4$ (voir méthode Monte Carlo sur Wikipédia). 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", "\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", "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)\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": [] } ], "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": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }