diff --git a/module2/exo1/toy_notebook_fr.ipynb b/module2/exo1/toy_notebook_fr.ipynb index 0bbbe371b01e359e381e43239412d77bf53fb1fb..5699761c5f82d84c7b46660313886394fc98eddd 100644 --- a/module2/exo1/toy_notebook_fr.ipynb +++ b/module2/exo1/toy_notebook_fr.ipynb @@ -1,8 +1,151 @@ { - "cells": [], + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 1. À propos du calcul de $\\pi$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1.1 En demandant à la lib maths\n", + "Mon ordinateur m'indique que $\\pi$ vaut *approximativement*" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "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": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3.128911138923655" + ] + }, + "execution_count": 3, + "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 $X\\sim U(0,1)$ et $Y\\sim U(0,1)$ alors $P[X^2+Y^2\\leq 1] = \\pi/4$ (voir [méthode de Monte Carlo sur Wikipedia](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": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "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)\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": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3.112" + ] + }, + "execution_count": 5, + "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", + "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, @@ -16,10 +159,9 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.3" + "version": "3.10.9" } }, "nbformat": 4, "nbformat_minor": 2 } -