{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# toy-notbook-fr\n",
    "\n",
    "## March 28, 2019\n",
    "\n",
    "### **1 À propos du calcul de** $\\pi$\n",
    "\n",
    "#### **1.1 En demandant à la lib maths**\n",
    "\n",
    "Mon ordinateur m'indique que $\\pi$ vaut *approximativement\n",
    "\n",
    "In [1]: >from math import *\n",
    "    >print (pi)\n",
    "    \n",
    "    3.141592653589793\n",
    "    \n",
    "\n",
    "#### **1.2 En utilisant la méthode des aiguilles de Buffon**\n",
    "\n",
    "Mais calculé avec la **méthode** des aiguilles de Buffon, on obtiendrait comme **approximation**\n",
    "\n",
    "In [2]: >import numpy as np\n",
    "    >np.random.seed(seed=42)\n",
    "    >N = 10000\n",
    "    >x = np.random.uniform(size=N, low=0, high=pi/2)\n",
    "    >2/(sum((x+np.sin(theta))>1)/N)\n",
    "    \n",
    "Out[2]: 3.1289111389236548\n",
    "\n",
    "#### **1.3 Avec un argument \"fréquentiel\" de surface\n",
    "\n",
    "Sinon, une méthode plus simple à comprendre et ne faisant pas intervenir d'appel à la fonction\n",
    "sinus se base sur le fait que si *X* $\\sim$ *U*(0,1) alors *P*[$X^2$ + $Y^2$ ≤ 1] = $^\\pi/_4$ (voir)"
   ]
  }
 ],
 "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
}