{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": true,
    "hidePrompt": true
   },
   "source": [
    "# toy_notebook_fr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": true,
    "hidePrompt": true
   },
   "source": [
    "date: \"`r Sys.Date()`\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": true,
    "hidePrompt": true
   },
   "source": [
    "## A propos du calcul de $\\pi$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": true,
    "hideOutput": true,
    "hidePrompt": true
   },
   "source": [
    "Mon ordinateur m'indique que $\\pi$ vaut *approximativement*\n",
    "\n"
   ]
  },
  {
   "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": [
    "## En utilisant la methode des aiguilles de Buffon"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mais calculé avec la **méthode** des aiguilles de Buffon, on obtiendrait comme **approximation :**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0"
      ]
     },
     "execution_count": 6,
     "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": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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