From c3bcf2a59c4674503167db30304e6eb971c393df Mon Sep 17 00:00:00 2001
From: 7db3512460936f19a53c773a40a4fd70
 <7db3512460936f19a53c773a40a4fd70@app-learninglab.inria.fr>
Date: Sun, 31 Jan 2021 23:20:30 +0000
Subject: [PATCH] kk

---
 module2/exo1/toy_notebook_fr.ipynb | 69 ++++++++++++++++++++++++------
 1 file changed, 55 insertions(+), 14 deletions(-)

diff --git a/module2/exo1/toy_notebook_fr.ipynb b/module2/exo1/toy_notebook_fr.ipynb
index 40047d1..e6647cb 100644
--- a/module2/exo1/toy_notebook_fr.ipynb
+++ b/module2/exo1/toy_notebook_fr.ipynb
@@ -1,8 +1,23 @@
 {
  "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# À propos du calcul de $\\pi$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## En demandant à la lib maths\n",
+    "Mon ordinateur m'indique que $\\pi$ vaut *approximativement*"
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [
     {
@@ -21,7 +36,9 @@
   {
    "cell_type": "code",
    "execution_count": 4,
-   "metadata": {},
+   "metadata": {
+    "scrolled": false
+   },
    "outputs": [
     {
      "data": {
@@ -43,6 +60,14 @@
     "2/(sum((x+np.sin(theta))>1)/N)"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 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": 5,
@@ -79,6 +104,34 @@
     "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": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "ename": "NameError",
+     "evalue": "name 'accept' is not defined",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
+      "\u001b[0;32m<ipython-input-6-b03d6d9f8ffa>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;36m4\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmean\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maccept\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[0;31mNameError\u001b[0m: name 'accept' is not defined"
+     ]
+    }
+   ],
+   "source": [
+    "4*np.mean(accept)"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -92,18 +145,6 @@
    "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,
-- 
2.18.1