From 6631439657bddba30a063c0f840649978eaff8a9 Mon Sep 17 00:00:00 2001
From: 8517fa92e97b3a318e653caefbfde6b5
 <8517fa92e97b3a318e653caefbfde6b5@app-learninglab.inria.fr>
Date: Tue, 31 Mar 2020 10:26:11 +0000
Subject: [PATCH] 1.2

---
 module2/exo1/toy_notebook_fr.ipynb | 63 +++++++++++++++++++++++-------
 1 file changed, 49 insertions(+), 14 deletions(-)

diff --git a/module2/exo1/toy_notebook_fr.ipynb b/module2/exo1/toy_notebook_fr.ipynb
index 9201359..3015eed 100644
--- a/module2/exo1/toy_notebook_fr.ipynb
+++ b/module2/exo1/toy_notebook_fr.ipynb
@@ -3,10 +3,12 @@
   {
    "cell_type": "markdown",
    "metadata": {
-    "hideCode": true,
-    "hidePrompt": true
+    "hideCode": false,
+    "hidePrompt": false
    },
    "source": [
+    "<p style=\"text-align:center\";>__toy\\_notebook\\_fr__</p>\n",
+    "\n",
     "<p style=\"text-align:center\";>March 28, 2019</p>\n",
     "\n",
     "#  propos du calcul de $\\pi$\n",
@@ -20,46 +22,79 @@
    "cell_type": "code",
    "execution_count": null,
    "metadata": {
-    "hideCode": true,
-    "hidePrompt": true
+    "hideCode": false,
+    "hidePrompt": false
    },
    "outputs": [],
    "source": [
-    "from math import * \n",
+    "from math import *\n",
     "print(pi)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {
-    "hideCode": true,
-    "hidePrompt": true
+    "hideCode": false,
+    "hidePrompt": false
    },
    "source": [
     "## En utilisant la méthode des aiguilles de Buffon"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "hideCode": false,
+    "hidePrompt": false
+   },
+   "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": null,
    "metadata": {
-    "hideCode": true,
-    "hidePrompt": true
+    "hideCode": false,
+    "hidePrompt": false
    },
    "outputs": [],
-   "source": []
+   "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": {
-    "hideCode": true,
-    "hidePrompt": true
+    "hideCode": false,
+    "hideOutput": true,
+    "hidePrompt": false
    },
-   "source": []
+   "source": [
+    "## Avec un argument \"fréquentiel\" de surface"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "hideCode": false,
+    "hidePrompt": false
+   },
+   "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\n",
+    "\n",
+    "\n",
+    "X\u0018U(0, 1)etY\u0018U(0, 1)alorsP[X2+Y2\u00141]=p/4 (voirméthode de Monte Carlo sur Wikipedia). Le code suivant illustre ce fait :"
+   ]
   }
  ],
  "metadata": {
-  "hide_code_all_hidden": true,
+  "hide_code_all_hidden": false,
   "kernelspec": {
    "display_name": "Python 3",
    "language": "python",
-- 
2.18.1