From 924a4776cb7630f9007b57c5d7e6ccb7358d214f Mon Sep 17 00:00:00 2001
From: c2818064e484f558fc9f864dffc2af47
 <c2818064e484f558fc9f864dffc2af47@app-learninglab.inria.fr>
Date: Wed, 20 May 2020 13:22:51 +0000
Subject: [PATCH] no commit message

---
 module2/exo1/toy_notebook_fr.ipynb | 55 ++++++++++++++++++++++++++++--
 1 file changed, 53 insertions(+), 2 deletions(-)

diff --git a/module2/exo1/toy_notebook_fr.ipynb b/module2/exo1/toy_notebook_fr.ipynb
index 956ed2f..1de7a19 100644
--- a/module2/exo1/toy_notebook_fr.ipynb
+++ b/module2/exo1/toy_notebook_fr.ipynb
@@ -4,7 +4,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# A propos du calcul de "
+    "# A propos du calcul de $\\pi$"
    ]
   },
   {
@@ -18,7 +18,58 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Mon ordinateur m'indique que "
+    "Mon ordinateur m'indique que $\\pi$ vaut *approximativement* "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "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 méthode des aiguilles de Buffon\n",
+    "Mais calculé avec la méthode des aiguilles de Buffon, on obtiendrait comme approximation : "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "3.128911138923655"
+      ]
+     },
+     "execution_count": 2,
+     "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)"
    ]
   },
   {
-- 
2.18.1