From fb5344912c35b0aa6314d4fca6e63fa9283af843 Mon Sep 17 00:00:00 2001
From: f50a28a8c82bf67ad820bc82fe37aad2
 <f50a28a8c82bf67ad820bc82fe37aad2@app-learninglab.inria.fr>
Date: Fri, 4 Jul 2025 16:27:09 +0000
Subject: [PATCH] Update toy_notebook_fr.ipynb

---
 module2/exo1/toy_notebook_fr.ipynb | 92 +++++++++++++++++++++++++-----
 1 file changed, 79 insertions(+), 13 deletions(-)

diff --git a/module2/exo1/toy_notebook_fr.ipynb b/module2/exo1/toy_notebook_fr.ipynb
index cf231d9..aefdfdb 100644
--- a/module2/exo1/toy_notebook_fr.ipynb
+++ b/module2/exo1/toy_notebook_fr.ipynb
@@ -1,5 +1,80 @@
-`{
- "cells": [],
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# À propos de π\n",
+    "\n",
+    "Dans ce mini-notebook, nous rappelons deux représentations classiques de π :\n",
+    "\n",
+    "$$ \\pi = \\frac{C}{D} $$  \n",
+    "$$ \\displaystyle \\pi = 4 \\sum_{k=0}^{\\infty} \\frac{(-1)^k}{2k+1} . $$\n",
+    "\n",
+    "La célèbre expérience des [aiguilles de Buffon](https://fr.wikipedia.org/wiki/Aiguille_de_Buffon) permet aussi d’estimer π de manière probabiliste."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import math\n",
+    "math.pi"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import random, math\n",
+    "\n",
+    "random.seed(42)        # pour reproduire la même estimation\n",
+    "N = 100_000            # nombre de lancers\n",
+    "l, d = 1.0, 1.0        # longueur de l’aiguille et espacement des lignes\n",
+    "\n",
+    "cross = 0\n",
+    "for _ in range(N):\n",
+    "    x      = random.uniform(0, d/2)          # distance centre-ligne la plus proche\n",
+    "    theta  = random.uniform(0, math.pi/2)    # angle avec la verticale\n",
+    "    if x <= (l/2) * math.sin(theta):\n",
+    "        cross += 1\n",
+    "\n",
+    "pi_est = (2 * l * N) / (cross * d)\n",
+    "pi_est"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "def buffon_once(n):\n",
+    "    \"\"\"Une estimation de π par Buffon sur n lancers\"\"\"\n",
+    "    crosses = sum(\n",
+    "        random.uniform(0, d/2) <= (l/2) * math.sin(random.uniform(0, math.pi/2))\n",
+    "        for _ in range(n)\n",
+    "    )\n",
+    "    return (2 * l * n) / (crosses * d)\n",
+    "\n",
+    "random.seed(0)\n",
+    "ests = [buffon_once(2_000) for _ in range(1_000)]\n",
+    "\n",
+    "plt.hist(ests, bins=30)\n",
+    "plt.axvline(math.pi, linestyle='--')\n",
+    "plt.title(\"Distribution des estimations de π (méthode de Buffon)\")\n",
+    "plt.xlabel(\"π estimé\")\n",
+    "plt.ylabel(\"Fréquence\")\n",
+    "plt.show()"
+   ]
+  }
+ ],
  "metadata": {
   "kernelspec": {
    "display_name": "Python 3",
@@ -7,19 +82,10 @@
    "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": "3.6.3"
+   "version": "3.10"
   }
  },
  "nbformat": 4,
- "nbformat_minor": 2
+ "nbformat_minor": 5
 }
-
-- 
2.18.1