Replace toy_notebook_fr.ipynb

parent 5bd2d2fb
{ {
"cells": [], "cells": [
{
"cell_type": "markdown",
"id": "formed-geneva",
"metadata": {},
"source": [
"# A propos calcul de $\\pi$ \n",
"\n",
"## En demandant à la lib maths\n",
"\n",
"Mon ordinateur m'indique que $\\pi$ vaut *approximativement*"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "bibliographic-montreal",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"3.141592653589793\n"
]
}
],
"source": [
"from math import *\n",
"print(pi)"
]
},
{
"cell_type": "markdown",
"id": "utility-buffer",
"metadata": {},
"source": [
"## En utilisant la méthode des aguilles de Buffon \n",
"\n",
"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": 3,
"id": "falling-garlic",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"3.128911138923655"
]
},
"execution_count": 3,
"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": "markdown",
"id": "funky-arcade",
"metadata": {},
"source": [
"## Avec un argument \"fréquentiel\" de surface\n",
"\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 $P[X^2+Y^2\\le1]=\\pi/4$ (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": 4,
"id": "armed-information",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"\n",
"np.random.seed(seed=42)\n",
"N = 1000\n",
"x = np.random.uniform(size=N, low=0, high=1)\n",
"y = np.random.uniform(size=N, low=0, high=1)\n",
"accept = (x*x+y*y) <= 1\n",
"reject = np.logical_not(accept)\n",
"\n",
"fig, ax = plt.subplots(1)\n",
"ax.scatter(x[accept], y[accept], c='b', alpha=0.2, edgecolor=None)\n",
"ax.scatter(x[reject], y[reject], c='r', alpha=0.2, edgecolor=None)\n",
"ax.set_aspect('equal')"
]
},
{
"cell_type": "markdown",
"id": "mechanical-plaintiff",
"metadata": {},
"source": [
"Il est alors aisé d'obtenir une approximation (pas terrible) de 𝜋 en comptant combien de fois, en moyenne, 𝑋2+𝑌2 est inférieur à 1 :"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "brazilian-palace",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"3.112"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"4*np.mean(accept)"
]
}
],
"metadata": { "metadata": {
"kernelspec": { "kernelspec": {
"display_name": "Python 3", "display_name": "Python 3",
...@@ -16,10 +159,9 @@ ...@@ -16,10 +159,9 @@
"name": "python", "name": "python",
"nbconvert_exporter": "python", "nbconvert_exporter": "python",
"pygments_lexer": "ipython3", "pygments_lexer": "ipython3",
"version": "3.6.3" "version": "3.9.2"
} }
}, },
"nbformat": 4, "nbformat": 4,
"nbformat_minor": 2 "nbformat_minor": 5
} }
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