diff --git a/module2/exo1/toy_notebook_en.ipynb b/module2/exo1/toy_notebook_en.ipynb index d96e2882a320058aa463ab539f4236da2e6369e8..27c1633c064dc795101f30530b60663da1004a01 100644 --- a/module2/exo1/toy_notebook_en.ipynb +++ b/module2/exo1/toy_notebook_en.ipynb @@ -4,6 +4,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ +<<<<<<< HEAD "# On the computation of $\\pi$" ] }, @@ -13,6 +14,11 @@ "source": [ "## Asking the maths library\n", "My computer tells me that $\\pi$ is *approximatively*" +======= + "# À propos du calcul de $\\pi$\n", + "## En demandant à la lib maths\n", + "Mon ordinateur m’indique que $\\pi$ vaut *approximativement*" +>>>>>>> ff5bf62e6a54b420ff906287a58051154df436c2 ] }, { @@ -37,8 +43,13 @@ "cell_type": "markdown", "metadata": {}, "source": [ +<<<<<<< HEAD "## Buffon's needle\n", "Applying the method of [Buffon's needle](https://en.wikipedia.org/wiki/Buffon%27s_needle_problem), we get the __approximation__\n" +======= + "## En utilisant la méthode des aiguilles de Buffon\n", + "Mais calculé avec la **méthode** [aiguilles de Buffon](https://fr.wikipedia.org/wiki/Aiguille_de_Buffon), on obtiendrait comme **approximation** :\n" +>>>>>>> ff5bf62e6a54b420ff906287a58051154df436c2 ] }, { @@ -70,8 +81,15 @@ "cell_type": "markdown", "metadata": {}, "source": [ +<<<<<<< HEAD "## Using a surface fraction argument\n", "A method that is easier to understand and does not make use of the $\\sin$ function is based on the fact that if $X\\sim U(0,1)$ and $Y\\sim U(0,1)$, then $P[X^2+Y^2\\leq 1] = \\pi/4$ (see [\"Monte Carlo method\" on Wikipedia](https://en.wikipedia.org/wiki/Monte_Carlo_method)). The following code uses this approach:\n" +======= + "## Avec un argument \"fréquentiel\" de surface\n", + "Sinon, une méthode plus simple à comprendre et ne faisant pas intervenir d’appel à la fonction\n", + "sinus se base sur le fait que si $X \\sim U(0,1)$ et $Y \\sim U(0, 1)$ alors $P[X^2 + Y^2 ≤ 1] = \\pi/4$\n", + "(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 :\n" +>>>>>>> ff5bf62e6a54b420ff906287a58051154df436c2 ] }, { @@ -114,7 +132,12 @@ "cell_type": "markdown", "metadata": {}, "source": [ +<<<<<<< HEAD "It is then straightforward to obtain a (not really good) approximation to $\\pi$ by counting how many times, on average, $X^2 + Y^2$ is smaller than 1:" +======= + "Il est alors aisé d’obtenir une approximation (pas terrible) de $\\pi$ en comptant combien de fois,\n", + "en moyenne, $X^2 + Y^2$ est inférieur à 1 :" +>>>>>>> ff5bf62e6a54b420ff906287a58051154df436c2 ] }, { diff --git a/module2/exo1/toy_notebook_fr.ipynb b/module2/exo1/toy_notebook_fr.ipynb index 0bbbe371b01e359e381e43239412d77bf53fb1fb..89d84c5c1490fe09d4281cee7ec10df55bb61115 100644 --- a/module2/exo1/toy_notebook_fr.ipynb +++ b/module2/exo1/toy_notebook_fr.ipynb @@ -23,3 +23,6 @@ "nbformat_minor": 2 } +# À propos du calcul de $\pi$ +## En demandant à la lib maths +Mon ordinateur m’indique que $\pi$ vaut *approximativement* diff --git a/module2/exo2/exercice.ipynb b/module2/exo2/exercice.ipynb index 0bbbe371b01e359e381e43239412d77bf53fb1fb..a46d325e2df8912f5d7146ca92c7a5f48efa19c6 100644 --- a/module2/exo2/exercice.ipynb +++ b/module2/exo2/exercice.ipynb @@ -1,5 +1,144 @@ { - "cells": [], + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "a = np.array([14.0, 7.6, 11.2, 12.8, 12.5, 9.9, 14.9, 9.4, 16.9, 10.2, 14.9, 18.1, 7.3, 9.8, 10.9,12.2, 9.9, 2.9, 2.8, 15.4, 15.7, 9.7, 13.1, 13.2, 12.3, 11.7, 16.0, 12.4, 17.9, 12.2, 16.2, 18.7, 8.9, 11.9, 12.1, 14.6, 12.1, 4.7, 3.9, 16.9, 16.8, 11.3, 14.4, 15.7, 14.0, 13.6, 18.0, 13.6, 19.9, 13.7, 17.0, 20.5, 9.9, 12.5, 13.2, 16.1, 13.5, 6.3, 6.4, 17.6, 19.1, 12.8, 15.5, 16.3, 15.2, 14.6, 19.1, 14.4, 21.4, 15.1, 19.6, 21.7, 11.3, 15.0, 14.3, 16.8, 14.0, 6.8, 8.2, 19.9, 20.4, 14.6, 16.4, 18.7, 16.8, 15.8, 20.4, 15.8, 22.4, 16.2, 20.3, 23.4, 12.1, 15.5, 15.4, 18.4, 15.7, 10.2, 8.9, 21.0])" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [], + "source": [ + "std = np.std(a, axis=None, dtype=None, out=None, ddof=1)\n", + "mini = min(a)\n", + "maxi = max(a)\n", + "med = np.median(a)\n", + "mean = np.mean(a)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "4.334094455301447" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "std" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "2.8" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "mini" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "23.4" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "maxi" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "14.5" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "med" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "14.113000000000001" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "mean" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], "metadata": { "kernelspec": { "display_name": "Python 3", @@ -16,10 +155,9 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.3" + "version": "3.6.4" } }, "nbformat": 4, "nbformat_minor": 2 } -