exo

parent 65eb02d0
...@@ -4,16 +4,16 @@ ...@@ -4,16 +4,16 @@
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
"source": [ "source": [
"# 1 À propos du calcul de π\n", "# À propos du calcul de π\n",
"\n", "\n",
"## 1.1 En demandant à la lib maths\n", "## En demandant à la lib maths\n",
"\n", "\n",
"Mon ordinateur m’indique que π vaut _approximativement_" "Mon ordinateur m’indique que π vaut _approximativement_"
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 7, "execution_count": 13,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
...@@ -33,13 +33,13 @@ ...@@ -33,13 +33,13 @@
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## 1.2 En utilisant la méthode des aiguilles de Buffon\n", "## En utilisant la méthode des aiguilles de Buffon\n",
"Mais calculé avec la **méthode** des [aiguilles de Buffon](https://fr.wikipedia.org/wiki/Aiguille_de_Buffon), on obtiendrait comme **approximation** :" "Mais calculé avec la **méthode** des [aiguilles de Buffon](https://fr.wikipedia.org/wiki/Aiguille_de_Buffon), on obtiendrait comme **approximation** :"
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 8, "execution_count": 14,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
...@@ -48,7 +48,7 @@ ...@@ -48,7 +48,7 @@
"3.128911138923655" "3.128911138923655"
] ]
}, },
"execution_count": 8, "execution_count": 14,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
...@@ -66,7 +66,7 @@ ...@@ -66,7 +66,7 @@
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## 1.3 Avec un argument \"fréquentiel\" de surface\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", "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 ∼ U(0, 1) et Y ∼ U(0, 1) alors P[X<sup>2</sup> + Y<sup>2</sup> ≤ 1] = π/4 (voir\n", "sinus se base sur le fait que si X ∼ U(0, 1) et Y ∼ U(0, 1) alors P[X<sup>2</sup> + Y<sup>2</sup> ≤ 1] = π/4 (voir\n",
"[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 :" "[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 :"
...@@ -74,7 +74,7 @@ ...@@ -74,7 +74,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 11, "execution_count": 15,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
...@@ -117,7 +117,7 @@ ...@@ -117,7 +117,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 12, "execution_count": 16,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
...@@ -126,7 +126,7 @@ ...@@ -126,7 +126,7 @@
"3.112" "3.112"
] ]
}, },
"execution_count": 12, "execution_count": 16,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
......
{ {
"cells": [], "cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"x = (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": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([4.33409446])"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.std(x, ddof=1, keepdims=True)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([2.8])"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.amin(x, keepdims=True)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"23.4"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.amax(x)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"14.113000000000001"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.mean(x)"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"14.5"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.median(x)"
]
}
],
"metadata": { "metadata": {
"kernelspec": { "kernelspec": {
"display_name": "Python 3", "display_name": "Python 3",
...@@ -16,10 +135,9 @@ ...@@ -16,10 +135,9 @@
"name": "python", "name": "python",
"nbconvert_exporter": "python", "nbconvert_exporter": "python",
"pygments_lexer": "ipython3", "pygments_lexer": "ipython3",
"version": "3.6.3" "version": "3.6.4"
} }
}, },
"nbformat": 4, "nbformat": 4,
"nbformat_minor": 2 "nbformat_minor": 2
} }
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