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Commit 74a2b064 authored by e6cfd8a10624671909b6755e01761c6e's avatar e6cfd8a10624671909b6755e01761c6e
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module2/exo1/toy_notebook_fr.ipynb
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...@@ -4,40 +4,20 @@ ...@@ -4,40 +4,20 @@
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
"source": [ "source": [
"# toy_notebook_fr" "# À propos du calcul de $\\pi$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# March 28, 2019"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**1 À propos du calcul de** $\\pi$ "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**1.1 En demandant à la lib maths**"
] ]
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## En demandant à la lib maths\n",
"mon ordinateur m'indique que $\\pi$ vaut approximativement " "mon ordinateur m'indique que $\\pi$ vaut approximativement "
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 1, "execution_count": 7,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
...@@ -49,7 +29,7 @@ ...@@ -49,7 +29,7 @@
} }
], ],
"source": [ "source": [
"from math import * \n", "from math import *\n",
"print(pi)" "print(pi)"
] ]
}, },
...@@ -57,19 +37,18 @@ ...@@ -57,19 +37,18 @@
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
"source": [ "source": [
"**1.2 En utilisant la méthodé des aiguilles de Buffon**" "## En utilisant la méthodé 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__: "
] ]
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
"source": [ "source": []
"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": 2, "execution_count": 8,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
...@@ -78,13 +57,13 @@ ...@@ -78,13 +57,13 @@
"3.128911138923655" "3.128911138923655"
] ]
}, },
"execution_count": 2, "execution_count": 8,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
], ],
"source": [ "source": [
"import numpy as np \n", "import numpy as np\n",
"np.random.seed(seed=42)\n", "np.random.seed(seed=42)\n",
"N = 10000\n", "N = 10000\n",
"x = np.random.uniform(size=N, low=0, high=1)\n", "x = np.random.uniform(size=N, low=0, high=1)\n",
...@@ -96,19 +75,13 @@ ...@@ -96,19 +75,13 @@
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
"source": [ "source": [
"**1.3 Avec un argument \"fréquentiel\" de surface**" "## 1.3 Avec un argument \"fréquentiel\" de surface\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 $P[ X^2 + Y^2 \\leq 1] = \\pi /4$ (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": "markdown",
"metadata": {},
"source": [
"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 $P\\left[ X^2 + Y^2 \\leq 1\\right] = \\pi /4$ (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", "cell_type": "code",
"execution_count": 3, "execution_count": 9,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
...@@ -125,13 +98,13 @@ ...@@ -125,13 +98,13 @@
} }
], ],
"source": [ "source": [
"%matplotlib inline \n", "%matplotlib inline\n",
"import matplotlib.pyplot as plt \n", "import matplotlib.pyplot as plt\n",
"np.random.seed(seed=42)\n", "np.random.seed(seed=42)\n",
"N = 1000\n", "N = 1000\n",
"x = np.random.uniform(size=N, low=0, high=1)\n", "x = np.random.uniform(size=N, low=0, high=1)\n",
"y = 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", "accept = (x*x+y*y) <= 1\n",
"reject = np.logical_not(accept)\n", "reject = np.logical_not(accept)\n",
"\n", "\n",
"fig, ax = plt.subplots(1)\n", "fig, ax = plt.subplots(1)\n",
...@@ -144,12 +117,12 @@ ...@@ -144,12 +117,12 @@
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Il est alors aisé d'obtenir une approxiamtion (pas terrible de $\\pi$ en comptant de fois, en moyenne, $X^2+Y^2$ est inférieur à 1: " "Il est alors aisé d'obtenir une approxiamtion (pas terrible de $\\pi$ en comptant de fois, en moyenne, $X^2+Y^2$ est inférieur à 1 :"
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 4, "execution_count": 10,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
...@@ -158,7 +131,7 @@ ...@@ -158,7 +131,7 @@
"3.112" "3.112"
] ]
}, },
"execution_count": 4, "execution_count": 10,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
......
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