{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"![En tête general](img/En_tete_general.png)\n",
"\n",
"\n",
"*(C) Copyright Franck CHEVRIER 2019-2020 http://www.python-lycee.com/*\n",
"\n",
" Pour exécuter une saisie Python, sélectionner la cellule et valider avec SHIFT+Entrée .\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Méthode de Monte Carlo"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Dans un repère orthonormé, on considère les surfaces $C$ et $P$ définies respectivement par :\n",
"\n",
"$ C=\\left\\{ \\;M(x;y) \\; / \\; 0 \\leqslant x \\leqslant 1 \\;; \\; 0 \\leqslant y \\leqslant 1 \\; \\right\\} $\n",
"\n",
"$ P=\\left\\{ \\;M(x;y) \\; / \\; 0 \\leqslant x \\leqslant 1 \\;; \\; 0 \\leqslant y \\leqslant x^2 \\; \\right\\} $\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__1. Identifier ces deux surfaces et les représenter dans le repère fourni.__\n",
"\n",
"![Repère à compléter](img/Monte_Carlo_repere.png)\n",
"\n",
"__Déterminer l’aire de $C$.__"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Le but de l’activité est de déterminer des valeurs approchées de l’aire de la surface $P$ à l’aide d’une méthode probabiliste.* \n",
"\n",
"*On admet que lorsqu’on tire aléatoirement un point dans $C$, la probabilité qu’il soit dans $P$ vaut $\\displaystyle \\frac{Aire(P)}{Aire(C)} $.* \n",
"\n",
"*Ainsi, lorsqu’on tire aléatoirement plusieurs points dans $C$, la fréquence de ces points qui sont dans $P$ fournit une valeur approchée de $\\displaystyle \\frac{Aire(P)}{Aire(C)} $, d’autant plus précise que le nombre de points est grand.* \n",
"\n",
" Pour une présentation de la méthode, voir la vidéo suivante. \n",
"\n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__2. Tester puis modifier la fonction MonteCarlo donnée ci-dessous pour qu’elle reçoive un entier $n$ en argument et place $n$ points aléatoires de $C$ sur le graphique.__\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# Modifier la fonction\n",
"\n",
"from random import random # import de la fonction pour gérer l'aléatoire\n",
"import matplotlib.pyplot as plt # import des fonctionnalités graphiques\n",
"\n",
"def MonteCarlo(n):\n",
" \n",
" # répétition n fois\n",
" for k in range(n):\n",
" # generation de coordonnees aleatoires entre 0 et 1 pour un point M dans C\n",
" x,y=random(),random() \n",
" # placement du point M dans le repere (en bleu)\n",
" plt.scatter(x,y,color='blue') \n",
" \n",
" # reglage des bornes des axes du repere\n",
" plt.axis([0,1,0,1]) \n",
" # ouverture de la fenetre graphique et affichage\n",
" plt.show() \n",
" \n",
" return None"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Tester la fonction\n",
"MonteCarlo(20)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__3. Créer une fonction dans_P qui reçoit en argument les coordonnées $(x;y)$ d’un point de $C$ et renvoie True si ce point appartient à $P$ et False sinon.__\n",
"\t"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"# Ecrire la fonction\n",
"def dans_P(x,y):\n",
" return y<=x**2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__4. Modifier la fonction MonteCarlo pour qu’elle place les points appartenant à $P$ en rouge et les autres en bleu.__ \n",
"$\\;\\;\\;$__On utilisera la fonction dans_P pour le test.__\n",
"\n",
"\n",
" Remarque : En cas de problème de perception des couleurs, on pourra remplacer la désignation des couleurs 'blue' et 'red' (rouge et bleu) par 'silver' et 'black' (gris argenté et noir).\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Modifier la fonction précédente et tester ici\n",
"def MonteCarlo_2(n):\n",
" \n",
" for k in range(n):\n",
" # generation de coordonnees aleatoires entre 0 et 1 pour un point M dans C\n",
" x,y=random(),random() \n",
" \n",
" if dans_P(x,y):\n",
" # placement du point M dans le repere (en rouge)\n",
" plt.scatter(x,y,color='red') \n",
" \n",
" else:\n",
" # placement du point M dans le repere (en bleu)\n",
" plt.scatter(x,y,color='blue') \n",
"\n",
" # reglage des bornes des axes du repere\n",
" plt.axis([0,1,0,1]) \n",
" # ouverture de la fenetre graphique et affichage\n",
" plt.show() \n",
" \n",
" return None\n",
"\n",
"MonteCarlo_2(250)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__5. Modifier la fonction MonteCarlo pour :__\n",
"* __qu’elle compte le nombre de points placés qui sont dans $P$ ;__\n",
"* __qu’elle calcule la fréquence $f$ de ces points ;__\n",
"* __qu’elle renvoie cette fréquence $f$.__\n",
"\n",
"\n",
"*On pourra également faire apparaître cette fréquence dans la fenêtre à l’aide de l’instruction suivante :* plt.text(0,-0.1,\"Fréquence des points dans P: \"+str(f))*.* \n"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"# Modifier la fonction précédente et tester ici\n",
"def MonteCarlo_3(n):\n",
" \n",
" # initialisation du compteur de points dans P\n",
" compteur=0\n",
" \n",
" for k in range(n):\n",
" # generation de coordonnees aleatoires entre 0 et 1 pour un point M dans C\n",
" x,y=random(),random() \n",
" \n",
" if dans_P(x,y):\n",
" # placement du point M dans le repere (en rouge)\n",
" plt.scatter(x,y,color='red') \n",
" # incrementation du compteur\n",
" compteur = compteur+1\n",
" else:\n",
" # placement du point M dans le repere (en bleu)\n",
" plt.scatter(x,y,color='blue') \n",
" \n",
" # calcul de la fréquence de points dans P\n",
" f=compteur/n\n",
" # affichage de la frequence dans la fenetre \n",
" plt.text(0,-0.2,\"Fréquence des points dans C: \"+str(f))\n",
" \n",
" # reglage des bornes des axes du repere\n",
" #\n",
" plt.axis('equal')\n",
" plt.axis([0,1,0,1]) \n",
" # ouverture de la fenetre graphique et affichage\n",
" plt.show() \n",
" \n",
" return f"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__6. En appelant la fonction MonteCarlo avec $n=100$ ; $n=1000$ ; $n=10000$ … donner des approximations de l’aire de la surface $P$.__"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"0.32"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Modifier la fonction précédente et tester ici\n",
"MonteCarlo_3(25)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__7. On considère la surface $ D=\\left\\{ \\;M(x;y) \\; / \\; 0 \\leqslant x \\leqslant 1 \\;; \\; 0 \\leqslant y \\leqslant 1 \\;; \\; x²+y² \\leqslant 1 \\; \\right\\} $.__\n",
"\n",
"__Identifier cette surface $D$, et représenter $C$ et $D$ dans le repère fourni.__\n",
"\n",
"![Repère à compléter](img/Monte_Carlo_repere.png)\n",
"\n",
"__Déterminer la valeur exacte de l’aire de $D$.__\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__Adapter la méthode vue précédemment pour obtenir des approximations de $\\pi$ par la méthode de Monte-Carlo.__ "
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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s1iRlzy1e9u+PI+vJqNc2btzoqRwaKktCV5f3OutxHwbeHRGP91tRRGyNiA0RsWHNmjUZQ7RGKntu8bJ/fxxZT0a9tnHbNk/l0FBZ2tBfBLwvIl6Vvn4PQES8v22ZuzmQ+FcDe4BNEfHFXut1G7rZGMa5UM1t67XWrw19RYbv3wAcL+k44B+As4A3tC8QEce1/dinga/0S+ZmNqa5udFrE2vXdu9UrUP/gfU1sMklIvYB5wFXArcDl0XErZI2S9o86QBtRO70sl7q3H9gfWW6UjQitkXECRHxjIjYkr53UUQc1AkaEW8aNGTRJmyc+ct9Imi+OvcfWF+ey6WJso5T7myH3bgRPvOZpR1mnoTLrFI8Ode0ydLp1SrFtydvqfv3pn16O7MK8eRc0ybLOOVudyHqdXL3jSzMasEJvYmydHoNk6Q9+sGsFpzQmyhLp1evJK2O68g8+sGsNpzQm6r9vqNbtiRNLO0jV3qV4jdv9ugHs5pyQm+6XkMYoXsp/uMfH/4G1HnG6iGTZiPzKJemq8uNGbuNuvGQSbODeJRL0/Ur2WadarUsrdjPOccTRpmNyQm97gZdFVrFeb9bSVyCc8/tXoNoqcqJx6wGnNDrrtt48vaSbdXm7Wg/AUHvse8tHjJplpkTet0NalKp2rwd3U5AvdRtyKQ7da1kTuh1l6VJpX0IY9EjVzplbUIp+8QzrHEmRGuq9hPc6tXJwye7iXJCr7uqNakMMqgJZWYG5ufLP/EMa1DTVx2NU+PoPME99FDy8MlusiKilMf69evDcjI/HzE7GyEl/87Plx1Rb/PzETMzEcmhnTyk5N+qx95Paxs6H1LZkY2m2//TzEz2/5/Z2e77o/0xOzvJLWgsYDF65FWPQ7fijXP7tKqqy3j/rMbdnl4zfrbzLe9G4nHoVi1VatPPS92avgYZ9/qFLKOTPIIpd07oZnmo2miicY17/UK3E1y7Op/sKswJ3ZqvqOGETap5dEvIK1fCo49m24+dJ7hVq5JHE052FeY2dGs2zxEzuva+jqOOgkcegb17D3zu/VgK34LOplfTOivL4v1YGe4UtelV9cnJ6sL7sRac0K3Zqjg5WR15P9aCE7o1W9OGE5bF+7EWnNCt2Zo2nLAsk9iPnswsd+4UNbPiefTRyNwpambV0sTJzCrACd3Mehu1WWTQ9zxqZiKc0C0fbg9tnlHneM/yPY+amQgn9KI1MfH55g7NNGqzSJbvedTMRDihF6mpia/s9tAmniSrYNRmkV43/W7/nkcfTYQTepHKTnyTUmZ7aFNPklUwSrPIwkKSoLN8b5jJzHzSzsQJvUhN7Qgqsz20qSfJKhilWeSCC7rf2EIavTnFJ+3MnNCL1NSOoDLbQ5t6kqyCUZpFeu33iNGbU3zSzixTQpd0mqQ7JO2QdH6Xz+ckbU8f10g6Kf9QG6CpHUFltoeOc5J0NX6wYed477XfZ2dHj8En7ex63Wy09QCWAz8Cng6sBH4IPLtjmRcDR6bPTwe+P2i9U3uT6Drd0LkORr2Z8bg3QbbuJrFfe91wekpvMk2fm0RnSegvAq5se/0e4D19lj8S+IdB653ahD5Nijp5jfI7/ZKET7rjyXv/+eS7xLgJ/Uzg4rbX5wIf67P8u9qX7/VwQm+4qh+EUveE3oqzqnFPK59kf6lfQs/Sht5tDFLXGb0k/SbwFuDdPT7fJGlR0uLu3bsz/LTVVtU7snq19S5fXu24y1CFvoYm3a91grIk9F3AsW2vjwHu71xI0nOBi4EzIuKhbiuKiK0RsSEiNqxZs2aUeK0uqt6R1auD+vHHuy9flbiL5iGDtZIlod8AHC/pOEkrgbOAK9oXkLQWuBw4NyLuzD9Mq52qD9HsNTKn12iMiOkcCVP1mpYtsWLQAhGxT9J5wJUkI14+GRG3Stqcfn4R8F5gFfBxJVeJ7Yse8/XalNiypft811Uaojk3173q3hl3S6t02vruNKh6TcuW8A0ubHIWFpKS3M6dScl8y5Z6JMJW3L3mJJmmO92vW9d9P0zTPqiYfje4cEI362XZst6Xse/fX3w8ZfCdhSrHdywyG0XV+wGK4FkRa8UJ3abXoOF4TZ2qYVgeMlgbTug2nbIMx3Pp1GrGbeg2ndzZZzXlNvRpVYUr/KrKw/GsgZzQm8pX+PXnDk9rICf0pvIVfv25w9MayAm9qdyk0J87PK2BBl76bzW1dm33Tj83KRzQ69J/s5pyCb2p3KQwndwRPtWc0JvKTQrTxx3hU8/j0M2awmPrp4LHodeRq842LHeETz0n9Cpy1dlG0cSx9S7YDMUJvYo8hry+ykxATesId8FmaE7oRctywLvqXE9lJ6CmdYS7YDM0J/QiZT3gm1h1LlNRpeYqJKAmTXXrgs3QnNCLlPWAb1rVuUxFlpqdgPLlgs3QnNCLlPWAb1rVuUxFlpqdgPLlgs3QnNCLNMwB36Sqc5mKLDU7AeXLBZuhOaEXyQd88YosNTsB5c8Fm6E4oRfJB3zxij6JOgFZiZzQi+YDvlhNPIn6YhvrwdPnWvM1aZrc1qidVkdva9QONGcbbWQuoZvVSVlj3V0rqAWX0M3qpIyx7q4V1IZL6HXlEtN0KmOsexWugO3Fx8ESTuh1VPacIVaeMoa+VvUKWB8HB3FCr6MsJSaXXJqpjFE7Vb0Ctso1h5I4oZdtlMQ7qMTkkkuzFT30taoXxFW15lAiJ/QyjZp4B5WYXHKxPFV1LH9Vaw4lckIv06iJd1CJadiSi5tnbJAqXhBX1ZpDiZzQyzRqlXFQiWmYkoubZ6yuqlpzKJETepnGqTL2KzENU3Jx80xzTGNNq4o1hxJlSuiSTpN0h6Qdks7v8rkkfTT9fLuk5+cfagNNqso4TMnFHUvN4JqWAYqI/gtIy4E7gVcAu4AbgLMj4ra2ZTYCbwc2Ai8EPhIRL+y33g0bNsTi4uJ40TfBwkJSGt65MymZb9lSbClj3brk4O80O5uUeKwe/P84NSTdGBEbun2WpYR+MrAjIu6KiMeAS4EzOpY5A/hsJK4DjpD01LGinhZlVxndsdQMrmkZ2eZyORq4r+31LpJS+KBljgYeaF9I0iYgnQSCRyXdMVS0B6wGHhzxu2WodLyr4ainwdGHwMr/C/v+ec+e+x4855yHOeecskPLotL7tsPEYn0uPOcQWNn5/t6Ix7ZLN4+4Wu/byRkn3tleH2RJ6OryXmc7TZZliIitwNYMv9k/IGmxV5WjiuoUb51ihXrFW6dYoV7x1ilWmFy8WZpcdgHHtr0+Brh/hGXMzGyCsiT0G4DjJR0naSVwFnBFxzJXAG9MR7ucAvw0Ih7oXJGZmU3OwCaXiNgn6TzgSmA58MmIuFXS5vTzi4BtJCNcdgB7gN+fXMhADs02BatTvHWKFeoVb51ihXrFW6dYYULxDhy2aGZm9eArRc3MGsIJ3cysIWqR0CUdJekbkv4+/ffILsscK+k7km6XdKukd5QQZ22mSMgQ61wa43ZJ10g6qYw401j6xtq23AskPS7pzCLj6xLHwHglnSrppvRv9btFx9gWx6C/gydJ+rKkH6axTrp/rCdJn5T0Y0m39Pi8MsdXGs+gePM/xiKi8g/gA8D56fPzgT/ussxTgeenzw8nma7g2QXGuBz4EfB0kgs8ftj5+yQdx39DMm7/FOD7Je3PLLG+GDgyfX56lWNtW+7bJB30Z5YR6xD79gjgNmBt+vrJFY71P7eON2AN8DCwsqR4XwY8H7ilx+eVOL6GiDf3Y6wWJXSSqQU+kz7/DPCazgUi4oGI+EH6/GfA7SRXqxalTlMkDIw1Iq6JiJ+kL68jubagDFn2KyRzCX0e+HGRwXWRJd43AJdHxE6AiCgr5iyxBnC4JAGHkST0fcWGmQYScXX6+71U5fgCBsc7iWOsLgn9KZGOa0//fXK/hSWtA/4V8P3Jh/ZLvaY/GHaZIgwbx1tISj5lGBirpKOB1wIXFRhXL1n27QnAkZKuknSjpDcWFt1SWWL9GPAskgsFbwbeERH7iwlvaFU5vkaRyzGW5dL/Qkj6JvAvunw01MTckg4jKam9MyIeySO2rD/d5b2RpkgoQOY4JP0myR/bSyYaUW9ZYv0w8O6IeDwpSJYqS7wrgPXAy4FDgWslXRcRd046uA5ZYn0VcBPwW8AzgG9I+l7Bx1ZWVTm+hpLnMVaZhB4Rv93rM0n/T9JTI+KBtArVtYoq6RCSZL4QEZdPKNRe6jRFQqY4JD0XuBg4PSIeKii2Tlli3QBcmibz1cBGSfsi4ouFRLhU1r+DByPi58DPJV0NnETS71OkLLH+PnBhJA29OyTdDZwIXF9MiEOpyvGVWd7HWF2aXK4Afi99/nvAlzoXSNv4/gdwe0T8aYGxtdRpioSBsUpaC1wOnFtCybHdwFgj4riIWBcR64DPAW8rKZlDtr+DLwEvlbRC0gzJ7KW3FxwnZIt1J0lNAklPAZ4J3FVolNlV5fjKZCLHWJm9wEP0Fq8CvgX8ffrvUen7TwO2pc9fQlK92k5SRbwJ2FhwnBtJSlk/Ai5I39sMbE6fC/jz9PObgQ0l7tNBsV4M/KRtXy5WNdaOZT9NiaNcssYL/AHJSJdbSJoHKxlreox9Pf17vQU4p8RYLyGZknsvSWn8LVU9vjLGm/sx5kv/zcwaoi5NLmZmNoATuplZQzihm5k1hBO6mVlDOKGbmTWEE7qZWUM4oZuZNYQTuplZQzihm5k1hBO6mVlDOKGbmTWEE7qZWUM4oZuZNYQTuplZQzihm5k1hBO6mVlDOKGbmTWEE7qZWUM4oVeQpFdLek7ZcZhZvTihF0TS45Juanus67HcacBvkNyQt3YkvU/Su0r43W2SjhiwzJskPW2M37hH0upRv59h/Sek27FD0u2SLpP0lAHfWS/p5vQ7H5WkLsvMdfzt7Zf0vPSz10vaLulWSR+Y0KZZQZzQi/OLiHhe2+Oe1gdKLAOIiK9FxH8K3717KBGxMSL+ccBibyK5i33lSPpV4KvAJyLi1yLiWcAngDUDvvoJYBNwfPo4rXOBiFho/d0B5wL3RMRNklYBHwReHhH/EniKpJfntlFWOCf0kkhal5bCPg78ADhW0h9IuiEtMf1R27IXSLpD0jclXdIqAUu6StKG9PlqSfekz5dL+mDbuv5d+v6p6Xc+J+nvJC20SnSSXiDpGkk/lHS9pMN7rafLtvwyPuCZbe8/Q9LXJN0o6XuSTkzff52kW9LfurrL+k6VdLWkL0i6TdJFrROepLPTEuktkv647Tv3pPugtV//Mi11fl3SoZLOBDYAC2kp9VBJF6br3y7pQ13iWJV+/28l/QWgts++mG7XrZI2tb3/qKQt6bZd1yphD9pm4A3AtRHx5dYbEfGdiOhZU5P0VOCJEXFtWgD4LPCaXsunzgYuSZ8/HbgzInanr78J/NsB37cqiwg/CngAjwM3pY8vAOuA/cAp6eevBLaSJI1lwFeAlwHrgZuBGeCJwA7gXel3rgI2pM9Xk5S8ICmx/WH6/FeAReA44FTgp8Ax6W9cC7wEWAncBbwg/c4TgRW91tOxXf3i+xZwfPr8hcC30+c3A0enz4/osq9OBf6JJOEsB74BnElSut5JUmpdAXwbeE36nXvSfbAO2Ac8L33/MuCcLvvrKOAOQH3i+Cjw3vT5q4EAVre+n/57KEnz2Kr0dQC/mz7/QNv+G7TNfwq8o8ffztOAbV3e3wB8s+31S4GvDPg7/BHw6+nzI4Fd6T5bAXwe+HLZx4ofoz9WYEX5RSRVXiApoQP3RsR16VuvTB9/m74+jKQKfTjwhYjYk37vigy/9UrguWmpFOBJ6boeA66PiF3pum4iOZh/CjwQETcARMQj6ee91nN322+9tFt8kg4DXgz8r7Zm3V9J//0/wKclXQZc3mMbro+Iu9J1XUJy4tkLXBVpiVLSAslJ74sd3707Im5Kn9+YbmOnR0hOGhdL+irJCbTTy4B/AxARX5X0k7bP/oOk16bPjyXZLw+R7OPWum4EXjHENncVEfcDG7t8dFB7OckJpStJLwT2RFrqj4ifSHor8NckhYtrSE6iVlNO6OX6edtzAe+PiL9oX0DSO+l9kO7jQLPZr3as6+0RcWXHuk4F/rntrcdJ/gbU4ze6rqeLbt9dBvxj+0nslwtHbE6Ty6uBmyQ9LyIeGrDOoHsC66ZzGw/tEsM+SScDLwfOAs4DfqvLug7atnQ//jbwoojYI+kqDuz/vRHR+k5r/2bZ5ltJOsOHsYukttVyDHB/n+XP4kBzC2lcXwa+nG7XpjRmqym3oVfHlcCb05Itko6W9GTgauC1aZvv4cDvtn3nHpImD0iaJNrX9VZJh6TrOkHSE/r89t8BT5P0gnT5wyWtyLiervGlpfy7Jb0u/a4knZQ+f0ZEfD8i3gs8SFLC7XSypOPStvPXA/8b+D7wG2lb+XKS9uDv9tmuTj8jqfG0ahBPiohtwDuB53VZ/mpgLl3+dJImCkhqKj9Jk/mJwCmDfjjDNv9P4MWSXt32ndPUZ/hqRDwA/EzSKUqqQW8EvtTj95cBrwMu7Xj/yem/RwJvAy4etC1WXS6hV0REfF3Ss4Br0yaKR0nafn8g6a9J2t7vBb7X9rUPAZdJOpekPbnlYpJmhh+kB/pu+nSWRcRjkl4P/JmkQ4FfkJRAB65nQHxzwCck/SFwCEky+SHwQUnHk5S4v5W+1+la4ELgOSSJ9QsRsV/Se4DvpN/dFhFdE1gPnwYukvQL4HTgS0pGlwj4j12W/yPgEkk/IDlx7Ezf/xqwWdJ2knb467p8t1PfbY6IX0j6HeDDkj5M0ry0HXiHkqGWF0dEt2aXt6bbdSjwN+kDSf+apL/gvelyLwN2tZqx2nykdaIF/mtE3JlhW6yidKB2aHUg6X3AoxFx0KiMpkibNN4VEb9TcihmteImFzOzhnAJ3cysIVxCNzNrCCd0M7OGcEI3M2sIJ3Qzs4ZwQjczawgndDOzhvj/IsDL8lSwQ7MAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"0.79"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Effectuer les saisies nécessaires\n",
"def dans_P(x,y):\n",
" return x**2+y**2<=1\n",
"\n",
"MonteCarlo_3(100)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*(C) Copyright Franck CHEVRIER 2019-2020 http://www.python-lycee.com/*\n"
]
}
],
"metadata": {
"celltoolbar": "Raw Cell Format",
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"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": "3.8.5"
}
},
"nbformat": 4,
"nbformat_minor": 2
}