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#+PROPERTY: header-args :eval never-export @@ -91,3 +91,65 @@ faisant ~1)/N)) +#+END_SRC + +#+RESULTS: +: 3.128911138923655 + +* Avec un argument "fréquentiel" de surface +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[X²+Y²\leq1]=\pi/4) (voir [[https://fr.wikipedia.org/wiki/M%C3%A9thode_de_Monte-Carlo#D%C3%A9termination_de_la_valeur_de_%CF%80][méthode de Monte Carlo sur Wikipedia]]). Le code suivant illustre ce fait : +#+BEGIN_SRC python :results output :exports both :session ma-session +import matplotlib.pyplot as plt + +np.random.seed(seed=42) +N = 1000 +x = np.random.uniform(size=N, low=0, high=1) +y = np.random.uniform(size=N, low=0, high=1) + +accept = (x*x+y*y) <= 1 +reject = np.logical_not(accept) + +fig, ax = plt.subplots(1) +ax.scatter(x[accept], y[accept], c='b', alpha=0.2, edgecolor=None) +ax.scatter(x[reject], y[reject], c='r', alpha=0.2, edgecolor=None) +ax.set_aspect('equal') + +plt.savefig(matplot_lib_filename) +print(matplot_lib_filename) +#+END_SRC + +#+RESULTS: + +Il est alors aisé d'obtenir une approximation (pas terrible) de \pi en comptant combien de fois, en moyenne, =insérer formule de maths= est inférieur à 1 : +#+BEGIN_SRC python :results output :exports both +4*np.mean(accept) +#+END_SRC + -- 2.18.1