From 95db713cfbd5bb5efabc661374ef7be3ffeb7009 Mon Sep 17 00:00:00 2001 From: "Anton Y." Date: Mon, 7 Jul 2025 02:26:50 +0300 Subject: [PATCH] task try 7 --- module2/exo1/toy_document_orgmode_python_en.org | 9 ++------- 1 file changed, 2 insertions(+), 7 deletions(-) diff --git a/module2/exo1/toy_document_orgmode_python_en.org b/module2/exo1/toy_document_orgmode_python_en.org index 7eb8662..29e7185 100644 --- a/module2/exo1/toy_document_orgmode_python_en.org +++ b/module2/exo1/toy_document_orgmode_python_en.org @@ -31,10 +31,7 @@ theta = np.random.uniform(size=N, low=0, high=pi/2) #+end_src * Using a surface fraction argument -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 [[https://en.wikipedia.org/wiki/Monte_Carlo_method]["Monte Carlo method" on -Wikipedia]]). The following code uses this approach: +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 [[https://en.wikipedia.org/wiki/Monte_Carlo_method]["Monte Carlo method" on Wikipedia]]). The following code uses this approach: #+begin_src python :results output file :var matplot_lib_filename="figure_pi_mc2.png" :exports both :session *python* import matplotlib.pyplot as plt @@ -56,9 +53,7 @@ plt.savefig(matplot_lib_filename) print(matplot_lib_filename) #+end_src -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: - +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: #+begin_src python :results output :session *python* :exports both 4*np.mean(accept) #+end_src -- 2.18.1