From 54bcdc4cd1fe90068c0e798ba24e1a90f1458c3e Mon Sep 17 00:00:00 2001 From: Tommy Rushton Date: Wed, 10 Apr 2024 10:26:42 +0200 Subject: [PATCH] Bring things closer into line with target notebook. --- module2/exo1/toy_document_orgmode_python_en.org | 8 +++----- 1 file changed, 3 insertions(+), 5 deletions(-) diff --git a/module2/exo1/toy_document_orgmode_python_en.org b/module2/exo1/toy_document_orgmode_python_en.org index 1184cc3..c8c264d 100644 --- a/module2/exo1/toy_document_orgmode_python_en.org +++ b/module2/exo1/toy_document_orgmode_python_en.org @@ -8,7 +8,7 @@ #+HTML_HEAD: #+HTML_HEAD: -# #+PROPERTY: header-args :session :exports both +#+PROPERTY: header-args :session :exports both * Asking the math library My computer tells me that $\pi$ is /approximatively/ @@ -38,8 +38,7 @@ theta = np.random.uniform(size=N, low=0, high=pi/2) * 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 :session :var matplot_lib_filename="figure_pi_mc2.png" :exports both import matplotlib.pyplot as plt @@ -65,8 +64,7 @@ print(matplot_lib_filename) [[file:figure_pi_mc2.png]] 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: +to $\pi$ by counting how many times, on average, $X^2 + Y^2$ is smaller than 1: #+begin_src python :results value :session :exports both 4*np.mean(accept) -- 2.18.1