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43800f9eebbeb989c35b6b37774edfea
mooc-rr
Commits
98da18ea
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Commit
98da18ea
authored
Jul 06, 2025
by
Anton Y.
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task try 3
parent
0423ead0
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module2/exo1/toy_document_orgmode_python_en.org
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98da18ea
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@@ -18,9 +18,6 @@ from math import *
pi
#+end_src
#+RESULTS:
: 3.141592653589793
* * Buffon's needle
Applying the method of [[https://en.wikipedia.org/wiki/Buffon%2527s_needle_problem][Buffon's needle]], we get the *approximation*
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@@ -33,9 +30,6 @@ theta = np.random.uniform(size=N, low=0, high=pi/2)
2/(sum((x+np.sin(theta))>1)/N)
#+end_src
#+RESULTS:
: 3.128911138923655
* 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
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@@ -62,9 +56,6 @@ plt.savefig(matplot_lib_filename)
print(matplot_lib_filename)
#+end_src
#+RESULTS:
[[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:
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@@ -72,5 +63,3 @@ than 1:
#+begin_src python :results output :session *python* :exports both
4*np.mean(accept)
#+end_src
#+RESULTS:
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