Commit 98da18ea authored by Anton Y.'s avatar Anton Y.

task try 3

parent 0423ead0
...@@ -18,9 +18,6 @@ from math import * ...@@ -18,9 +18,6 @@ from math import *
pi pi
#+end_src #+end_src
#+RESULTS:
: 3.141592653589793
* * Buffon's needle * * Buffon's needle
Applying the method of [[https://en.wikipedia.org/wiki/Buffon%2527s_needle_problem][Buffon's needle]], we get the *approximation* Applying the method of [[https://en.wikipedia.org/wiki/Buffon%2527s_needle_problem][Buffon's needle]], we get the *approximation*
...@@ -33,9 +30,6 @@ theta = np.random.uniform(size=N, low=0, high=pi/2) ...@@ -33,9 +30,6 @@ theta = np.random.uniform(size=N, low=0, high=pi/2)
2/(sum((x+np.sin(theta))>1)/N) 2/(sum((x+np.sin(theta))>1)/N)
#+end_src #+end_src
#+RESULTS:
: 3.128911138923655
* Using a surface fraction argument * Using a surface fraction argument
A method that is easier to understand and does not make use of the 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 $\sin$ function is based on the fact that if $X\sim U(0,1)$ and $Y\sim
...@@ -62,9 +56,6 @@ plt.savefig(matplot_lib_filename) ...@@ -62,9 +56,6 @@ plt.savefig(matplot_lib_filename)
print(matplot_lib_filename) print(matplot_lib_filename)
#+end_src #+end_src
#+RESULTS:
[[file:figure_pi_mc2.png]]
It is then straightforward to obtain a (not really good) approximation 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 to $\pi$ by counting how many times, on average, $X^2 + Y^2$ is smaller
than 1: than 1:
...@@ -72,5 +63,3 @@ than 1: ...@@ -72,5 +63,3 @@ than 1:
#+begin_src python :results output :session *python* :exports both #+begin_src python :results output :session *python* :exports both
4*np.mean(accept) 4*np.mean(accept)
#+end_src #+end_src
#+RESULTS:
Markdown is supported
0% or
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment