Commit e06f6a7c authored by Anton Y.'s avatar Anton Y.

task try 5

parent ad1703eb
...@@ -31,8 +31,7 @@ theta = np.random.uniform(size=N, low=0, high=pi/2) ...@@ -31,8 +31,7 @@ theta = np.random.uniform(size=N, low=0, high=pi/2)
#+end_src #+end_src
* 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 $Y\sim
U(0,1)$, then $P[X^2+Y^2\leq 1] = \pi/4$ (see [[https://en.wikipedia.org/wiki/Monte_Carlo_method]["Monte Carlo method" on 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: Wikipedia]]). The following code uses this approach:
...@@ -56,7 +55,7 @@ plt.savefig(matplot_lib_filename) ...@@ -56,7 +55,7 @@ plt.savefig(matplot_lib_filename)
print(matplot_lib_filename) print(matplot_lib_filename)
#+end_src #+end_src
It is then straightforward to obtain a (not really good) approximation It is then straightforward to obtain a (not really good) approximatin
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:
......
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