Buffon's needle simulation in python

Question

import numpy as np
import matplotlib.pylab as plt

class Buffon_needle_problem:

    def __init__(self,x,y,n,m):
        self.x = x #width of the needle
        self.y =         


        

Answer 1

I would say that the problem is that you are defining the alignment of the needle by a simple linear function, when in fact the effective length of the needle from its centre is defined by a sinusoidal function.

You want to calculate the effective length of the needle (at 90° to the lines) by using a function that will calculate it from its angle.

Something like:

self.z.append(np.cos(np.random.uniform(-np.pi/2, np.pi/2))*self.x)

This will give the cosine of a random angle between -90° and +90°, times the length of the needle.

For reference, cos(+/-90) = 0 and cos(0) = 1, so at 90°, the needle with have effectively zero length, and at 0°, its full length.

I have neither mathplotlib or numpy installed on this machine, so I can't see if this fixes it, but it's definitely necessary.