#Simulation of Buffon Needle Problem,

from pylab import *
def buffon(throws,needle_length=1):
#draw the floor planks
    ylim(0,6)
    xlim(0,8)
    for j in range(1,6):
        axhline(y=j,xmin=0,xmax=8,color='k',linewidth=3)
    axis('scaled') #important! otherwise apparent length of
                  #needle changes with the angle.
    axis([0,8,0,6])
#throw the needles
    count=0
    for j in range(throws):
        x=8*rand()#x-coordinate is just for show.
                #we allow any visible position on the grid for the
                #lower point of the needle, so some throws extend
                #out of bounds, and only one endpoint will be visible.
        y=6*rand() #the y-coordinate of the lower end of the needle.
        theta=pi*rand() #the angle, between 0 and pi
        if throws<=5000:
            plot([x,x+needle_length*cos(theta)],[y,y+needle_length*sin(theta)],'r-')
        #This next, together with the loop initialization and the call
        #to generate random y, is really the whole simulation!  Everything
        #else is just there to draw the picture.
        if (y-floor(y))+needle_length*sin(theta)>1:#crossed a line
            count +=1
    title(str(throws)+""" throws,
crossing rate """+str(1.0*count/throws))
    show()