code for generating the empirical distribution of max-segment lengths

randomSegments.py

from random import uniform
from numpy import array
from math import pi

def MaxArc(N):
    cuts = [ uniform(0, 2*pi) for x in range(N) ]
    cuts.sort()
    other = [x for x in cuts]
    other.insert(0, other.pop())
    cuts[0]+=2*pi
    out = zip(cuts, other)
    lengths = [ abs(x-y) for x,y in out ]
    lengths.sort()
    return lengths.pop()

def harmonic(N):
    data = array([ 1/float(x+1) for x in range(N)])
    return data.sum()