Cosine distance between two random vectors is normally distributed around 0.75

cosine_distance_background.py

import numpy as np

mag = np.linalg.norm
r = np.random.random

def cosdist(x,y):
    return sum(x * y) / (mag(x) * mag(y))

def repeat(f,n):
    return [f() for _ in range(n)]

d = repeat(lambda: cosdist(r(100),r(100)),100000)

plt.hist(d,bins = 100); # cosine distance centered on 0.75