import numpy as np
test_dimensions = [2, 100000]
print('Average distance between 2 points in a unit hypercube')
for n_dim in test_dimensions:
    distances = []
    for i in range(100000):
        rand_point_1 = np.random.uniform(size=n_dim)
        rand_point_2 = np.random.uniform(size=n_dim)
        dist = np.linalg.norm(rand_point_1-rand_point_2)
        distances.append(dist)
    avg_distance = np.mean(distances)
    print('{} dimensions: {}'.format(n_dim, avg_distance))