Zip Zap and Poof!

Computer Science Level 5

What is the expected distance between 2 points chosen uniformly (by volume) in a unit cube?


The answer is 0.66170.

Kunal Gupta by Kunal Gupta , 23, India

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2 solutions

Abdelhamid Saadi
Jan 14, 2017

This solution in python based on Monte Carlo. 

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"Zip Zap and Poof!"

from random import random as rand

def distance(p, q):
    return ((p[0] -q[0])**2 + (p[1] -q[1])**2 + (p[2] -q[2])**2)**.5

def randPoint():
    return (rand(), rand(), rand())


for k in range(40):
    n = 2**k
    print(n, sum(distance(randPoint(), randPoint()) for p in range(n))/n)

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Aaghaz Mahajan
Jan 22, 2019

This is known as the Robbin's Constant

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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