Pi Day!

gcd.js

const iterations = 1000000;
const max = 1000000;

let count = 0;

const random = () => {
  return Math.floor(Math.random() * max);
}

const euclid_gcd = (a, b) => {
  if (b) {
    return euclid_gcd(b, a % b);
  } else {
    return Math.abs(a);
  }
}

for (let i = 0; i < iterations; i++) {
  const gcd = euclid_gcd(random(), random());
  if (gcd === 1) {
    count++;
  }
}

console.log(Math.sqrt(6 / (count / iterations)));

gcd.rb

ITERATIONS = 1000000
MAX = 1000000
prng = Random.new
count = 0

ITERATIONS.times do
  gcd = prng.rand(MAX).gcd(prng.rand(MAX))
  count += 1 if gcd == 1
end

puts Math.sqrt(6.0 / (count.to_f / ITERATIONS.to_f))

Estimating the value of Pi by sampling the greatest common denominator between two large random numbers. First sample a large number of large integer pairs, taking note of each pair that does not share a common denominator greater than 1. Next, find the ratio of this count to the number of samples taken. The relationship between this ratio and pi is the square root of the quotient of 6 divided by that ratio.

sqrt(6 / (count / samples))

Inspired by Matt Parker's ridiculous dice-based sampling video for this year's Pi Day.
https://www.youtube.com/watch?v=RZBhSi_PwHU