points_on_square.js

// generate two points on unit square and return true if lte radius
function within(radius)
{
	const rand_one = toVector(Math.random()*4)
	const rand_two = toVector(Math.random()*4)

	return dist(rand_one,rand_two) <= radius
}

// map float between 0 and 4 to sides of unit square
function toVector(num)
{
	const side = Math.floor(num)

	// top left going clockwise
	switch(side)
	{
		case 0:
		 return {x:num%1,y:0}
		case 1:
		 return {x:1,y:num%1}
		case 2:
		 return {x:1-num%1,y:1}
		case 3:
		 return {x:0,y:1-num%1}
	}
}

function dist(v1,v2)
{
	return Math.sqrt(Math.pow(v1.x-v2.x,2) + Math.pow(v1.y-v2.y,2))
}

const radius = 0.5
const loops = 1000000000
let close_points = 0

for(var i=0;i<loops;i++)
{
	close_points += (within(radius) ? 1 : 0)
}

console.log(close_points.toLocaleString() + " points within " + radius + " over " + loops.toLocaleString() + " loops: " + (close_points/loops*100).toFixed(2) +"%" )