const PHI = (Math.sqrt(5) + 1) / 2

function divisor (n) {
  if (n === 0) return Math.sqrt(2 + PHI)

  var last = divisor(n - 1)
  return Math.sqrt(2 + last)
}

function pi (n) {
  if (n === 0) return 5 / PHI

  var last = pi(n - 1)
  return last * 2 / divisor(n)
}

console.log(pi(50))
//=> 3.1415926535897927

console.log(Math.PI)
//=> 3.141592653589793