AGM Method

agm.js

var pi = agm(3);
console.log(pi);

function agm(n) {
  var a = 1,
    b = 1 / Math.sqrt(2),
    t = 1 / 4,
    p = 1,
    an;
  for (var i = 0; i < n; i++) {
    an = (a + b) / 2;
    b = Math.sqrt(a * b);
    t = t - p * (Math.pow(a, 2) - 2 * a * an + Math.pow(an, 2));
    p = 2 * p;
    a = an;
  }
  return Math.pow(a + b, 2) / (4 * t);
}