#!/usr/bin/env python3
import random, math

inside = 0
total = 10000000

for i in range(0, total):
    x = random.random()
    y = random.random()
    z = random.random()
    t = random.random()
    if math.sqrt(x**2 + y**2 + z**2 + t**2) < 1.0:
    # will also work:
    # if x**2 + y**2 + z**2 + t**2 < 1.0:
        inside += 1

area = float(inside) / total*(2**4)
print("volume of tesseract", 2**4)
print("volume 4-sphere", area)