circlearea.py

from math import gcd, sqrt
import random


def area(radius):
    c = 0
    
    for total in range(4_631_219):
        a = random.randint(1, 666)
        b = random.randint(1, 666)

        if gcd(a, b) == 1:
            c += 1

    return sqrt(6 * total / c * (radius ** 4))


if __name__ == "__main__":
    while True:
        radius = input("circle's radius: ")
        try:
            radius = float(radius)
            break
        except ValueError:
            continue

    print(area(radius))