The idea is nice, but the code is a little flaky. For example, change the number of decimals from 1000 to 2000 and it enters an infinite loop, but 4000 works a

The idea is nice, but the code is a little flaky. For example, change the number of decimals from 1000 to 2000 and it enters an infinite loop, but 4000 works again. This occurs because due to rounding a and b might not converge to the exact same value. A more reliable way to write the algorithm is this: n = 0 while not almosteq(a, b): n, a, b = n + 1, (a + b)/2, sqrt(a*b) series += 2**(n+1) * (a*a - b*b)