Is there a better way to calculate π in one line?

Question

I've written solution of how to calculate pi number in python in one line:

def calc_pi(n=100):
    return 4.0 * sum([1 for i in range(n) if hypot(random(), random()) < 1]) / (n + 1)

I would like to know if there is a better solution for that and how to make it simpler?

P.S. I want to practice complex one-line functions, list comprehensions etc. Monte Carlo method is just an example.

Answer 1

4 * atan(1)

sum([1 for i in range(n) if hypot(random(), random()) < 1]) / n

will tend to atan(1) for large n, so you might as well calculate it directly:

>>> import math
>>> 4 * math.atan(1)
3.141592653589793

It at least looks like your formula and doesn't explicitely use math.pi.

By the way, I don't think you should divide by n+1 but by n. range(n) has n elements.

Code improvements

Also, you don't need to create a huge list just to calculate its sum. sum works fine with a generator.

I guess your hypot function uses sqrt. No need for it, since you're comparing to 1 and sqrt(1) == 1:

>>> from random import random
>>> n = 10000000
>>> 4.0 * sum(1 for i in range(n) if (random()**2 + random()**2) <= 1) / n
3.1418616

As mentioned by @Blender, you could also sum booleans:

>>> 4.0 * sum((random()**2 + random()**2) <= 1 for _ in range(n)) / n
3.1417656

Other series

Finally, there are better methods. This one is slow-ish, but it's concise and deterministic:

>>> 4 * sum(1.0/(2*i + 1)*(-1)**i for i in range(1000000))
3.1415916535897743

There are others, faster methods.