From-scratch PI approximation (based on Archimedes' method using inscribed regular hexagons)

gistfile1.py

def approx_pi (iterations):
	''' pi approximation based on Archimedes' geometric method (find the
		perimeter of a regular hexagon subdivided n times, and use that
		as an approximation to C = 2*pi*r, with r = 1.0).
	
		Note: Becomes increasingly inaccurate when iterations > 15 due to 
		the limitations of Python's floating point numbers. Would have to
		implement bignums w/ an extremely accurate sqrt fcn to get better
		precision.
	'''

	d = 1.0
	for i in range(iterations):
		d = (2.0 - (4.0 - d ** 2) ** 0.5) ** 0.5
	d *= 2.0 ** iterations
	return 3.0 * d

if __name__ == '__main__':
	from math import pi

	print('approx: {0}'.format(approx_pi(15)))
	print('actual: {0}'.format(pi))
	
# Outputs:
#	 approx: 3.14159264532
#	 actual: 3.14159265359