'''Archimedes method for calculating value of pi'''

import math

def archimedes(numSides):
    # Approximate the value of pi by inscribing a polygon
    # within a circle and measuring the lengths of the sides.

    # The polygon will have numSides sides of length sideS.
    # The trick is to calculate the value of sideS.
    # Assume a unit circle (meaning radius is 1).

    # Angle B is the the angle of the triangle that has a side
    # as one edge and connects each end of that edge to the center.
    # This angle is determined by the number of sides.
    innerAngleB = 360.0 / numSides

    # We want half of B, to get a right triangle.
    halfAngleA = innerAngleB/2

    # Then we can calculate the length of the outer side of
    # this triangle to be the sin(A).
    # Python expects radians, so convert.
    oneHalfSideS = math.sin(math.radians(halfAngleA))

    # s is this length doubled.
    sideS = oneHalfSideS*2

    # The circumference is just s times the number of sides.
    circumference = numSides * sideS

    # Divide by 2 because that is the diameter of a unit circle.
    pi = circumference/2

    return pi