To prove algebraically that all sections of the shape have an equal area:
Begin with the smallest semi-circle.
Let r be the radius of the semi-circle.
A = (Ï€r^2)/ 2
As the radius for the second-smallest semi-circle is twice the size of the smallest, this formula may be doubled to achieve the result.The number that the original formula is multiplied by according to the size of the other semi -circles may be shown as n. Note that n is always less than or equal to the total number of portions in the shape. For example, in a three-part image, n could only be 3, 2 or 1.
A = n(Ï€r^2)/ 2
Therefore, once the area occupied by the smaller shapes within the respective area is subtracted, each 'curvy area' will be equivelant to the other's in it's problem.