How could you accurately find the perimeter of an ellipse accurately? This formula:
$$p\approx 2\pi\sqrt{\dfrac{a^2+b^2}{2}}$$
(Where 'a' is the distance from the center of the ellipse to the farthest point and 'b' is the distance from the center to the nearest point) does the job, but it isn't exact. It also doesn't work if 'a' is three times greater than 'b'. What is another formula that I could use to find the exact perimeter of an ellipse?
The perfectly accurate formula for the perimeter of a non-circular ellipse cannot be expressed in more-elementary terms. It involves "elliptic integrals" (so-named because they arise in such a problem) that in the non-circle case do not simplify to anything expressible in more elementary terms.