I am shocked that I have walked the surface of this planet for over 5 decades without realizing that there is no exact closed-form solution for the perimeter of an ellipse. In school, we learn the perimeter of shapes like triangles, squares, rectangles, circles, parallelograms, and so on, but I feel like schools and teachers conveniently skipped over ellipses.
(An ellipse, in case it’s been a while, is the set of points where the sum of the distances from two points – the foci – is a constant.)
Your challenge, should you choose to accept it, is to correct that oversight. Create a Mathcad worksheet that:
- Derives, depicts, or shows one (or more) of the various approximation formulas / methods for the perimeter of an ellipse.
- Create a calculator whereby someone can change the values of the semi-major and semi-minor axis lengths in order to find the perimeter.
- Create a 3D plot of the perimeter as a function of the ellipse semi-major and semi-minor axis lengths.
Although there is no exact solution for the perimeter of an ellipse, this is a fairly well-documented problem. Therefore, your documentation in your worksheet is key! This worksheet should be able to stand on its own and be understood by someone with a basic knowledge of calculus (since integrals and infinite series are involved).
Good luck and have fun!
Find the Mathcad Community Challenge Guidelines here!
Not the right expression for the kernel of the integral Fred. Should be as follows:
Alan
