Ellipse circumference quickfur Junior Member Posts: 32 Threads: 9 Joined: Dec 2006 Reputation: 0 2007-02-19, 02:49 Hi all! Just a quick question... Recently I tried to look up the formula for the circumference of an ellipse, and found that it is highly non-trivial (involving elliptical integrals). However, I wonder if the following special case may be easier to calculate: given a circle of fixed circumference C and radius r, how easy is it to find an ellipse E with one of the axes already given, such that E has circumference C? E.g., if I deform a circle into an ellipse with major radius R, what must the minor radius be in order for its circumference to be constant? Thanks. quickfur Junior Member Posts: 32 Threads: 9 Joined: Dec 2006 Reputation: 0 2007-02-19, 03:10 Hmm, OK, I just found an approximation of elliptic circumference with radii $a$ and $b$: $C \approx \pi\left(3(a+b) - \sqrt{(3a+b)(a+3b)}\right)$ (Ramanujan's approximation). Does anyone know how accurate this approximation is? bo198214 Administrator Posts: 53 Threads: 7 Joined: Dec 2006 Reputation: 0 2007-02-20, 21:41 Hm in my formula reference the formula $\approx \frac{3}{2} (a+b) - \sqrt{ab}$ is given ... *headscratch* Ever thought about the volume of a polyhedron given by its vertices? Seams a similar but completely different difficulty. quickfur Junior Member Posts: 32 Threads: 9 Joined: Dec 2006 Reputation: 0 2007-02-22, 05:34 bo198214 Wrote:Hm in my formula reference the formula $\approx \frac{3}{2} (a+b) - \sqrt{ab}$ is given ... *headscratch* Ever thought about the volume of a polyhedron given by its vertices? Seams a similar but completely different difficulty. Well, Ramanujan's formula is supposed to be "very accurate", so I don't know. But I like your version better, it's definitely a lot easier to remember! But regarding polyhedral volumes... isn't it just a matter of dissecting the polyhedron into right pyramids and summing them up? This isn't too hard to do from the vertex coordinates. bo198214 Administrator Posts: 53 Threads: 7 Joined: Dec 2006 Reputation: 0 2008-02-07, 17:41 Ellipses seem to be a really hard topic. There is not even a closed formula for the location of a planet revolving around the sun as a function of time. Instead we have all those Kepler's laws. « Next Oldest | Next Newest »