2006-08-30 09:53:14 · 4 answers · asked by jus_thinking 1 in Science & Mathematics ➔ Mathematics
There is no simple formula for this. If you set up the integral for this arc length, it turns out not to be expressible simply. In fact, new functions, called elliptic integrals are defined for exactly this reason.
2006-08-30 10:02:15 · answer #1 · answered by mathematician 7 · 1⤊ 0⤋
First responder is correct. The second responder presents an integral that cannot be reduced to a closed form. There are approximations that can be used which work well if the ellipticity is very small.
2006-08-30 10:35:11 · answer #2 · answered by Anonymous · 0⤊ 1⤋
4a Integral[ Sqrt[ 1 - (a^2 - b^2) Sin^2[x] / a^2 ], {x, 0, Pi/2}]
being a the radius longest , and b the shortest.
2006-08-30 10:09:21 · answer #3 · answered by Pedromdrp 2 · 0⤊ 1⤋
http://mathforum.org/dr.math/faq/formulas/faq.ellipse.html
2006-08-30 17:11:18 · answer #4 · answered by Sherman81 6 · 0⤊ 0⤋