```Date: Jul 18, 2004 10:29 AM
Author: Stephanie
Subject: .Re: Partial perimeter of ellipse

> > Stephanie wrote:> > In other words find the arbitrary (meaning between the two> > points...not the "complete" from 0 to 2pi) elliptic integral of the> > second kind?> > Lengths of arcs of ellipses can be given precisely in terms of incomplete> (which is perhaps what you called "arbitrary") elliptic integrals of the> second kind. See Gerard Michon's Numericana page on this topic:> http://www.numericana.com/answer/geometry.htm#ellipticarc. You might> also be interested in a very simple approximation, providing> |relative error| < 0.006, which I posted to sci.math at the end of 2002:> http://mathforum.org/discuss/sci.math/t/469668 .> > David W. Cantrell---------------------------------------------------As I said to the other person, I might not have been clearin what I meant.I mean the AVERAGE radius BETWEEN and including the twopoints (not just the median radius between the two points)!That is why I referred to the elliptic integral, becauseI know it is not just the simple median.The reason I ask is because I was talking with someone whosays it is an elliptic integral based on the "meridian radiusof curvature", which equals the elliptic integral of thesecond kind in the COMPLETE (meaning from 0 to 90^o) case, butnot any other "incomplete", arbitrary one.++For instance, at 90^othe radius equals "b", but the "meridian radius of curvature"equals a^2/b.++It seems obvious the answer should be "b", butmy friend says no.-------------- ??????????????????????????????????????????????? ????????????????????????????????????????????????????????? KORNET -------------
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