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 clear

in what I meant.

I mean the AVERAGE radius BETWEEN and including the two

points (not just the median radius between the two points)!

That is why I referred to the elliptic integral, because

I know it is not just the simple median.

The reason I ask is because I was talking with someone who

says it is an elliptic integral based on the "meridian radius

of curvature", which equals the elliptic integral of the

second kind in the COMPLETE (meaning from 0 to 90^o) case, but

not any other "incomplete", arbitrary one.++For instance, at 90^o

the radius equals "b", but the "meridian radius of curvature"

equals a^2/b.++It seems obvious the answer should be "b", but

my friend says no.

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