Formula for the Circumference of an EllipseDate: 6/27/96 at 14:1:21 From: mike reese Subject: Circumference of an Ellipse Please divulge the correct formula or equation for solving the circumference of an ellipse. Date: 6/28/96 at 14:34:15 From: Doctor Mike Subject: Re: Circumference of an Ellipse Hello, Nice to hear from another Mike. This is an interesting question, and I did not know the answer, so I looked it up on our web site (see below). Turns out it is a VERY interesting question with a lot of history. There is a simple formula for the area of an ellipse, but not for the circumference (or perimeter). Here's what I found out. I started out by picking the SEARCH DR. MATH ARCHIVES link on the Web site and entered ELLIPSE as the search word. I got a lot of things to look at, which led me to further links, and eventually found my way to a document with the net URL address: http://www.astro.virginia.edu/~eww6n/math/math.html This is literally a Treasure Trove of math information, and I looked up the Ellipse subject in this alphabetical arrangement. If the ellipse has semi-radius values A and B, then the area is pi(A*B) which is a nice generalization of the pi(R^2) formula for the circle. The only available formulas for the perimeter involve Elliptic Integrals, which doesn't do you much good. There is an approximation formula by Ramanujan: pi( (3A+3B) - sqrt((A+3B)*(B+3A)) ) which is about as good as you are going to get. I invite you to look around at these Internet sites. Enjoy. I hope this helps. -Doctor Mike, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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