Circumference of an EllipseDate: 5/18/96 at 15:54:16 From: Anonymous Subject: Circumference of an ellipse Is there a formula for determining the circumference or distance around an ellipse? I have looked in several geometry books, and searched newsgroup archives. Thanks. Chan Peas Date: 6/5/96 at 17:7:16 From: Doctor Ceeks Subject: Re: Circumference of an ellipse Determining the circumference of an ellipse to any degree of accuracy is a well understood problem. In principle, computation of the arc length of any explicitly given curve to any degree of accuracy has been understood since the time of Newton (maybe Archimedes knew too!). The ideas of integral Calculus are applicable to the problem and give an algorithm for such a computation. Note that the circumference of a circle can be computed to any degree of accuracy (in principle) because we know how to compute pi to any degree of accuracy (using, implicitly or explicitly, ideas of integral Calculus). Assuming the value of pi, the circumference of a circle is 2*pi*r, where r is the radius. An ellipse is specified by two parameters (major and minor axis) and there is no simple formula for the circumference of the ellipse in terms of these two parameters. The area, however, is pi*a*b/4 where a and b are the lengths of the major and minor axes. -Doctor Ceeks, The Math Forum http://mathforum.org/dr.math/ |
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