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Circumference of an Ellipse

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Date: 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,

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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Associated Topics:
High School Conic Sections/Circles
High School Geometry

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