Circumference of an Ellipse

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, 
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/