2007-02-19, 02:49

Hi all! Just a quick question...

Recently I tried to look up the formula for the circumference of an ellipse, and found that it is highly non-trivial (involving elliptical integrals). However, I wonder if the following special case may be easier to calculate: given a circle of fixed circumference C and radius r, how easy is it to find an ellipse E with one of the axes already given, such that E has circumference C? E.g., if I deform a circle into an ellipse with major radius R, what must the minor radius be in order for its circumference to be constant? Thanks.

Recently I tried to look up the formula for the circumference of an ellipse, and found that it is highly non-trivial (involving elliptical integrals). However, I wonder if the following special case may be easier to calculate: given a circle of fixed circumference C and radius r, how easy is it to find an ellipse E with one of the axes already given, such that E has circumference C? E.g., if I deform a circle into an ellipse with major radius R, what must the minor radius be in order for its circumference to be constant? Thanks.