Find a closed plane curve of a given length which encloses the greatest Area. The solution is a Circle. If
the class of curves to be considered is limited to smooth curves, the isoperimetric problem can be stated symbolically as
follows: find an arc with parametric equations , for such that ,
(where no further intersections occur) constrained by

such that

is a Maximum.

**References**

Bogomolny, A. ``Isoperimetric Theorem and Inequality.'' http://www.cut-the-knot.com/do_you_know/isoperimetric.html.

Isenberg, C. Appendix V in *The Science of Soap Films and Soap Bubbles.* New York: Dover, 1992.

© 1996-9

1999-05-26