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
See also Dido's Problem, Isovolume Problem
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.