A Metacalibration Proof of the Isoperimetric Problem

Authors

James Dilts, Brigham Young UniversityFollow

Abstract

The isoperimetric problem asks, among all figures with the same perimeter (iso-perimetric means ``same perimeter''), which has the greatest area. This paper proves the classic isoperimetric problem using a generalization of calibration techniques which we call metacalibration. We then generalize to arbitrary dimensions and to spherical spaces.

Author Bio

I am a math major at Brigham Young University, and started working with Dr. Lawlor at BYU a year ago. After showing me the methods he had developed to solve minimization problems, I went off and started working. This paper is the result. I plan on earning my Ph.D. and becoming a college professor.

Faculty Sponsor

Gary Lawlor

Recommended Citation

Dilts, James (2010) "A Metacalibration Proof of the Isoperimetric Problem," Rose-Hulman Undergraduate Mathematics Journal: Vol. 11: Iss. 2, Article 2.
Available at: https://scholar.rose-hulman.edu/rhumj/vol11/iss2/2