Abstract
In this note, we introduce a method called Strict Steiner Symmetrization (see Section 2.2) that is an altered form of Steiner Symmetrization that fixes the number of vertices. The context of this paper will be to prove the Isoperimetric Inequality in R2 via approximation by polygons. Specifically, to establish that among all n-gon domains in the plane, the regular m-gon, m ≥ n, uniquely minimizes the isoperimetric ratio and that the limit of this regular polygon (that is the circle) achieves equality in the isoperimetric inequality. This note is an extracted portion of my junior thesis (A Polygonal Proof of the Isoperimetric Inequality in R2) where we focus on the Strict Steiner Symmetrization Method.
Recommended Citation
Chai, Joseph and Chang, Sun-Yung Alice
(2026)
"Strict Steiner Symmetrization for Polygons,"
Electronic Proceedings of Undergraduate Mathematics Day: Vol. 9, Article 4.
Available at:
https://ecommons.udayton.edu/epumd/vol9/iss1/4