Date of Award

2014

Document Type

Thesis

Degree Name

Bachelor of Science (B.S.) in Mathematics and University Honors

Department

Mathematics and Statistics

First Advisor

Mau Nam Nguyen

Subjects

Convex geometry, Mathematical optimization, Mathematical analysis

DOI

10.15760/honors.62

Abstract

Helly's theorem is an important result from Convex Geometry. It gives sufficient conditions for a family of convex sets to have a nonempty intersection. A large variety of proofs as well as applications are known. Helly's theorem also has close connections to two other well-known theorems from Convex Geometry: Radon's theorem and Carathéodory's theorem. In this project we study Helly's theorem and its relations to Radon's theorem and Carathéodory's theorem by using tools of Convex Analysis and Optimization. More precisely, we will give a novel proof of Helly's theorem, and in addition we show in a complete way that these three famous theorems are equivalent in the sense that using one of them allows us to derive the others.

Persistent Identifier

http://archives.pdx.edu/ds/psu/11983

Download

Share

COinS