First Advisor
Mau Nam Nguyen
Date of Award
2014
Document Type
Thesis
Degree Name
Bachelor of Science (B.S.) in Mathematics and University Honors
Department
Mathematics and Statistics
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.
Rights
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Persistent Identifier
http://archives.pdx.edu/ds/psu/11983
Recommended Citation
Robinson, Adam, "Helly's Theorem and its Equivalences via Convex Analysis" (2014). University Honors Theses. Paper 67.
https://doi.org/10.15760/honors.62