Abstract

Bodies of constant width have been studied mathematically since Euler and have found various applications in engineering and other areas. In this paper, we seek to develop novel tools to gain deeper insights into these shapes and to better be able to analyze them. The idea which motivates the development in this paper is as follows: a body has constant width if and only if the chord connecting the intersections of the boundary of the body with each pair of parallel hyper planes which lie tangent to a body lies perpendicular to the hyper planes.This is a known fact and fairly simple to prove. However, most proofs in current literature either restrict themselves to a special case of the theorem or rely on some measure of visual geometric intuition. In this paper, we will develop a tool we will call the width vector function which allows this fact to be proven purely analytically using the tools of linear algebra.

Degree

College and Department

Computational, Mathematical, and Physical Sciences; Mathematics

Rights

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