Master's Theses

Document Type

Thesis - campus only access

Date of Award

Summer 1969

Degree Name

Master of Arts (MA)

Department

Math

Advisor

Wilmont Toalson

Abstract

The object of this paper is to present (1) a logical development of properties of plane curves of constant width, (2) some examples of such curves, and (3) applications of their properties. Investigation of available literature has yielded proofs of several characterizing theorems and some interesting, if not so essential properties, these sources also report a variety of practical applications in kinematics and intuitively present some examples of curves of constant width made up entirely of circular arcs (all special cases of a more general curve for which this paper gives a rigorous proof). In addition, this paper verifies the constant width of curves different from any types given in the literature, thereby establishing that there are some curves of constant width made up partly of circular and partly of non-circular arcs, and some no part of which is circular. Also included in this paper are a number of original proofs. One of these demonstrates that curves of constant diameter are curves of constant width; another establishes the convexity of such curves.

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Rights

© 1969 Judith Ann Nusse

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