Date of Award

2010

Level of Access Assigned by Author

Campus-Only Dissertation

Degree Name

Master of Arts (MA)

Department

Mathematics

Advisor

William Snyder

Second Committee Member

Ali Özlük

Third Committee Member

David Bradley

Abstract

Since the time of the Greeks straightedge and compass constructions have been studied extensively. These constructions represent geometry in its purist form and have been taught to students of mathematics since. As elegant as these constructions are they have very real limitations. The Greeks suspected these limitations and modern algebra fully exposed them. In spite of these limitations innovative tools have found their way into mathematical literature and have enabled us to construct cube roots and trisect any angle. Some of these tools have been fully characterized while some have not. This thesis investigates marked straightedge and compass constructions through an intriguing analog tool set that is coined as q-construction. It is known that taking cube roots and finding an arbitrary angle trisection is possible with marked straightedge and compass. At least one construction that is unknown is the taking of fifth roots. We show that it is possible to take fifth roots using q-construction. This non-trivial result suggests that it is possible to take fifth roots using a marked ruler and compass.

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