Publication Date

8-27-2009

Abstract

The role of the epicycloid in both historical and mathematical contexts was studied through readings and research. Throughout history, circles have been considered perfect and thus very important shapes. Because epicycloids are constructed by combining circular motions, their historical value is evident. Epicycloids are traced through history, with special emphasis on their use in astronomy. The epicycloid is also important from a purely mathematical perspective. The connection of the figure with Fourier series is analyzed and illustrated with various Matlab plots. Because of this connection, the power of the epicycloid as a modeling tool becomes clear. The epicycloid has also made some more recent appearances and these are presented as well. Of note here is the Antikythera mechanism which is an ancient device incorporating epicycloids that was fairly recently discovered. Also of interest is a toy called the Spirograph, which uses epicycloids to create intricate patterns.

Degree Name

Mathematics

Level of Degree

Masters

Department Name

Mathematics & Statistics

First Committee Member (Chair)

Alexander Stone

Second Committee Member

Pedro Embid

Third Committee Member

John Hamm

Language

English

Keywords

Epicycloids and hypocycloids, Epicycloids and hypocycloids--History, Fourier analysis.

Document Type

Thesis

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