LoboVault Home
 

The mathematics of the epicycloid : a historical journey with a modern perspective

LoboVault

Please use this identifier to cite or link to this item: http://hdl.handle.net/1928/9799

The mathematics of the epicycloid : a historical journey with a modern perspective

Show full item record

Title: The mathematics of the epicycloid : a historical journey with a modern perspective
Author: Andrew, Precious
Advisor(s): Stone, Alexander
Committee Member(s): Embid, Pedro
Hamm, John
Department: University of New Mexico. Dept. of Mathematics and Statistics
Subject(s): Mathematics
History
Epicycloid
Epicycle
LC Subject(s): Epicycloids and hypocycloids.
Epicycloids and hypocycloids--History.
Fourier analysis.
Degree Level: Masters
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.
Graduation Date: July 2009
URI: http://hdl.handle.net/1928/9799

Files in this item

Files Size Format View
PAndrewThesis.pdf 1.529Mb PDF View/Open

This item appears in the following Collection(s)

Show full item record

UNM Libraries

Search LoboVault


Advanced Search

Browse

My Account