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A Family of Circles in a Window

For Ford Circles on the real line, [0; 1], G.T. Williams and D.H. Browne discovered that this arrangement of infinite circles has an area-sum \pi+\pi\frac{\zeta(3)}{\zeta(4)}, where \zeta(s) is the Riemann-Zeta function from complex analysis and number theory. The purpose of this paper is to explore their findings in detail and provide alternative methods to prove the statements found in the paper. Then we will attempt to show similar results on the Apollonian Window packing using inversion through circles and the results of Williams and Browne.

Identiferoai:union.ndltd.org:siu.edu/oai:opensiuc.lib.siu.edu:theses-2661
Date01 May 2015
CreatorsLightfoot, Ethan Taylor
PublisherOpenSIUC
Source SetsSouthern Illinois University Carbondale
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceTheses

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