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.
| Identifer | oai:union.ndltd.org:siu.edu/oai:opensiuc.lib.siu.edu:theses-2661 |
| Date | 01 May 2015 |
| Creators | Lightfoot, Ethan Taylor |
| Publisher | OpenSIUC |
| Source Sets | Southern Illinois University Carbondale |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Theses |
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