Type
Text
Type
Dissertation
Advisor
Kontorovich, Alex
Date
2014-12-01
Keywords
Mathematics
Department
Department of Mathematics.
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/76415
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
Starting with three mutually tangent circles, in each of the two gaps we inscribe three circles, and then we inscribe three new circles into the newly generated circles, so on so forth? We obtain a packing of infinitely many circles, and we give a name Apollonian-3 packings. It turns out there exist packings of this type with curvatures (1 over radius) all integers. I will discuss what we know about the integers arising as curvatures from these packings. I will discuss the reduction theorem, the symmetry group, and a density one theorem towards the local-global conjecture. | 47 pages
Recommended Citation
Zhang, Xin, "On the Local-global Principle for Integral Apollonian" (2014). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 2338.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/2338