An illustrated introduction to the arithmetic of Apollonian circle packings, continued fractions, and other thin orbits

Autor:	Stange, Katherine E.
Rok vydání:	2024
Předmět:	Mathematics - Number Theory Mathematics - Dynamical Systems Mathematics - Metric Geometry 11A55 11J70 11J99 52C26 51M10 11E41 11G99 11A15 37D40
Druh dokumentu:	Working Paper
Popis:	These notes cover and expand upon the material for two summer schools: The first, which was held at CIRM, Marseille, France, July 10-14, 2023, as part of "Renormalization and Visualization for packing, billiard and surfaces", was titled "Number theory as a door to geometry, dynamics and illustration". The second was held at NSU IMS in Singapore, June 3-7, 2024, as part of "Computational Aspects of Thin Groups", and was titled "Integral packings and number theory". Both courses were put together by a number theorist for students and researchers in other fields. They cover a web of ideas relating to Apollonian circle packings, integral orbits, thin groups, hyperbolic geometry, continued fractions, and Diophantine approximation. The connection of geometry and dynamics to number theory gives an opportunity to illustrate arithmetic by appealing to our visual intuition. Comment: 66 pages, 40 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.02050 Zobrazit plný text záznamu View this record from Arxiv