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Febuary 2020 Apollonian sets in taxicab geometry
Eric Bahuaud, Shana Crawford, Aaron Fish, Dylan Helliwell, Anna Miller, Freddy Nungaray, Suki Shergill, Julian Tiffay, Nico Velez
Rocky Mountain J. Math. 50(1): 25-39 (Febuary 2020). DOI: 10.1216/rmj.2020.50.25

Abstract

Fix two points p and q in the plane and a positive number k1. A result credited to Apollonius of Perga states that the set of points x that satisfy d(x,p)d(x,q)=k forms a circle. In this paper we study the analogous set in taxicab geometry. We find that while Apollonian sets are not taxicab circles, more complicated Apollonian sets can be characterized in terms of simpler ones.

Citation

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Eric Bahuaud. Shana Crawford. Aaron Fish. Dylan Helliwell. Anna Miller. Freddy Nungaray. Suki Shergill. Julian Tiffay. Nico Velez. "Apollonian sets in taxicab geometry." Rocky Mountain J. Math. 50 (1) 25 - 39, Febuary 2020. https://doi.org/10.1216/rmj.2020.50.25

Information

Received: 31 October 2018; Revised: 13 September 2019; Accepted: 14 September 2019; Published: Febuary 2020
First available in Project Euclid: 30 April 2020

zbMATH: 07201552
MathSciNet: MR4092542
Digital Object Identifier: 10.1216/rmj.2020.50.25

Subjects:
Primary: 51M05, 51M15

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 1 • Febuary 2020
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