Abstract
Fix two points and in the plane and a positive number . A result credited to Apollonius of Perga states that the set of points that satisfy 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
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
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