Apollonian sets in taxicab geometry
Apollonian sets in taxicab geometry
Fix two points p and q in the plane and a positive number k≠1. 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 …