arXiv subjects

Suki Shergill

Publications and source records attributed to Suki Shergill.

2 recordsLinked to original sources

arXiv2022

A new perspective on taxicab conic sections

We explore taxicab conic sections from the perspective of slicing taxicab cones by planes, as opposed to the more well-studied approach from the perspective of distance formulations. After establishing a significant amount of structural framework, a complete characterization of the resulting taxicab conic sections is established, and a number of special cases are explored.

math.MG↗

arXiv2018

Apollonian sets in taxicab geometry

Fix two points $p$ and $q$ in the plane and a positive number $k \neq 1$. 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 sets are not taxicab circles, more complicated Apollonian sets can be characterized in terms of simpler ones.

math.MG↗