A new perspective on taxicab conic sections

Abstract

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.

42 pages, 17 figures, submitted to The Art of Discrete and Applied Mathematics