A new perspective on taxicab conic sections
Emily Frost, Dylan Helliwell, Suki Shergill
TL;DR
This paper offers a novel geometric perspective on taxicab conic sections by analyzing their formation through plane slicing of taxicab cones, leading to a comprehensive structural characterization.
Contribution
It introduces a new approach to taxicab conic sections via slicing, providing a complete structural characterization and exploring special cases.
Findings
Complete classification of taxicab conic sections
Structural framework for taxicab conic analysis
Identification of special cases within taxicab conics
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.
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Taxonomy
TopicsMechanical Engineering and Vibrations Research · Advanced Theoretical and Applied Studies in Material Sciences and Geometry · Robotic Mechanisms and Dynamics