Revisiting Taxicab Apollonius Circles
Kevin P. Thompson
TL;DR
This paper explores the properties of excircles and Apollonius circles within taxicab geometry, highlighting their relationship to inscribed triangles and revisiting classical Euclidean concepts in a non-Euclidean setting.
Contribution
It introduces the concept of excircles and Apollonius circles in taxicab geometry, extending classical triangle circle properties to this non-Euclidean metric.
Findings
Excircles exist in taxicab geometry under certain conditions.
Apollonius circles can be characterized in taxicab geometry.
Connections between inscribed triangles and these circles are established.
Abstract
The existence of excircles and an Apollonius circle for a triangle in taxicab geometry are connected to the concept of inscribed triangles.
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Taxonomy
TopicsMathematics and Applications · Historical Geography and Cartography