Taxicab Angles and Trigonometry
Kevin Thompson, Tevian Dray
TL;DR
This paper develops an analogue of angles and trigonometry within taxicab geometry, analyzing congruence relations and applying the concepts to determine distances using parallax.
Contribution
It introduces a novel framework for angles and trigonometry in taxicab geometry and explores its properties and applications.
Findings
Certain congruence relations hold in taxicab geometry
A method for using parallax to measure taxicab distances is proposed
The structure differs from Euclidean trigonometry in key ways
Abstract
A natural analogue to angles and trigonometry is developed in taxicab geometry. This structure is then analyzed to see which, if any, congruent triangle relations hold. A nice application involving the use of parallax to determine the exact (taxicab) distance to an object is also discussed.
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Taxonomy
TopicsMathematics and Applications · Advanced Theoretical and Applied Studies in Material Sciences and Geometry · Historical Geography and Cartography