Equivalence conditions of two systems of vectors in the taxicab plane and its applications to taxicab polygons

Authors : İdris ÖREN, Hüsnü Anıl ÇOBAN

Pages : 413-430

Doi:10.31801/cfsuasmas.666357

View : 30 | Download : 7

Publication Date : 2020-06-30

Article Type : Research Paper

Abstract :This study presents the conditions of M_{T}insert ignore into journalissuearticles values(2);-equivalence for two systems of vectors {x₁,x₂,x₃} and {y₁,y₂,y₃} in R_{T}², where M_{T}insert ignore into journalissuearticles values(2); is the group of all isometries of the 2-dimensional taxicab space R_{T}². Firstly a minimal complete system of M_{T}insert ignore into journalissuearticles values(2);-invariants of {x₁,x₂,x₃} is obtained. Then, using the conditions of M_{T}insert ignore into journalissuearticles values(2);-equivalence, an answer is given to the open problem posed in sch . Furthermore, an algorithm is given for constructing taxicab regular polygons in terms of M_{T}insert ignore into journalissuearticles values(2);-invariants. This algorithm is general and useful to construct the taxicab regular 2n-gons and gives a tool to solve special cases of the open problem posed in col . Besides, both the conditions of the taxicab regularity of Euclidean regular polygons and Euclidean regularity of taxicab regular polygons are given in terms of M_{T}insert ignore into journalissuearticles values(2);-invariants.
Keywords : Invariant, regular polygon, taxicab geometry

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