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November 2014 Invariant Properties of Curves in the Taxicab Geometry
Idris Oren, H. Anil Coban
Missouri J. Math. Sci. 26(2): 107-114 (November 2014). DOI: 10.35834/mjms/1418931952

Abstract

Let $E^{2}_{T}$ be the group of all isometries of the $2$-dimensional taxicab space $R^{2}_{T}$. For the taxicab group $E^{2}_{T}$, the taxicab type of curves is introduced. All possible taxicab types are found. For every taxicab type, an invariant parametrization of a curve is described. The $E^{2}_{T}$-equivalence of curves is reduced to the problem of the $E^{2}_{T}$-equivalence of paths.

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Idris Oren. H. Anil Coban. "Invariant Properties of Curves in the Taxicab Geometry." Missouri J. Math. Sci. 26 (2) 107 - 114, November 2014. https://doi.org/10.35834/mjms/1418931952

Information

Published: November 2014
First available in Project Euclid: 18 December 2014

zbMATH: 1311.51010
MathSciNet: MR3293808
Digital Object Identifier: 10.35834/mjms/1418931952

Subjects:
Primary: 51F20 , 51K05 , 51K99 , 51N30
Secondary: 53A35 , 53A55

Keywords: curve , Invariant parametrization , Taxicab geometry

Rights: Copyright © 2014 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.26 • No. 2 • November 2014
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