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

This study presents the conditions of M_{T}(2)-equivalence for two systems of vectors {x₁,x₂,x₃} and {y₁,y₂,y₃} in R_{T}², where M_{T}(2) is the group of all isometries of the 2-dimensional taxicab space R_{T}². Firstly a minimal complete system of M_{T}(2)-invariants of {x₁,x₂,x₃} is obtained. Then, using the conditions of M_{T}(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}(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}(2)-invariants.

• Publication year

  2019

• Venue

  Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics

• Publication date

  2019-12-27

• Fields of study

  Mathematics

• Identifiers
  DOI 10.31801/cfsuasmas.666357
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Equivalence Conditions of Two Bézier Curves in the Euclidean Geometry

  2018cited by this paper
• On Some Regular Polygons in the Taxicab 3-Space

  2016cited by this paper
• Regular polygons in taxicab geometry

  2014influential reference
• Invariant Properties of Curves in the Taxicab Geometry

  2014cited by this paper
• Linear Algebra

  2012cited by this paper
• AYA Regular Polygons in the Taxicab Plane

  2009cited by this paper
• Environmental Niche Equivalency versus Conservatism: Quantitative Approaches to Niche Evolution

  2008cited by this paper
• Niche overlap and diet breadth in bumblebees; are rare species more specialized in their choice of flowers?

  2004cited by this paper
• Ecologically meaningful transformations for ordination of species data

  2001cited by this paper
• Distance and cosine measures of niche overlap

  2001cited by this paper
• The Norm in Taxicab Geometry

  1999cited by this paper
• Algorithms in invariant theory

  1993cited by this paper
• The Taxicab Group

  1984influential reference
• SOME COMMENTS ON MEASURING NICHE OVERLAP

  1980cited by this paper
• Measures of Niche Overlap

  1980cited by this paper
• Nonlinear Differential Equations

  1963cited by this paper
• W.Liller編: Space Astrophsics, Mc Graw-Hill Book Co., New York, 1961, 272頁, 16×24cm, $10).

  1962cited by this paper
• The Classical Groups

  1940cited by this paper

• No citing papers are available for this paper.