EQUIVALENCE CONDITIONS OF TWO SYSTEMS OF VECTORS IN THE TAXICAB PLANE AND ITS APPLICATIONS TO TAXICAB POLYGONS

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Atıf İçin Kopyala

ÖREN İ., ÇOBAN H. A.

COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, cilt.69, sa.1, ss.413-430, 2020 (ESCI)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 69 Sayı: 1
• Basım Tarihi: 2020
• Doi Numarası: 10.31801/cfsuasmas.666357
• Dergi Adı: COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS
• Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
• Sayfa Sayıları: ss.413-430
• Anahtar Kelimeler: Invariant, regular polygon, taxicab geometry, NICHE, CURVES
• Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

This study presents the conditions of M-T (2)-equivalence for two systems of vectors {x(1), x(2,) x(3)} and {y(1), y(2), y(3)} 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 {x(1), x(2), x(3)} is obtained. Then, using the conditions of M-T (2)-equivalence, an answer is given to the open problem posed in [10, p.428]. 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 [2, p.32]. 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.