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

ören, idris; ÇOBAN, HÜSNÜ ANIL

doi:10.31801/cfsuasmas.666357

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

İdris ÖREN, (Karadeniz Teknik Üniversitesi, Fen Fakültesi, Matematik Bölümü, Trabzon, Türkiye)

Hüsnü Anıl ÇOBAN (Karadeniz Teknik Üniversitesi, Fen Fakültesi, Matematik Bölümü, Trabzon, Türkiye)

Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics

0 0

Yıl: 2020 Cilt: 69 Sayı: 1 Sayfa Aralığı: 413 - 430 Metin Dili: İngilizce DOI: 10.31801/cfsuasmas.666357 İndeks Tarihi: 30-10-2023

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

Öz:

This study presents the conditions of MT (2)-equivalence for two systems of vectors fx1; x2; x3g and fy1; y2; y3g in R2 T , where MT (2) is the group of all isometries of the 2-dimensional taxicab space R2 T . Firstly a min- imal complete system of MT (2)-invariants of fx1; x2; x3g is obtained. Then, using the conditions of MT (2)-equivalence, an answer is given to the open prob- lem posed in [10, p.428]. Furthermore, an algorithm is given for constructing taxicab regular polygons in terms of MT (2)-invariants. This algorithm is gen- eral 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 con- ditions of the taxicab regularity of Euclidean regular polygons and Euclidean regularity of taxicab regular polygons are given in terms of MT (2)-invariants.

Anahtar Kelime: Invariant regular polygon taxicab geometry

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] Abrams, P., Some comments on measuring niche overlap, Ecology, 61(1) (1980), 44-49.
[2] Çolakoğlu, H. B., Kaya, R., Regular polygons in the taxicab plane, KoG, 12 (2008), 27-33.
[3] Ekici, Kocayusufoğlu, İ., Akça, Z. The norm in taxicab geometry, Turk. J. Math, 22(3) (1998), 295-307.
[4] Goulson, D., Darvill, B., Niche overlap and diet breadth in bumblebees; are rare species more specialized in their choice of áowers?, Apidologie, 35 (2004), 55-63.
[5] Greub, W., Linear algebra, Berlin-Heidelberg-New York:Springer-Verlag, 1967.
[6] Hanson, J. R., Regular polygons in taxicab geometry, Int. J. Math. Educ. Sci. Technol., 45(7) (2014), 1084-1095.
[7] Legendre, P., Gallagher, E., Ecologically meaningful transformations for ordination of species data, Oecologia, 129 (2001), 271-280.
[8]Ören İ, Çoban, H. A., Some invariant properties of curves in the taxicab geometry, Missouri J. Math. Sci., 26 (2014), 107-114.
[9] Ören İ., Equivalence conditions of two BÈzier Curves in the Euclidean geometry, Iran. J. Technol. A. Sci., 42(3) (2018), 1563-1577.
[10] Schattschneider, D. J., The taxicab group, Am. Math. Mon., 91 (1984), 423-428.
[11] Slobodchiko§, C. N., Schulz, W. C. Measures of niche overlap, Ecology, 61(7) (1980), 1051- 1055.
[12] Sohn, M. W., Distance and cosine measures of niche overlap, Soc. Networks, 23 (2001), 141-165.
[13] Struble, R. A., Non-Linear di§erential equations, New York:Mc Graw-Hill, 1962.
[14] Sturmfels, B. Algorithms in invariant theory, Wien:Springer, 2008.
[15] Y ̧ksel, S., ÷zcan, M., Some regular polygons in the taxicab 3-space, KoG, 19 (2005), 32-41.
[16] Warren, D. L., Glor, R. E., Turelli, M., Environmental niche equivalency versus conservatism: quantitative approaches to niche evolution, Evolution, 62(11) (2008), 2868-2883.
[17] Weyl, H., The classical groups, their invariants and representations, New Delhi: Princeton University Press, 2013.

APA	ören i, ÇOBAN H (2020). EQUIVALENCE CONDITIONS OF TWO SYSTEMS OF VECTORS IN THE TAXICAB PLANE AND ITS APPLICATIONS TO TAXICAB POLYGONS. , 413 - 430. 10.31801/cfsuasmas.666357
Chicago	ören idris,ÇOBAN HÜSNÜ ANIL EQUIVALENCE CONDITIONS OF TWO SYSTEMS OF VECTORS IN THE TAXICAB PLANE AND ITS APPLICATIONS TO TAXICAB POLYGONS. (2020): 413 - 430. 10.31801/cfsuasmas.666357
MLA	ören idris,ÇOBAN HÜSNÜ ANIL EQUIVALENCE CONDITIONS OF TWO SYSTEMS OF VECTORS IN THE TAXICAB PLANE AND ITS APPLICATIONS TO TAXICAB POLYGONS. , 2020, ss.413 - 430. 10.31801/cfsuasmas.666357
AMA	ören i,ÇOBAN H EQUIVALENCE CONDITIONS OF TWO SYSTEMS OF VECTORS IN THE TAXICAB PLANE AND ITS APPLICATIONS TO TAXICAB POLYGONS. . 2020; 413 - 430. 10.31801/cfsuasmas.666357
Vancouver	ören i,ÇOBAN H EQUIVALENCE CONDITIONS OF TWO SYSTEMS OF VECTORS IN THE TAXICAB PLANE AND ITS APPLICATIONS TO TAXICAB POLYGONS. . 2020; 413 - 430. 10.31801/cfsuasmas.666357
IEEE	ören i,ÇOBAN H "EQUIVALENCE CONDITIONS OF TWO SYSTEMS OF VECTORS IN THE TAXICAB PLANE AND ITS APPLICATIONS TO TAXICAB POLYGONS." , ss.413 - 430, 2020. 10.31801/cfsuasmas.666357
ISNAD	ören, idris - ÇOBAN, HÜSNÜ ANIL. "EQUIVALENCE CONDITIONS OF TWO SYSTEMS OF VECTORS IN THE TAXICAB PLANE AND ITS APPLICATIONS TO TAXICAB POLYGONS". (2020), 413-430. https://doi.org/10.31801/cfsuasmas.666357

APA	ören i, ÇOBAN H (2020). EQUIVALENCE CONDITIONS OF TWO SYSTEMS OF VECTORS IN THE TAXICAB PLANE AND ITS APPLICATIONS TO TAXICAB POLYGONS. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 69(1), 413 - 430. 10.31801/cfsuasmas.666357
Chicago	ören idris,ÇOBAN HÜSNÜ ANIL EQUIVALENCE CONDITIONS OF TWO SYSTEMS OF VECTORS IN THE TAXICAB PLANE AND ITS APPLICATIONS TO TAXICAB POLYGONS. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 69, no.1 (2020): 413 - 430. 10.31801/cfsuasmas.666357
MLA	ören idris,ÇOBAN HÜSNÜ ANIL EQUIVALENCE CONDITIONS OF TWO SYSTEMS OF VECTORS IN THE TAXICAB PLANE AND ITS APPLICATIONS TO TAXICAB POLYGONS. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, vol.69, no.1, 2020, ss.413 - 430. 10.31801/cfsuasmas.666357
AMA	ören i,ÇOBAN H EQUIVALENCE CONDITIONS OF TWO SYSTEMS OF VECTORS IN THE TAXICAB PLANE AND ITS APPLICATIONS TO TAXICAB POLYGONS. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics. 2020; 69(1): 413 - 430. 10.31801/cfsuasmas.666357
Vancouver	ören i,ÇOBAN H EQUIVALENCE CONDITIONS OF TWO SYSTEMS OF VECTORS IN THE TAXICAB PLANE AND ITS APPLICATIONS TO TAXICAB POLYGONS. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics. 2020; 69(1): 413 - 430. 10.31801/cfsuasmas.666357
IEEE	ören i,ÇOBAN H "EQUIVALENCE CONDITIONS OF TWO SYSTEMS OF VECTORS IN THE TAXICAB PLANE AND ITS APPLICATIONS TO TAXICAB POLYGONS." Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 69, ss.413 - 430, 2020. 10.31801/cfsuasmas.666357
ISNAD	ören, idris - ÇOBAN, HÜSNÜ ANIL. "EQUIVALENCE CONDITIONS OF TWO SYSTEMS OF VECTORS IN THE TAXICAB PLANE AND ITS APPLICATIONS TO TAXICAB POLYGONS". Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 69/1 (2020), 413-430. https://doi.org/10.31801/cfsuasmas.666357