Yıl 2018, Cilt 6, Sayı 1, Sayfalar 158 - 162 2018-04-15

A Generalization of The Taxicab Metric And Related Isometries

Harun Barış Çolakoğlu [1]

65 87

In this paper, we define a family of distance functions in the real plane, \textit{m}-generalized taxicab distance function, which includes the generalized taxicab distance and so the taxicab distance functions as special cases, and we show that the \textit{m}-generalized taxicab distance function determines a metric. Then we give some properties of the \textit{m}-generalized taxicab metric, and determine Euclidean isometries that preserve the \textit{m}-generalized taxicab metric.
metric, taxicab distance, generalized taxicab distance, isometry
  • [1] Çolakoğlu, H.B. and Kaya, R. A generalization of some well-known distances and related isometries, Math. Commun. Vol:16 (2011), 21-35.
  • [2] Ekmekçi, S., Bayar, A. and Altıntas¸, A.K. On the group of isometries of the generalized taxicab plane, International Journal of Contemporary Mathematical Sciences Vol:10, No.4 (2015), 159-166.
  • [3] Ekmekçi, S., Akça, Z. and Altıntas¸, A.K. On trigonometric functions and norm in the generalized taxicab metric, Mathematical Sciences And Applications E-Notes Vol:3, No.2 (2015), 27-33.
  • [4] Krause, E.F. Taxicab Geometry, Addison-Wesley, Menlo Park, California, 1975.
  • [5] Menger, K. You Will Like Geometry, Guidebook of Illinois Institute of Technology Geometry Exhibit, Museum of Science and Industry, Chicago, Illinois, 1952.
  • [6] Richard, S.M. and George, D.P. Geometry, A Metric Approach with Models, Springer-Verlag, New York, 1981.
  • [7] Schattschneider, D.J. The taxicab group, American Mathematical Monthly Vol:91, No.7 (1984), 423-428.
  • [8] Wallen, L.J. Kepler, the taxicab metric, and beyond: An isoperimetric primer, The College Mathematics Journal Vol:26, No.3 (1995), 178-190.
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Orcid: http://orcid.org/0000-0001-5559-9768
Yazar: Harun Barış Çolakoğlu
Kurum: AKDENİZ ÜNİVERSİTESİ
Ülke: Turkey


Bibtex @araştırma makalesi { konuralpjournalmath311979, journal = {Konuralp Journal of Mathematics}, issn = {}, eissn = {2147-625X}, address = {Mehmet Zeki SARIKAYA}, year = {2018}, volume = {6}, pages = {158 - 162}, doi = {}, title = {A Generalization of The Taxicab Metric And Related Isometries}, key = {cite}, author = {Çolakoğlu, Harun Barış} }
APA Çolakoğlu, H . (2018). A Generalization of The Taxicab Metric And Related Isometries. Konuralp Journal of Mathematics, 6 (1), 158-162. Retrieved from http://dergipark.gov.tr/konuralpjournalmath/issue/31478/311979
MLA Çolakoğlu, H . "A Generalization of The Taxicab Metric And Related Isometries". Konuralp Journal of Mathematics 6 (2018): 158-162 <http://dergipark.gov.tr/konuralpjournalmath/issue/31478/311979>
Chicago Çolakoğlu, H . "A Generalization of The Taxicab Metric And Related Isometries". Konuralp Journal of Mathematics 6 (2018): 158-162
RIS TY - JOUR T1 - A Generalization of The Taxicab Metric And Related Isometries AU - Harun Barış Çolakoğlu Y1 - 2018 PY - 2018 N1 - DO - T2 - Konuralp Journal of Mathematics JF - Journal JO - JOR SP - 158 EP - 162 VL - 6 IS - 1 SN - -2147-625X M3 - UR - Y2 - 2018 ER -
EndNote %0 Konuralp Journal of Mathematics A Generalization of The Taxicab Metric And Related Isometries %A Harun Barış Çolakoğlu %T A Generalization of The Taxicab Metric And Related Isometries %D 2018 %J Konuralp Journal of Mathematics %P -2147-625X %V 6 %N 1 %R %U
ISNAD Çolakoğlu, Harun Barış . "A Generalization of The Taxicab Metric And Related Isometries". Konuralp Journal of Mathematics 6 / 1 (Nisan 2018): 158-162.