A Generalization of The Taxicab Metric And Related Isometries

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.

Keywords:

metric, taxicab distance, generalized taxicab distance isometry,

PDF

___

[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.

Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2013
Yayıncı: Mehmet Zeki SARIKAYA

Arşiv