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Dergiler / Konuralp Journal of Mathematics / 2018 / Cilt: 6 - Sayı: 1

A Generalization of The Taxicab Metric And Related Isometries

Harun Barış Çolakoğlu
Sayfa
158–162
Yayın Tarihi
2018-04-15
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Then we give some properties of the \textit{m}-generalized taxicab metric, and determine Euclidean isometries that preserve the \textit{m}-generalized taxicab metric.

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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.
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Temel Bulgular & Veri: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.
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Sonuç & Katkı:Then we give some properties of the \textit{m}-generalized taxicab metric, and determine Euclidean isometries that preserve the \textit{m}-generalized taxicab metric.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:metric · taxicab distance · generalized taxicab distance

Abstract

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.

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Bu Makaleye Atıf Yap

Çolakoğlu, H. B. (2018). A Generalization of The Taxicab Metric And Related Isometries. Konuralp Journal of Mathematics, Cilt: 6 - Sayı: 1, 158–162. https://ajindex.com/articles/786592

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Kaynakça (8)

  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.