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On generalized taxicab metric in three dimensional space

Year 2019, Volume: 68 Issue: 2, 1359 - 1369, 01.08.2019
https://doi.org/10.31801/cfsuasmas.530441

Abstract

In this paper, we define the generalized taxicab distance function in three dimensional space, which includes the taxicab distance function as a special case, and we show that three dimensional generalized taxicab distance function determines a metric. Then we give some properties of three dimensional generalized taxicab metric, and determine Euclidean isometries of the space preserving the generalized taxicab metric.

References

  • Akça, Z. and Kaya, R., On the distance formulae in three dimensional taxicab space, Hadronic Journal, 27, No.5 (2004), 521-532.
  • Akça, Z. and Kaya, R., On the taxicab trigonometry, Jour. of Inst. of Math. & Comp. Sci. (Math. Ser.), 10, No.3 (1997), 151-159.
  • Çolakoğlu H. B., Concerning the alpha distance, Algebras Groups Geom. 8(2011), 1-14.
  • Ekici, C., Kocayusufoğlu, İ. and Akça, Z., The norm in taxicab geometry, Tr. J. of Mathematics, 22 (1998), 295-307.
  • Ekmekçi, E., Bayar, A. and Altıntaş, A. K., On the group of isometries of the generalized taxicab plane, International Journal of Contemporary Mathematical Sciences, 10, No.4 (2015), 159-166.
  • Ekmekçi, S., Akça, Z. and Altıntaş, A. K., On trigonometric functions and norm in the generalized taxicab metric, Mathematical Sciences And Applications E-Notes, 3, No.2 (2015), 27-33.
  • Gelişgen, Ö. and Kaya, R., The taxicab space group, Acta Math. Hungar., 122, Issue 1â€"2 (2009), 187â€"200.
  • Gelişgen, Ö. and Kaya, R., On α-distance in three dimensional space, Applied Science, 8 (2006), 65-69.
  • Gelişgen, Ö. and Kaya, R., Generalization of α-distance to n-dimensional Space, KoG, 10 (2006), 33-35.
  • Kaya, R., Akça, Z., Günaltılı, İ. and Ö zcan, M., General equation for taxicab conics and their classification, Mitt. Math. Ges. Hamburg, 19 (2000), 135-148.
  • Kaya, R. and Çolakoğlu, H. B., Taxicab versions of some Euclidean theorems, International Journal of Pure And Applied Mathematics, 26, No.1 (2006), 69-81.
  • Kocayusufoglu, İ. and Özdamar, E., Isometries of taxicab geometry, Commum. Fac. Sci. Univ. Ank. Series A1, 47 (1998), 73-83.
  • Krause, E. F., Taxicab Geometry, Addison-Wesley, Menlo Park, California, 1975.
  • Martin, G. E., Transformation Geometry, Springer-Verlag, New York Inc., 1997, pp.182.
  • Menger, K., You Will Like Geometry, Guidebook of Illinois Institute of Technology Geometry Exhibit, Museum of Science and Industry, Chicago, Illinois, 1952.
  • Schattschneider, D. J., The taxicab group, American Mathematical Monthly, 91, No.7 (1984), 423-428.
  • Thompson, K. P., The nature of length, area, and volume in taxicab geometry, International Electronic Journal of Geometry, 4, No.2 (2011), 193-207.
  • Wallen, L. J., Kepler, the taxicab metric, and beyond: An isoperimetric primer, The College Mathematics Journal, 26, No.3 (1995), 178-190.
Year 2019, Volume: 68 Issue: 2, 1359 - 1369, 01.08.2019
https://doi.org/10.31801/cfsuasmas.530441

Abstract

References

  • Akça, Z. and Kaya, R., On the distance formulae in three dimensional taxicab space, Hadronic Journal, 27, No.5 (2004), 521-532.
  • Akça, Z. and Kaya, R., On the taxicab trigonometry, Jour. of Inst. of Math. & Comp. Sci. (Math. Ser.), 10, No.3 (1997), 151-159.
  • Çolakoğlu H. B., Concerning the alpha distance, Algebras Groups Geom. 8(2011), 1-14.
  • Ekici, C., Kocayusufoğlu, İ. and Akça, Z., The norm in taxicab geometry, Tr. J. of Mathematics, 22 (1998), 295-307.
  • Ekmekçi, E., Bayar, A. and Altıntaş, A. K., On the group of isometries of the generalized taxicab plane, International Journal of Contemporary Mathematical Sciences, 10, No.4 (2015), 159-166.
  • Ekmekçi, S., Akça, Z. and Altıntaş, A. K., On trigonometric functions and norm in the generalized taxicab metric, Mathematical Sciences And Applications E-Notes, 3, No.2 (2015), 27-33.
  • Gelişgen, Ö. and Kaya, R., The taxicab space group, Acta Math. Hungar., 122, Issue 1â€"2 (2009), 187â€"200.
  • Gelişgen, Ö. and Kaya, R., On α-distance in three dimensional space, Applied Science, 8 (2006), 65-69.
  • Gelişgen, Ö. and Kaya, R., Generalization of α-distance to n-dimensional Space, KoG, 10 (2006), 33-35.
  • Kaya, R., Akça, Z., Günaltılı, İ. and Ö zcan, M., General equation for taxicab conics and their classification, Mitt. Math. Ges. Hamburg, 19 (2000), 135-148.
  • Kaya, R. and Çolakoğlu, H. B., Taxicab versions of some Euclidean theorems, International Journal of Pure And Applied Mathematics, 26, No.1 (2006), 69-81.
  • Kocayusufoglu, İ. and Özdamar, E., Isometries of taxicab geometry, Commum. Fac. Sci. Univ. Ank. Series A1, 47 (1998), 73-83.
  • Krause, E. F., Taxicab Geometry, Addison-Wesley, Menlo Park, California, 1975.
  • Martin, G. E., Transformation Geometry, Springer-Verlag, New York Inc., 1997, pp.182.
  • Menger, K., You Will Like Geometry, Guidebook of Illinois Institute of Technology Geometry Exhibit, Museum of Science and Industry, Chicago, Illinois, 1952.
  • Schattschneider, D. J., The taxicab group, American Mathematical Monthly, 91, No.7 (1984), 423-428.
  • Thompson, K. P., The nature of length, area, and volume in taxicab geometry, International Electronic Journal of Geometry, 4, No.2 (2011), 193-207.
  • Wallen, L. J., Kepler, the taxicab metric, and beyond: An isoperimetric primer, The College Mathematics Journal, 26, No.3 (1995), 178-190.
There are 18 citations in total.

Details

Primary Language English
Journal Section Review Articles
Authors

Harun Barış Çolakoğlu 0000-0001-5559-9768

Publication Date August 1, 2019
Submission Date March 8, 2017
Acceptance Date August 10, 2018
Published in Issue Year 2019 Volume: 68 Issue: 2

Cite

APA Çolakoğlu, H. B. (2019). On generalized taxicab metric in three dimensional space. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1359-1369. https://doi.org/10.31801/cfsuasmas.530441
AMA Çolakoğlu HB. On generalized taxicab metric in three dimensional space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2019;68(2):1359-1369. doi:10.31801/cfsuasmas.530441
Chicago Çolakoğlu, Harun Barış. “On Generalized Taxicab Metric in Three Dimensional Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 2 (August 2019): 1359-69. https://doi.org/10.31801/cfsuasmas.530441.
EndNote Çolakoğlu HB (August 1, 2019) On generalized taxicab metric in three dimensional space. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 1359–1369.
IEEE H. B. Çolakoğlu, “On generalized taxicab metric in three dimensional space”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 1359–1369, 2019, doi: 10.31801/cfsuasmas.530441.
ISNAD Çolakoğlu, Harun Barış. “On Generalized Taxicab Metric in Three Dimensional Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (August 2019), 1359-1369. https://doi.org/10.31801/cfsuasmas.530441.
JAMA Çolakoğlu HB. On generalized taxicab metric in three dimensional space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1359–1369.
MLA Çolakoğlu, Harun Barış. “On Generalized Taxicab Metric in Three Dimensional Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, 2019, pp. 1359-6, doi:10.31801/cfsuasmas.530441.
Vancouver Çolakoğlu HB. On generalized taxicab metric in three dimensional space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):1359-6.

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

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