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Year 2019, Volume: 7 Issue: 1, 222 - 227, 15.04.2019

Abstract

References

  • [1] C.H. Oh, I.S. Ko and B.H. Kim, Area of a triangle in the plane with alpha distance function, J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math., 19 (4) (2012), 337-347.
  • [2] H.B. Colakoglu, O. Gelis¸gen and R. Kaya, Area formulas for a triangle in the alpha plane, Math. Commun., 18 (1) (2013), 123-132.
  • [3] H.B. Colakoglu, A generalization of the taxicab metric and related isometries, Konuralp Journal of Mathematics, 6 (1) (2018), 158-162.
  • [4] H.B. Colakoglu, The generalized taxicab group, Int. Electron. J. Geom., 11 (2) (2018), 83-89.
  • [5] H.B. Colakoglu, On generalized taxicab metric in three dimensional space, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 68 (2) (2019), 1359-1369.
  • [6] S. Ekmekçi, A. Bayar and A.K. Altıntas, On the group of isometries of the generalized taxicab plane, International Journal of Contemporary Mathematical Sciences, 10 (4) (2015), 159-166.
  • [7] O. Gelisgen and T. Ermis¸, Area formulas for a triangle in the m-plane, Konuralp Journal of Mathematics, 2 (2) (2014), 85-95.
  • [8] R. Kaya, Area formula for taxicab triangles, Pi Mu Epsilon Journal, 12 (4) (2006), 219-220.
  • [9] R. Kaya and H.B. C¸ olakoglu, Taxicab versions of some Euclidean theorems, International Journal of Pure And Applied Mathematics, 26 (1) (2006), 69-81.
  • [10] E.F. Krause, Taxicab Geometry, Addison-Wesley, Menlo Park, California, 1975.
  • [11] K. Menger, You will like geometry, Guidebook of Illinois Institute of Technology Geometry Exhibit, Museum of Science and Industry, Chicago, Illinois, 1952.
  • [12] S.M. Richard and D.P. George, Geometry, A Metric Approach with Models, Springer-Verlag, New York, 1981.
  • [13] K.P. Thompson, The nature of length, area, and volume in taxicab geometry, International Electronic Journal of Geometry, 4 (2) (2011), 193-207.
  • [14] M. Ozcan and R. Kaya, Area of a triangle in terms of the taxicab distance, Missouri J. of Math. Sci., 15 (3) (2003), 178-185.
  • [15] L.J. Wallen, Kepler, the taxicab metric, and beyond: An isoperimetric primer, The College Mathematics Journal, 26 (3) (1995), 78-190.

Area Of A Triangle In Terms Of The m-Generalized Taxicab Distance

Year 2019, Volume: 7 Issue: 1, 222 - 227, 15.04.2019

Abstract

In this paper, we give three area formulas for a triangle in the $m$-generalized taxicab plane in terms of the $m$-generalized taxicab distance. The two of them are $m$-generalized taxicab versions of the standard area formula for a triangle, and the other one is an $m$-generalized taxicab version of the well-known Heron's formula.

References

  • [1] C.H. Oh, I.S. Ko and B.H. Kim, Area of a triangle in the plane with alpha distance function, J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math., 19 (4) (2012), 337-347.
  • [2] H.B. Colakoglu, O. Gelis¸gen and R. Kaya, Area formulas for a triangle in the alpha plane, Math. Commun., 18 (1) (2013), 123-132.
  • [3] H.B. Colakoglu, A generalization of the taxicab metric and related isometries, Konuralp Journal of Mathematics, 6 (1) (2018), 158-162.
  • [4] H.B. Colakoglu, The generalized taxicab group, Int. Electron. J. Geom., 11 (2) (2018), 83-89.
  • [5] H.B. Colakoglu, On generalized taxicab metric in three dimensional space, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 68 (2) (2019), 1359-1369.
  • [6] S. Ekmekçi, A. Bayar and A.K. Altıntas, On the group of isometries of the generalized taxicab plane, International Journal of Contemporary Mathematical Sciences, 10 (4) (2015), 159-166.
  • [7] O. Gelisgen and T. Ermis¸, Area formulas for a triangle in the m-plane, Konuralp Journal of Mathematics, 2 (2) (2014), 85-95.
  • [8] R. Kaya, Area formula for taxicab triangles, Pi Mu Epsilon Journal, 12 (4) (2006), 219-220.
  • [9] R. Kaya and H.B. C¸ olakoglu, Taxicab versions of some Euclidean theorems, International Journal of Pure And Applied Mathematics, 26 (1) (2006), 69-81.
  • [10] E.F. Krause, Taxicab Geometry, Addison-Wesley, Menlo Park, California, 1975.
  • [11] K. Menger, You will like geometry, Guidebook of Illinois Institute of Technology Geometry Exhibit, Museum of Science and Industry, Chicago, Illinois, 1952.
  • [12] S.M. Richard and D.P. George, Geometry, A Metric Approach with Models, Springer-Verlag, New York, 1981.
  • [13] K.P. Thompson, The nature of length, area, and volume in taxicab geometry, International Electronic Journal of Geometry, 4 (2) (2011), 193-207.
  • [14] M. Ozcan and R. Kaya, Area of a triangle in terms of the taxicab distance, Missouri J. of Math. Sci., 15 (3) (2003), 178-185.
  • [15] L.J. Wallen, Kepler, the taxicab metric, and beyond: An isoperimetric primer, The College Mathematics Journal, 26 (3) (1995), 78-190.
There are 15 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Harun Barış Çolakoğlu 0000-0001-5559-9768

Publication Date April 15, 2019
Submission Date February 19, 2018
Acceptance Date April 15, 2019
Published in Issue Year 2019 Volume: 7 Issue: 1

Cite

APA Çolakoğlu, H. B. (2019). Area Of A Triangle In Terms Of The m-Generalized Taxicab Distance. Konuralp Journal of Mathematics, 7(1), 222-227.
AMA Çolakoğlu HB. Area Of A Triangle In Terms Of The m-Generalized Taxicab Distance. Konuralp J. Math. April 2019;7(1):222-227.
Chicago Çolakoğlu, Harun Barış. “Area Of A Triangle In Terms Of The M-Generalized Taxicab Distance”. Konuralp Journal of Mathematics 7, no. 1 (April 2019): 222-27.
EndNote Çolakoğlu HB (April 1, 2019) Area Of A Triangle In Terms Of The m-Generalized Taxicab Distance. Konuralp Journal of Mathematics 7 1 222–227.
IEEE H. B. Çolakoğlu, “Area Of A Triangle In Terms Of The m-Generalized Taxicab Distance”, Konuralp J. Math., vol. 7, no. 1, pp. 222–227, 2019.
ISNAD Çolakoğlu, Harun Barış. “Area Of A Triangle In Terms Of The M-Generalized Taxicab Distance”. Konuralp Journal of Mathematics 7/1 (April 2019), 222-227.
JAMA Çolakoğlu HB. Area Of A Triangle In Terms Of The m-Generalized Taxicab Distance. Konuralp J. Math. 2019;7:222–227.
MLA Çolakoğlu, Harun Barış. “Area Of A Triangle In Terms Of The M-Generalized Taxicab Distance”. Konuralp Journal of Mathematics, vol. 7, no. 1, 2019, pp. 222-7.
Vancouver Çolakoğlu HB. Area Of A Triangle In Terms Of The m-Generalized Taxicab Distance. Konuralp J. Math. 2019;7(1):222-7.
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