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

Yıl 2019, Cilt: 7 Sayı: 1, 222 - 227, 15.04.2019

Harun Barış Çolakoğlu

Öz

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.

Anahtar Kelimeler

taxicab distance, m-generalized taxicab distance, area, Heron's formula

Kaynakça

• [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.