AREA FORMULAS FOR A TRIANGLE IN THE m-PLANE

AREA FORMULAS FOR A TRIANGLE IN THE m-PLANE

In this paper, we give three area formulas for a triangle in them-plane in terms of the m−distance. The two of them are m−version of thestandart area formula for a triangle in the Euclidean plane, and the third oneis a m−version of the well-known Heron s formula

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  • Chen G., Lines and Circles in Taxicab Geometry, Master Thesis, Department of Mathematics and Computer Science, University of Central Missouri, 1992.
  • C¸ olako˘glu H. B., Taksi, Maksimum, C¸ in dama ve Alfa D¨uzlemlerinin Bazı ¨Ozellikleri ve Bir Genelle¸stirilmesi, PhD thesis, Eski¸sehir Osmangazi ¨Universitesi, 2009..
  • C¸ olako˘glu H. B. and Kaya R., Taxicab Versions of the Pythagorean Theorem, Pi Mu Epsilon J. (PMEJ), (in press). C¸ olako˘glu H. B. and Kaya R., Chinese Checker Versions of the Pythagorean Theorem, Int. J. Contemp. Math. Sciences. (IJCMS), 4 (2) (2009), 61-69.
  • C¸ olako˘glu H. B. and Kaya R., A Generalization of Some Well-Known Distances and Related Isometries, Mathematical Communications, 16 (1), (2011), 21-35.
  • C¸ olako˘glu H. B.,Geli¸sgen ¨O. and Kaya R., Area formulas for a triangle in the alpha plane, Mathematical Communications, 18 (1), (2013), 123-132.
  • Geli¸sgen ¨O. and Kaya R., On α-distance in Three Dimensional Space, Applied Sciences (APPS), 8 (2006), 65-69.
  • Geli¸sgen ¨O. and Kaya R., Generalization of α-distance to n-dimensional Space, Scientific- Professional Information Journal of Croatian Society for Constructive Geometry and Com- puter Graphics (KoG), 10 (2006), 33-35.
  • Geli¸sgen ¨O. and Kaya R., CC Analog of the Theorem of Pythagoras, Algebras, Groups and Geometries (AGG), 23 (2) (2006), 179-188.
  • Geli¸sgen ¨O. and Kaya R., Alpha(i) Distance in n-dimensional Space, Applied Sciences, 10, (2008), 88-93.
  • Geli¸sgen ¨O. and Kaya R., CC-Version of The Heron’s Formula, Missouri Journal of Mathe- matical Sciences, 21 (2), (2009), 94-110.
  • Kaya R. and Colakoglu H. B., Taxicab Versions of Some Euclidean Theorems, Int. Jour. of Pure and Appl. Math. (IJPAM), 26 (1), (2006), 69-81.
  • Krause E. F., Taxicab Geometry, Addison-Wesley, Menlo Park, California, 1975; Dover Pub- lications, New York, 1987.
  • Minkowski H., Gesammelte Abhandlungen, Chelsa Publishing Co. New York, 1967.
  • ¨Ozcan M. and Kaya R., Area of a Triangle in terms of the Taxicab Distance, Missouri J. of Math. Sci., 15 (3) (2003), 178-185.
  • Tian S., Alpha Distance-A Generalization of Chinese Checker Distance and Taxicab Distance, Missouri J. of Math. Sci. (MJMS), 17 (1), (2005), 35-40.
  • Eskisehir Osmangazi University, Art and Sciences Faculty,, Mathematics-Computer Department, 26480 Eskisehir-TURKEY
  • E-mail address: gelisgen@ogu.edu.tr, termis@ogu.edu.tr