The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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AREA OF TRIANGLE IN THE PLANE WITH ALPHA DISTANCE FUNCTION

  • Oh, Chae Hee (Gyeonggi Science High School) ;
  • Ko, Il Seog (Gyeonggi Science High School) ;
  • Kim, Byung Hak (Department of Applied Mathematics, College of Applied Science, Kyung Hee University)
  • Received : 2012.06.20
  • Accepted : 2012.09.03
  • Published : 2012.11.30
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Abstract

The taxicab distance and Chinese-checker distance in the plane are practical distance notions with a wide range of applications compared to the Euclidean distance. The ${\alpha}$-distance was introduced as a generalization of these two distance functions. In this paper, we study alpha circle, trigonometry, and the area of a triangle in the plane with ${\alpha}$-distance.

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References

  1. Z. Akca & R. Kaya: On the Distance Formulae in three Dimensional Taxicab Space. Hadronic J. 27 (2004), 521-532.
  2. A. Bayar & R. Kaya: On a Taxicab Distance on a Sphere. Missouri J. Math. Sci. 17 (2005), 41-51.
  3. G. Chen: Lines and Circles in Taxicab Geometry. Master Thesis, Department of Mathematics and Computer Sciences, Central Missouri State University (1992).
  4. O. Gelisgen & R. Kaya: Generalization of $\alpha$-distance to n-dimensional space. Scientific and Professional Journal of the Croatian Society for Geometry and Graphics (KoG). 10 (2006), 33-35.
  5. O. Gelisgen & R. Kaya: On $\alpha_{i}$-distance in n-dimensional space. Appl. Sci.(APPS). 10 (2008), 88-94.
  6. O. Gelisgen, R. Kaya & M. Ozcan: Distance formulae in the Chinese checker space. Int. J. Pure Appl. Math.. 26 (2006), no. 1, 35-44.
  7. R. Kaya & H.B. Colakoglu: Taxicab Versions of some Euclidean Theorems. Int. J. Pure Appl. Math.. 26 (2006), no. 1, 69-81.
  8. E.F. Krause: Taxicab Geometry. Addison-Wesley Publishing Company, Menlo Park, 1975.
  9. K.M. Kwak, S.M. Baik, W.S. Choi, J.B. Choi, I.S. Ko & B.H. Kim: On the plane geometry using the taxicab distance function. J. Korean Soc. Math. Ed. Ser. E: Commun. Math. Educ.. 24 (2010), no. 3, 659-989.
  10. M. Ozcan & R. Kaya: Area of a triangle in terms of the taxicab distance. Missouri J. Math. Sci.. 15 (2003), 178-185
  11. K. Thompson & T. Dray: Taxicab angles and trigonometry. The Pi Mu Epsilon Journal. 11 (2000), no. 2, 87-96.
  12. S. Tian: Alpha-distance - a generalization of Chinese checker distance and taxicab distance. Missouri J. Math. Sci.. 17 (2005), no. 1, 35-40.
  13. S. Tian, S.S. So & G. Chen: Concerning circles in taxicab geometry. Int. J. Math. Educ. Sci. Tech.. 28 (1997), no. 5, 727-733. https://doi.org/10.1080/0020739970280509

Cited by

  1. A STUDY ON QUADRATIC CURVES AND GENERALIZED ECCENTRICITY IN POLAR TAXICAB GEOMETRY vol.22, pp.3, 2012, https://doi.org/10.11568/kjm.2014.22.3.567