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AREA OF TRIANGLE IN THE PLANE WITH ALPHA DISTANCE FUNCTION

고일석|김병학|오채희
한국수학교육학회|2012.11|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제19권 제4호|pp. 337-347

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참고문헌

키워드

alpha distance functionalpha trigonometrytriangle in alpha distance plane.
주제분류수학

초록

The taxicab distance and Chinese-checker distance in the plane are practical distance notions with a wide range of applications compared to the Eu-clidean distance. The α-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 α-distance.

Abstract

The taxicab distance and Chinese-checker distance in the plane are practical distance notions with a wide range of applications compared to the Eu-clidean distance. The α-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 α-distance.

참고문헌 (13)

  1. Z. Akca, "On the Distance Formulae in three Dimensional Taxicab Space", Hadronic J, 27, pp.521~532 (2004)
  2. A. Bayar, "On a Taxicab Distance on a Sphere", Missouri J. Math. Sci, 17, pp.41~51 (2005)
  3. G. Chen, "Lines and Circles in Taxicab Geometry", 석사, Department of Mathematics and Computer Sciences, pp.1992
  4. O. Gelisgen, "Generalization of n-distance to n-dimensional space", Scientic and Professional Journal of the Croatian Society for Geometry and Graphics (KoG), 10, pp.33~35 (2006)
  5. O. Gelisgen, "On ai-distance in n-dimensional space", Appl. Sci.(APPS), 10, pp.88~94 (2008)
  6. O. Gelisgen, "Distance formulae in the Chinese checker space", Int. J. Pure Appl. Math, 26(1), pp.35~44 (2006)
  7. R. Kaya, "Taxicab Versions of some Euclidean Theorems", Int. J. Pure Appl. Math, 26(1), pp.69~81 (2006)
  8. E.F. Krause, "Taxicab Geometry" (1975), Addison-Wesley Publishing Company
  9. 곽경민, "택시거리함수를 이용한 평면기하에 관한 연구", 수학교육 논문집, 24(3), pp.659~689 (2010), 한국수학교육학회
  10. M. Ozcan, "Area of a triangle in terms of the taxicab distance", Missouri J. Math. Sci, 15, pp.178~185 (2003)
  11. K. Thompson, "Taxicab angles and trigonometry", The Pi Mu Epsilon Journal, 11(2), pp.87~96 (2000)
  12. S. Tian, "Alpha-distance - a generalization of Chinese checker distance and taxicab distance", Missouri J. Math. Sci, 17(1), pp.35~40 (2005)
  13. S. Tian, "Concerning circles in taxicab geometry", Int. J. Math. Educ. Sci. Tech, 28(5), pp.727~733 (1997)

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