Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

CLASSIFICATIONS OF METRIC FUNCTIONS ON THE PLANE

  • Received : 2017.08.05
  • Accepted : 2017.10.20
  • Published : 2018.01.30
Download PDF
⟨ Previous Next ⟩

Abstract

There are many metric functions in the plane. In this paper we are to classify the metric functions on the plane using two ways such as using sum of distances between some points when start point and end point is fixed, and using area of transferred triangle consisted of distances between 3 points.

Keywords

References

  1. C. O'Brien, Minimization via the Subway Metric, Honors thesis, Ithaca College, 2003
  2. O, Gelisgen and R. Kaya, On ${\alpha}$-distance in three dimensional space, Applied Sciences 8 (2006), 65-69.
  3. O. Gelisgen and R. Kaya, Generalization of ${\alpha}$-distance to n-dimensional case, professional paper(accepted 28.11.2006)
  4. E.F. Krause, Taxicab geometry, Addison-Wesley Publishing Company, Menlo Park, 1975
  5. Y.J. Lee, C.H. Cho, I.S. Ko and B.H. Kim, On the characterization of the quadratic curves in the plane with subway metric Proceeding of the 2014 International Math. Education Workshop, 471-474
  6. M.H. Mortad, Introductory Topology, World Scientific Publishing Co. 2014
  7. H.G. Park, K.R. Kim, I.S. Ko and B.H. Kim, On polar taxicab geometry in a plane, Journal of Applied Mathematics and Informatics 32 (2014), 783-790 https://doi.org/10.14317/jami.2014.783
  8. S. Tian, ${\alpha}$-distance : A generalization of Chinese checker distance3 and Taxicab distance, Misouri Joural of Mathematical sciences 17 (2005), 35-40