Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ISOPERIMETRIC INEQUALITY IN α-PLANE

  • Received : 2011.11.30
  • Accepted : 2012.08.21
  • Published : 2013.01.30
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Abstract

Taxicab plane geometry and Cinese-Checker plane geometry are non-Euclidean and more practical notion than Euclidean geometry in the real world. The ${\alpha}$-distance is a generalization of the Taxicab distance and Chinese-Checker distance. It was first introduced by Songlin Tian in 2005, and generalized to n-dimensional space by Ozcan Gelisgen in 2006. In this paper, we studied the isoperimetric inequality in ${\alpha}$-plane.

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References

  1. G.Chen, Lines and circles in Taxicab geometry, Masters Thesis, Central Missouri State University, Warrensburg, MO, (1992).
  2. O.Gelisgen and R.Kaya, Generalization of alpha-distance to n-dimensional space, Professional Paper, (2006), 33-35.
  3. O.Gelisgen, R.Kaya and M.Ozcan, Distance formulae in the Chinese checker space, International Journal of pure and applied Mathematics, 26(2006), 35-44.
  4. E.Krause, Taxicab geometry, Addison-Wesley Publishing Company, Menlo Park, CA(1975).
  5. Kyung Min Kwak, Seung Min Baik, Woo Seok Choi, Jun Bum Choi, Il Seog Ko and Byung Hak Kim, On the plane geometry using taxicab distance function, J. Korean Society of Math. Education 24(2010), 497-504.
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  7. Songlin Tian, Alpha-distance - a generalization of chinese checker distance and taxicab distance, Missouri Journal of Mathematical Sciences 17(2005), 35-40.

Cited by

  1. ON POLAR TAXICAB GEOMETRY IN A PLANE vol.32, pp.5_6, 2014, https://doi.org/10.14317/jami.2014.783