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A CHARACTERIZATION OF PARABOLA

  • Yu, Yanhua (DEPARTMENT OF MATHEMATICS NORTHEASTERN UNIVERSITY) ;
  • Liu, Huili (DEPARTMENT OF MATHEMATICS NORTHEASTERN UNIVERSITY)
  • Published : 2008.11.30

Abstract

In this paper, the parabola will be characterized as the plane curve whose curvature function and support function satisfy a condition, where we define the support function as the distance from origin to the tangent line.

References

  1. M. P. Do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, New Jerse, 1976
  2. D.-S. Kim and Y. H. Kim, A characterization of ellipses, Amer. Math. Monthly 114 (2007), no. 1, 66-70 https://doi.org/10.1080/00029890.2007.11920393

Cited by

  1. SOME EQUIVALENT CONDITIONS FOR CONIC SECTIONS vol.19, pp.4, 2012, https://doi.org/10.7468/jksmeb.2012.19.4.315
  2. Some Characterizations of Parabolas vol.53, pp.1, 2013, https://doi.org/10.5666/KMJ.2013.53.1.99
  3. A CHARACTERIZATION OF CONIC SECTIONS vol.33, pp.3, 2011, https://doi.org/10.5831/HMJ.2011.33.3.335