Kyungpook Mathematical Journal

  • 제53권1호
  • /
  • Pages.99-104
  • /
  • 2013
  • /
  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Some Characterizations of Parabolas

  • Kim, Dong-Soo (Department of Mathematics, Chonnam National University) ;
  • Park, Jong Ho (Department of Mathematics, Chonnam National University) ;
  • Kim, Young Ho (Department of Mathematics, Teachers' College, Kyungpook National University)
  • 투고 : 2011.10.11
  • 심사 : 2012.04.18
  • 발행 : 2013.03.23
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초록

We study some properties of tangent lines of parabolas. As a result, we establish some characterizations of parabolas.

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참고문헌

  1. Y. D. Chai, Yong Il Kim, Curves of constant relative breadth, Kyungpook Mathematical Journal, 37(2)(1997), 365-370.
  2. B.-Y. Chen, D.-S. Kim and Y. H. Kim, New characterizations of W-curves, Publ. Math. Debrecen, 69(2006), 457-472.
  3. Luther P. Eisenhart, A treatise on the differential geometry of curves and surfaces, Dover Publications, Inc., New York, 1960.
  4. P. C. Hammer and T. Jefferson Smith, Conditions equivalent to central symmetry of convex curves, Proc. Cambridge Philos. Soc., 60(1964), 779-785.
  5. D.-S. Kim, Y. H. Kim, A characterization of ellipses, Amer. Math. Monthly, 114(1)(2007), 65-69.
  6. George F. Simmons, Calculus with analytic geometry, 2nd ed., The McGraw-Hill Companies, Inc., New York, 1996.
  7. S. Stein, Archimedes. What did he do besides cry Eureka?, Mathematical Association of America, Washington, DC, 1999.
  8. M. Stenlund, On the tangent lines of a parabola, College Math. J., 32(3)(2001), 194- 196. https://doi.org/10.2307/2687469
  9. Y. Yu, L. Liu, A characterization of parabola, Bull. Korean Math. Soc., 45(4)(2008), 631-634. https://doi.org/10.4134/BKMS.2008.45.4.631

피인용 문헌

  1. CENTROID OF TRIANGLES ASSOCIATED WITH A CURVE vol.52, pp.2, 2015, https://doi.org/10.4134/BKMS.2015.52.2.571
  2. Areas associated with a Strictly Locally Convex Curve vol.56, pp.2, 2016, https://doi.org/10.5666/KMJ.2016.56.2.583
  3. AREA OF TRIANGLES ASSOCIATED WITH A CURVE II vol.52, pp.1, 2015, https://doi.org/10.4134/BKMS.2015.52.1.275
  4. ON TRIANGLES ASSOCIATED WITH A CURVE vol.52, pp.3, 2015, https://doi.org/10.4134/BKMS.2015.52.3.925
  5. AREA OF TRIANGLES ASSOCIATED WITH A CURVE vol.51, pp.3, 2014, https://doi.org/10.4134/BKMS.2014.51.3.901
  6. AREA OF TRIANGLES ASSOCIATED WITH A STRICTLY LOCALLY CONVEX CURVE vol.37, pp.1, 2015, https://doi.org/10.5831/HMJ.2015.37.1.41
  7. Center of Gravity and a Characterization of Parabolas vol.55, pp.2, 2015, https://doi.org/10.5666/KMJ.2015.55.2.473