Browse > Article
http://dx.doi.org/10.5666/KMJ.2013.53.1.99

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)
Publication Information
Kyungpook Mathematical Journal / v.53, no.1, 2013 , pp. 99-104 More about this Journal
Abstract
We study some properties of tangent lines of parabolas. As a result, we establish some characterizations of parabolas.
Keywords
parabola; tangent line; envelope; 1-parameter family of lines;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 Y. D. Chai, Yong Il Kim, Curves of constant relative breadth, Kyungpook Mathematical Journal, 37(2)(1997), 365-370.   과학기술학회마을
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.   DOI   ScienceOn
9 Y. Yu, L. Liu, A characterization of parabola, Bull. Korean Math. Soc., 45(4)(2008), 631-634.   과학기술학회마을   DOI   ScienceOn