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AREA OF TRIANGLES ASSOCIATED WITH A CURVE II
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 Title & Authors
AREA OF TRIANGLES ASSOCIATED WITH A CURVE II
Kim, Dong-Soo; Kim, Wonyong; Kim, Young Ho; Park, Dae Heui;
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 Abstract
It is well known that the area U of the triangle formed by three tangents to a parabola X is half of the area T of the triangle formed by joining their points of contact. In this article, we consider whether this property and similar ones characterizes parabolas. As a result, we present three conditions which are necessary and sufficient for a strictly convex curve in the plane to be an open part of a parabola.
 Keywords
triangle;area;parabola;strictly convex curve;plane curvature;
 Language
English
 Cited by
1.
AREA OF TRIANGLES ASSOCIATED WITH A STRICTLY LOCALLY CONVEX CURVE,;;;;

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2.
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ON TRIANGLES ASSOCIATED WITH A CURVE,;;;

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4.
Center of Gravity and a Characterization of Parabolas,;;;

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5.
Areas associated with a Strictly Locally Convex Curve,;;;;

Kyungpook mathematical journal, 2016. vol.56. 2, pp.583-595 crossref(new window)
1.
ON TRIANGLES ASSOCIATED WITH A CURVE, Bulletin of the Korean Mathematical Society, 2015, 52, 3, 925  crossref(new windwow)
2.
Areas associated with a Strictly Locally Convex Curve, Kyungpook mathematical journal, 2016, 56, 2, 583  crossref(new windwow)
3.
CENTROID OF TRIANGLES ASSOCIATED WITH A CURVE, Bulletin of the Korean Mathematical Society, 2015, 52, 2, 571  crossref(new windwow)
4.
Center of Gravity and a Characterization of Parabolas, Kyungpook mathematical journal, 2015, 55, 2, 473  crossref(new windwow)
 References
1.
W. A. Day, Inequalities for areas associated with conics, Amer. Math. Monthly 98 (1991), no. 1, 36-39. crossref(new window)

2.
M. P. do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, Englewood Cliffs, NJ, 1976.

3.
D.-S. Kim and S. H. Kang, A characterization of conic sections, Honam Math. J. 33 (2011), no. 3, 335-340. crossref(new window)

4.
D.-S. Kim and Y. H. Kim, A characterization of ellipses, Amer. Math. Monthly 114 (2007), no. 1, 66-70.

5.
D.-S. Kim and Y. H. Kim, Some characterizations of spheres and elliptic paraboloids, Linear Algebra Appl. 437 (2012), no. 1, 113-120. crossref(new window)

6.
D.-S. Kim and Y. H. Kim, Some characterizations of spheres and elliptic paraboloids II, Linear Algebra Appl. 438 (2013), no. 3, 1356-1364. crossref(new window)

7.
D.-S. Kim and Y. H. Kim, On the Archimedean characterization of parabolas, Bull. Korean Math. Soc. 50 (2013), no. 6, 2103-2114. crossref(new window)

8.
D.-S. Kim, Y. H. Kim, and J. H. Park, Some characterizations of parabolas, Kyungpook Math. J. 53 (2013), no. 1, 99-104. crossref(new window)

9.
D.-S. Kim and K.-C. Shim, Area of triangles associated with a curve, Bull. Korean Math. Soc. To appear. arXiv:1401.4751.

10.
J. Krawczyk, On areas associated with a curve, Zesz. Nauk. Uniw.Opol. Mat. 29 (1995), 97-101.

11.
B. Richmond and T. Richmond, How to recognize a parabola, Amer. Math. Monthly 116 (2009), no. 10, 910-922. crossref(new window)

12.
S. Stein, Archimedes, What did he do besides cry Eureka? Mathematical Association of America, Washington, DC, 1999.