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Center of Gravity and a Characterization of Parabolas
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  • Journal title : Kyungpook mathematical journal
  • Volume 55, Issue 2,  2015, pp.473-484
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2015.55.2.473
 Title & Authors
Center of Gravity and a Characterization of Parabolas
KIM, DONG-SOO; PARK, SOOKHEE; KIM, YOUNG HO;
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 Abstract
Archimedes determined the center of gravity of a parabolic section as follows. For a parabolic section between a parabola and any chord AB on the parabola, let us denote by P the point on the parabola where the tangent is parallel to AB and by V the point where the line through P parallel to the axis of the parabola meets the chord AB. Then the center G of gravity of the section lies on PV called the axis of the parabolic section with $PG
 Keywords
Archimedes;center of gravity;area;parabolic section;locally strictly convex curve;curvature;
 Language
English
 Cited by
1.
CENTROID OF TRIANGLES ASSOCIATED WITH A CURVE,;;

대한수학회보, 2015. vol.52. 2, pp.571-579 crossref(new window)
1.
CENTROIDS AND SOME CHARACTERIZATIONS OF PARALLELOGRAMS, Communications of the Korean Mathematical Society, 2016, 31, 3, 637  crossref(new windwow)
 References
1.
Bae J.-S., Kim D.-S. and Kim Y. H., A characterization of the unit sphere, Amer. Math. Monthly, 110(9)(2003), 830-833. crossref(new window)

2.
Benyi A., Szeptycki P. and Van Vleck F., Archimedean properties of parabolas, Amer. Math. Monthly, 107(2000), 945-949. crossref(new window)

3.
Benyi A., Szeptycki P. and Van Vleck F., A generalized Archimedean property, Real Anal. Exchange, 29(2003/04), 881-889.

4.
Chen B.-Y., Kim D.-S. and Kim Y. H., New characterizations of W-curves, Publ. Math. Debrecen., 69/4(2006), 457-472.

5.
do Carmo, M. P., Differential Geometry of Curves and Surfaces, Prentice-Hall, Englewood Cliffs, NJ, 1976.

6.
Kim D.-S., A characterization of the hypersphere, Honam Math. J., 27(2)(2005), 267-271.

7.
Kim D.-S., Ellipsoids and elliptic hyperboloids in the Euclidean space $E^{n+1}$, Linear Algebra Appl., 471 (2015), 28-45. crossref(new window)

8.
Kim D.-S. and Kang S. H., A characterization of conic sections, Honam Math. J., 33(3)(2011), 335-340. crossref(new window)

9.
Kim D.-S. and Kim D. S., Centroid of triangles associated with a curve, Bull. Korean Math. Soc., 52(2)(2015), 571-579. crossref(new window)

10.
Kim D.-S., Kim D. S., Bae H. S. and Kim H.-J., Area of triangles associated with a strictly locally convex curve, Honam Math. J., 37(1)(2015), 41-52. crossref(new window)

11.
Kim D.-S., Kim D. S. and Kim Young Ho, On triangles associated with a curve, Bull. Korean Math. Soc., 52(3)(2015), 925-933. crossref(new window)

12.
Kim D.-S., Kim W., Kim Y. H. and Park D. H., Area of triangles associated with a curve II, Bull. Korean Math. Soc., 52(1)(2015), 275-286. crossref(new window)

13.
Kim D.-S. and Kim Y. H., A characterization of space forms, Bull. Korean Math. Soc., 35(4)(1998), 757-767.

14.
Kim D.-S. and Kim Y. H., A characterization of ellipses, Amer. Math. Monthly, 114(1)(2007), 66-70.

15.
Kim D.-S. and Kim Y. H., New characterizations of spheres, cylinders and W-curves, Linear Algebra Appl., 432(11)(2010), 3002-3006. crossref(new window)

16.
Kim D.-S. and Kim Y. H., Some characterizations of spheres and elliptic paraboloids, Linear Algebra Appl., 437(2012), 113-120. crossref(new window)

17.
Kim D.-S. and Kim Y. H., Some characterizations of spheres and elliptic paraboloids II, Linear Algebra Appl., 438(2013), 1356-1364. crossref(new window)

18.
Kim D.-S. and Kim Y. H., On the Archimedean characterization of parabolas, Bull. Korean Math. Soc., 50(2013), 2103-2114. crossref(new window)

19.
Kim D.-S., Kim Y. H. and Yoon D. W., On standard imbeddings of hyperbolic spaces in the Minkowski space, C. R. Math. Acad. Sci. Paris, Ser. I, 352(2014), 1033-1038. crossref(new window)

20.
Kim D.-S., Park J. H. and Kim Y. H., Some characterizations of parabolas, Kyungpook Math. J., 53(1)(2013), 99-104. crossref(new window)

21.
Kim D.-S. and Shim K.-C., Area of triangles associated with a curve, Bull. Korean Math. Soc., 51(3)(2014), 901-909. crossref(new window)

22.
Kim D.-S. and Song B., A characterization of elliptic hyperboloids, Honam Math. J., 35(1)(2013), 37-49. crossref(new window)

23.
Krawczyk J., On areas associated with a curve, Zesz. Nauk. Uniw. Opol. Mat., 29(1995), 97-101.

24.
Richmond B. and Richmond T., How to recognize a parabola, Amer. Math. Monthly, 116(2009), 910-922. crossref(new window)

25.
Stein S., Archimedes. What did he do besides cry Eureka?, Mathematical Association of America, Washington, DC, 1999.