References
- Bae J.-S., Kim D.-S. and Kim Y. H., A characterization of the unit sphere, Amer. Math. Monthly, 110(9)(2003), 830-833. https://doi.org/10.2307/3647802
- Benyi A., Szeptycki P. and Van Vleck F., Archimedean properties of parabolas, Amer. Math. Monthly, 107(2000), 945-949. https://doi.org/10.2307/2695591
- Benyi A., Szeptycki P. and Van Vleck F., A generalized Archimedean property, Real Anal. Exchange, 29(2003/04), 881-889.
- Chen B.-Y., Kim D.-S. and Kim Y. H., New characterizations of W-curves, Publ. Math. Debrecen., 69/4(2006), 457-472.
- do Carmo, M. P., Differential Geometry of Curves and Surfaces, Prentice-Hall, Englewood Cliffs, NJ, 1976.
- Kim D.-S., A characterization of the hypersphere, Honam Math. J., 27(2)(2005), 267-271.
-
Kim D.-S., Ellipsoids and elliptic hyperboloids in the Euclidean space
$E^{n+1}$ , Linear Algebra Appl., 471 (2015), 28-45. https://doi.org/10.1016/j.laa.2014.12.014 - Kim D.-S. and Kang S. H., A characterization of conic sections, Honam Math. J., 33(3)(2011), 335-340. https://doi.org/10.5831/HMJ.2011.33.3.335
- Kim D.-S. and Kim D. S., Centroid of triangles associated with a curve, Bull. Korean Math. Soc., 52(2)(2015), 571-579. https://doi.org/10.4134/BKMS.2015.52.2.571
- 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. https://doi.org/10.5831/HMJ.2015.37.1.41
- 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. https://doi.org/10.4134/BKMS.2015.52.3.925
- 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. https://doi.org/10.4134/BKMS.2015.52.1.275
- Kim D.-S. and Kim Y. H., A characterization of space forms, Bull. Korean Math. Soc., 35(4)(1998), 757-767.
- Kim D.-S. and Kim Y. H., A characterization of ellipses, Amer. Math. Monthly, 114(1)(2007), 66-70.
- Kim D.-S. and Kim Y. H., New characterizations of spheres, cylinders and W-curves, Linear Algebra Appl., 432(11)(2010), 3002-3006. https://doi.org/10.1016/j.laa.2010.01.006
- Kim D.-S. and Kim Y. H., Some characterizations of spheres and elliptic paraboloids, Linear Algebra Appl., 437(2012), 113-120. https://doi.org/10.1016/j.laa.2012.02.013
- Kim D.-S. and Kim Y. H., Some characterizations of spheres and elliptic paraboloids II, Linear Algebra Appl., 438(2013), 1356-1364. https://doi.org/10.1016/j.laa.2012.08.024
- Kim D.-S. and Kim Y. H., On the Archimedean characterization of parabolas, Bull. Korean Math. Soc., 50(2013), 2103-2114. https://doi.org/10.4134/BKMS.2013.50.6.2103
- 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. https://doi.org/10.1016/j.crma.2014.09.003
- Kim D.-S., Park J. H. and Kim Y. H., Some characterizations of parabolas, Kyungpook Math. J., 53(1)(2013), 99-104. https://doi.org/10.5666/KMJ.2013.53.1.99
- Kim D.-S. and Shim K.-C., Area of triangles associated with a curve, Bull. Korean Math. Soc., 51(3)(2014), 901-909. https://doi.org/10.4134/BKMS.2014.51.3.901
- Kim D.-S. and Song B., A characterization of elliptic hyperboloids, Honam Math. J., 35(1)(2013), 37-49. https://doi.org/10.5831/HMJ.2013.35.1.37
- Krawczyk J., On areas associated with a curve, Zesz. Nauk. Uniw. Opol. Mat., 29(1995), 97-101.
- Richmond B. and Richmond T., How to recognize a parabola, Amer. Math. Monthly, 116(2009), 910-922. https://doi.org/10.4169/000298909X477023
- Stein S., Archimedes. What did he do besides cry Eureka?, Mathematical Association of America, Washington, DC, 1999.
Cited by
- CENTROIDS AND SOME CHARACTERIZATIONS OF PARALLELOGRAMS vol.31, pp.3, 2016, https://doi.org/10.4134/CKMS.c150165
- Various centroids and some characterizations of catenary rotation hypersurfaces vol.42, pp.13036149, 2018, https://doi.org/10.3906/mat-1703-61