References
- A. Benyi, P. Szeptycki and F. Van Vleck, Archimedean properties of parabolas, Amer. Math. Monthly, 107 (2000), 945-949.
- A. Benyi, P. Szeptycki and F. Van Vleck, A generalized Archimedean property, Real Anal. Exchange, 29 (2003/04), 881-889. https://doi.org/10.14321/realanalexch.29.2.0881
- W. Blaschke, Vorlesungen uber Differentialgeometrie und geometrische Grundlagen von Einsteins Relativitatstheorie, Band I, Elementare Differentialgeometrie, (German) 3rd ed., Dover Publications, New York, N. Y., 1945.
- O. Ciaurri, E. Fernandez and L. Roncal, Revisiting floating bodies, Expo. Math., 34 (2016), no. 4, 396-422. https://doi.org/10.1016/j.exmath.2016.06.001
- K. Jorgens, Uber die Losungen der Differentialgleichung rt-s2 = 1, Math. Ann., 127(1954), 130-134. https://doi.org/10.1007/BF01361114
- D.-S. Kim, Ellipsoids and elliptic hyperboloids in the Euclidean space 𝔼n+1, Linear Algebra Appl., 471 (2015), 28-45.
- D.-S. Kim and S. H. Kang, A characterization of conic sections, Honam Math. J., 33 (2011), 335-340. https://doi.org/10.5831/HMJ.2011.33.3.335
- D.-S. Kim and Y. H. Kim, A characterization of ellipses, Amer. Math. Monthly, 114 (2007), 66-70. https://doi.org/10.1080/00029890.2007.11920393
- D.-S. Kim and Y. H. Kim, New characterizations of spheres, cylinders and W-curves, Linear Algebra Appl., 432 (2010), 3002-3006. https://doi.org/10.1016/j.laa.2010.01.006
- D.-S. Kim and Y. H. Kim, Some characterizations of spheres and elliptic paraboloids, Linear Algebra Appl., 437 (2012), no. 1, 113-120. https://doi.org/10.1016/j.laa.2012.02.013
- D.-S. Kim and Y. H. Kim, Some characterizations of spheres and elliptic paraboloids II, Linear Algebra Appl., 438 (2013) no.3, 1356-1364. https://doi.org/10.1016/j.laa.2012.08.024
- D.-S. Kim and Y. H. Kim, On the Archimedean characterization of parabolas, Bull. Korean Math. Soc., 50 (2013), no. 6, 2103-2114. https://doi.org/10.4134/BKMS.2013.50.6.2103
- D.-S. Kim and Y. H. Kim, A characterization of concentric hyperspheres in ℝn, Bull. Korean Math. Soc., 51 (2014), 531-538. https://doi.org/10.4134/BKMS.2014.51.2.531
- D.-S. Kim, Y. H. Kim and J. H. Park, Some characterizations of parabolas, Kyungpook Math. J., 53 (2013), 99-104. https://doi.org/10.5666/KMJ.2013.53.1.99
- D.-S. Kim, S. Park and Y. H. Kim, Center of gravity and a characterization of parabolas, Kyungpook Math. J., 55 (2015), no. 2, 473-484. https://doi.org/10.5666/KMJ.2015.55.2.473
- D.-S. Kim, Y. H. Kim and D. W. Yoon, On standard imbeddings of hyperbolic spaces in the Minkowski space, C. R. Math. Acad. Sci. Paris, 352 (2014), 1033-1038. https://doi.org/10.1016/j.crma.2014.09.003
- D.-S. Kim and K.-C. Shim, Area of triangles associated with a curve, Bull. Korean Math. Soc., 51 (2014), 901-909. https://doi.org/10.4134/BKMS.2014.51.3.901
- D.-S. Kim and B. Song, A characterization of elliptic hyperboloids, Honam Math. J., 35 (2013), 37-49. https://doi.org/10.5831/HMJ.2013.35.1.37
- J. Krawczyk, On areas associated with a curve, Zesz. Nauk. Uniw. Opol. Mat., 29 (1995), 97-101.
- A. V. Pogorelov, On the improper convex affine hyperspheres, Geom. Dedicata, 1 (1972), no. 1, 33-46. https://doi.org/10.1007/BF00147379
- B. Richmond and T. Richmond, How to recognize a parabola, Amer. Math. Monthly, 116 (2009), 910-922. https://doi.org/10.4169/000298909X477023
- O. Stamm, Umkehrung eines Satzes von Archimedes uber die Kugel, Abh. Math. Sem. Univ. Hamburg, 17 (1951), 112-132. https://doi.org/10.1007/BF02950746
- J. A. Thorpe, Elementary topics in differential geometry, Undergraduate Texts in Mathematics, Springer-Verlag, New York-Heidelberg, 1979.
- Y. Yu and H. Liu, A characterization of parabola, Bull. Korean Math. Soc., 45 (2008), 631-634. https://doi.org/10.4134/BKMS.2008.45.4.631