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Visualization of Geodesic Curves, Spheres and Equidistant Surfaces in S^2×R Space

János Pallagi ; Institute of Mathematics, Department of Geometry, Budapest University of Technology and Economics, Budapest, Hungary
Benedek Schultz ; Institute of Mathematics, Department of Geometry, Budapest University of Technology and Economics, Budapest, Hungary
Jenő Szirmai   ORCID icon orcid.org/0000-0001-9610-7993 ; Institute of Mathematics, Department of Geometry, Budapest University of Technology and Economics, Budapest, Hungary

Puni tekst: engleski, pdf (387 KB) str. 35-40 preuzimanja: 811* citiraj
APA 6th Edition
Pallagi, J., Schultz, B. i Szirmai, J. (2010). Visualization of Geodesic Curves, Spheres and Equidistant Surfaces in S^2×R Space. KoG, 14. (14.), 35-40. Preuzeto s https://hrcak.srce.hr/62863
MLA 8th Edition
Pallagi, János, et al. "Visualization of Geodesic Curves, Spheres and Equidistant Surfaces in S^2×R Space." KoG, vol. 14., br. 14., 2010, str. 35-40. https://hrcak.srce.hr/62863. Citirano 07.12.2021.
Chicago 17th Edition
Pallagi, János, Benedek Schultz i Jenő Szirmai. "Visualization of Geodesic Curves, Spheres and Equidistant Surfaces in S^2×R Space." KoG 14., br. 14. (2010): 35-40. https://hrcak.srce.hr/62863
Harvard
Pallagi, J., Schultz, B., i Szirmai, J. (2010). 'Visualization of Geodesic Curves, Spheres and Equidistant Surfaces in S^2×R Space', KoG, 14.(14.), str. 35-40. Preuzeto s: https://hrcak.srce.hr/62863 (Datum pristupa: 07.12.2021.)
Vancouver
Pallagi J, Schultz B, Szirmai J. Visualization of Geodesic Curves, Spheres and Equidistant Surfaces in S^2×R Space. KoG [Internet]. 2010 [pristupljeno 07.12.2021.];14.(14.):35-40. Dostupno na: https://hrcak.srce.hr/62863
IEEE
J. Pallagi, B. Schultz i J. Szirmai, "Visualization of Geodesic Curves, Spheres and Equidistant Surfaces in S^2×R Space", KoG, vol.14., br. 14., str. 35-40, 2010. [Online]. Dostupno na: https://hrcak.srce.hr/62863. [Citirano: 07.12.2021.]

Sažetak
The S^2×R geometry is derived by direct product of the
spherical plane S^2 and the real line R. In [9] the third author has determined the geodesic curves, geodesic balls of S^2×R space, computed their volume and defined the notion of the geodesic ball packing and its density. Moreover, he has developed a procedure to determine the density of the geodesic ball packing for generalized Coxeter space groups of S^2×R and applied this algorithm to them.
E. MOLNÁR showed in [3], that the homogeneous 3-spaces have a unified interpretation in the projective 3-sphere
PS^3(V^4,V_ 4,R). In our work we shall use this projective
model of S^2×R geometry and in this manner the geodesic
lines, geodesic spheres can be visualized on the Euclidean
screen of computer.
Furthermore, we shall define the notion of the equidistant surface to two points, determine its equation and visualize it in some cases. We shall also show a possible way of making the computation simpler and obtain the equation of an equidistant surface with more possible geometric meaning. The pictures were made by the Wolfram Mathematica software.

Ključne riječi
non-Euclidean geometries; projective geometry; geodesic sphere; equidistant surface

Hrčak ID: 62863

URI
https://hrcak.srce.hr/62863

[hrvatski]

Posjeta: 1.350 *