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On the Isoptic Hypersurfaces in the n-Dimensional Euclidean Space

Géza Csima ; Institute of Mathematics, Budapest University of Technology and Economics, Budapest, Hungary
Jenő Szirmai   ORCID icon orcid.org/0000-0001-9610-7993 ; Institute of Mathematics, Budapest University of Technology and Economics, Budapest, Hungary

Puni tekst: engleski, pdf (436 KB) str. 53-57 preuzimanja: 216* citiraj
APA 6th Edition
Csima, G. i Szirmai, J. (2013). On the Isoptic Hypersurfaces in the n-Dimensional Euclidean Space. KoG, 17. (17.), 53-57. Preuzeto s https://hrcak.srce.hr/114277
MLA 8th Edition
Csima, Géza i Jenő Szirmai. "On the Isoptic Hypersurfaces in the n-Dimensional Euclidean Space." KoG, vol. 17., br. 17., 2013, str. 53-57. https://hrcak.srce.hr/114277. Citirano 25.01.2020.
Chicago 17th Edition
Csima, Géza i Jenő Szirmai. "On the Isoptic Hypersurfaces in the n-Dimensional Euclidean Space." KoG 17., br. 17. (2013): 53-57. https://hrcak.srce.hr/114277
Harvard
Csima, G., i Szirmai, J. (2013). 'On the Isoptic Hypersurfaces in the n-Dimensional Euclidean Space', KoG, 17.(17.), str. 53-57. Preuzeto s: https://hrcak.srce.hr/114277 (Datum pristupa: 25.01.2020.)
Vancouver
Csima G, Szirmai J. On the Isoptic Hypersurfaces in the n-Dimensional Euclidean Space. KoG [Internet]. 2013 [pristupljeno 25.01.2020.];17.(17.):53-57. Dostupno na: https://hrcak.srce.hr/114277
IEEE
G. Csima i J. Szirmai, "On the Isoptic Hypersurfaces in the n-Dimensional Euclidean Space", KoG, vol.17., br. 17., str. 53-57, 2013. [Online]. Dostupno na: https://hrcak.srce.hr/114277. [Citirano: 25.01.2020.]

Sažetak
The theory of the isoptic curves is widely studied in the Euclidean plane E^2 (see [1] and [13] and the references given there). The analogous question was investigated by the authors in the hyperbolic H^2 and elliptic E^2 planes (see [3], [4]), but in the higher dimensional spaces there is no result according to this topic.
In this paper we give a natural extension of the notion
of the isoptic curves to the n-dimensional Euclidean space E^n (n\geq 3) which are called isoptic hypersurfaces. We develope an algorithm to determine the isoptic hypersurface H_D of an arbitrary (n−1) dimensional compact parametric domain D lying in a hyperplane in the Euclidean n-space.
We will determine the equation of the isoptic hypersurfaces of rectangles D \subset  E^2 and visualize them with Wolfram Mathematica. Moreover, we will show some possible
applications of the isoptic hypersurfaces.

Ključne riječi
isoptic curves; hypersurfaces; differential geometry; elliptic geometry

Hrčak ID: 114277

URI
https://hrcak.srce.hr/114277

[hrvatski]

Posjeta: 367 *