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KoG, Vol. 13. No. 13., 2009.

Izvorni znanstveni članak

Osculating Circles of Conics in Cayley-Klein Planes

Gunter Weiss ; Institute for Geometry, Technical University of Dresden, Dresden, Germany
Ana Sliepčević ; Faculty of Civil Engineering, University of Zagreb, Zagreb, Hrvatska

Puni tekst: engleski, pdf (176 KB) str. 7-12 preuzimanja: 585* citiraj
APA 6th Edition
Weiss, G. i Sliepčević, A. (2009). Osculating Circles of Conics in Cayley-Klein Planes. KoG, 13. (13.), 7-12. Preuzeto s https://hrcak.srce.hr/47616
MLA 8th Edition
Weiss, Gunter i Ana Sliepčević. "Osculating Circles of Conics in Cayley-Klein Planes." KoG, vol. 13., br. 13., 2009, str. 7-12. https://hrcak.srce.hr/47616. Citirano 25.05.2020.
Chicago 17th Edition
Weiss, Gunter i Ana Sliepčević. "Osculating Circles of Conics in Cayley-Klein Planes." KoG 13., br. 13. (2009): 7-12. https://hrcak.srce.hr/47616
Harvard
Weiss, G., i Sliepčević, A. (2009). 'Osculating Circles of Conics in Cayley-Klein Planes', KoG, 13.(13.), str. 7-12. Preuzeto s: https://hrcak.srce.hr/47616 (Datum pristupa: 25.05.2020.)
Vancouver
Weiss G, Sliepčević A. Osculating Circles of Conics in Cayley-Klein Planes. KoG [Internet]. 2009 [pristupljeno 25.05.2020.];13.(13.):7-12. Dostupno na: https://hrcak.srce.hr/47616
IEEE
G. Weiss i A. Sliepčević, "Osculating Circles of Conics in Cayley-Klein Planes", KoG, vol.13., br. 13., str. 7-12, 2009. [Online]. Dostupno na: https://hrcak.srce.hr/47616. [Citirano: 25.05.2020.]

Sažetak
In the Euclidean plane there are several well-known methods of constructing an osculating (Euclidean) circle to a conic. We show that at least one of these methods can be “translated” into a construction scheme of finding the osculating non-Euclidean circle to a given conic in a hyperbolic or elliptic plane. As an example we will deal with the
Klein-model of these non-Euclidean planes, as the projective geometric point of view is common to the Euclidean as well as to the non-Euclidean cases.

Ključne riječi
Cayley-Klein plane; elation; pencil of conics; osculating circle; curvature centre

Hrčak ID: 47616

URI
https://hrcak.srce.hr/47616

[hrvatski]

Posjeta: 855 *