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On Central Collineations which Transform a Given Conic to a Circle

Sonja Gorjanc ; Faculty of Civil Engineering, University of Zagreb, Zagreb, Croatia
Tibor Schwarcz ; Department of Computer Graphics and Image Processing, University of Debrecen, Debrecen, Hungary
Miklós Hoffmann   ORCID icon orcid.org/0000-0001-8846-232X ; Institute of Mathematics and Computer Science, Károly Eszterházy College, Eger, Hungary

Puni tekst: engleski, pdf (791 KB) str. 47-54 preuzimanja: 280* citiraj
APA 6th Edition
Gorjanc, S., Schwarcz, T. i Hoffmann, M. (2010). On Central Collineations which Transform a Given Conic to a Circle. KoG, 14. (14.), 47-54. Preuzeto s https://hrcak.srce.hr/62865
MLA 8th Edition
Gorjanc, Sonja, et al. "On Central Collineations which Transform a Given Conic to a Circle." KoG, vol. 14., br. 14., 2010, str. 47-54. https://hrcak.srce.hr/62865. Citirano 28.11.2021.
Chicago 17th Edition
Gorjanc, Sonja, Tibor Schwarcz i Miklós Hoffmann. "On Central Collineations which Transform a Given Conic to a Circle." KoG 14., br. 14. (2010): 47-54. https://hrcak.srce.hr/62865
Harvard
Gorjanc, S., Schwarcz, T., i Hoffmann, M. (2010). 'On Central Collineations which Transform a Given Conic to a Circle', KoG, 14.(14.), str. 47-54. Preuzeto s: https://hrcak.srce.hr/62865 (Datum pristupa: 28.11.2021.)
Vancouver
Gorjanc S, Schwarcz T, Hoffmann M. On Central Collineations which Transform a Given Conic to a Circle. KoG [Internet]. 2010 [pristupljeno 28.11.2021.];14.(14.):47-54. Dostupno na: https://hrcak.srce.hr/62865
IEEE
S. Gorjanc, T. Schwarcz i M. Hoffmann, "On Central Collineations which Transform a Given Conic to a Circle", KoG, vol.14., br. 14., str. 47-54, 2010. [Online]. Dostupno na: https://hrcak.srce.hr/62865. [Citirano: 28.11.2021.]

Sažetak
In this paper we prove that for a given axis the centers of all central collineations which transform a given proper conic c into a circle, lie on one conic cc confocal to the original one. The conics c and cc intersect into real points and their common diametral chord is conjugate to the direction of the given axis.
Furthermore, for a given center S the axes of all central collineations that transform conic c into a circle form two pencils of parallel lines. The directions of these pencils are conjugate to two common diametral chords of c and the confocal conic through S that cuts c at real points.
Finally, we formulate a theorem about the connection of
the pair of confocal conics and the fundamental elements of central collineations that transform these conics into circles.

Ključne riječi
central collineation; confocal conics; Apollonian circles

Hrčak ID: 62865

URI
https://hrcak.srce.hr/62865

[hrvatski]

Posjeta: 636 *