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Original scientific paper

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

Fulltext: english, pdf (791 KB) pages 47-54 downloads: 280* cite
APA 6th Edition
Gorjanc, S., Schwarcz, T. & Hoffmann, M. (2010). On Central Collineations which Transform a Given Conic to a Circle. KoG, 14. (14.), 47-54. Retrieved from 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., no. 14., 2010, pp. 47-54. https://hrcak.srce.hr/62865. Accessed 27 Nov. 2021.
Chicago 17th Edition
Gorjanc, Sonja, Tibor Schwarcz and Miklós Hoffmann. "On Central Collineations which Transform a Given Conic to a Circle." KoG 14., no. 14. (2010): 47-54. https://hrcak.srce.hr/62865
Harvard
Gorjanc, S., Schwarcz, T., and Hoffmann, M. (2010). 'On Central Collineations which Transform a Given Conic to a Circle', KoG, 14.(14.), pp. 47-54. Available at: https://hrcak.srce.hr/62865 (Accessed 27 November 2021)
Vancouver
Gorjanc S, Schwarcz T, Hoffmann M. On Central Collineations which Transform a Given Conic to a Circle. KoG [Internet]. 2010 [cited 2021 November 27];14.(14.):47-54. Available from: https://hrcak.srce.hr/62865
IEEE
S. Gorjanc, T. Schwarcz and M. Hoffmann, "On Central Collineations which Transform a Given Conic to a Circle", KoG, vol.14., no. 14., pp. 47-54, 2010. [Online]. Available: https://hrcak.srce.hr/62865. [Accessed: 27 November 2021]

Abstracts
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.

Keywords
central collineation; confocal conics; Apollonian circles

Hrčak ID: 62865

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

[croatian]

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