KoG, Vol. 14. No. 14., 2010.
Izvorni znanstveni članak
On Central Collineations which Transform a Given Conic to a Circle
Sonja Gorjanc
; Građevinski fakultet Sveučilišta u Zagrebu, Zagreb, Hrvatska
Tibor Schwarcz
; Department of Computer Graphics and Image Processing, University of Debrecen, Debrecen, Hungary
Miklós Hoffmann
orcid.org/0000-0001-8846-232X
; Institute of Mathematics and Computer Science, Károly Eszterházy College, Eger, Hungary
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
Datum izdavanja:
29.12.2010.
Posjeta: 1.150 *