KoG, Vol. 26 No. 26, 2022.
Izvorni znanstveni članak
https://doi.org/10.31896/k.26.3
Pencils of Frégier Conics
Boris Odehnal
orcid.org/0000-0002-7265-5132
; University of Applied Arts Vienna, Vienna, Austria
Sažetak
For each point P on a conic c, the involution of right angles at P induces an elliptic involution on c whose center
F is called the Frégier point of P. Replacing the right angles at P between assigned pairs of lines with an arbitrary angle \fi yields a projective mapping of lines in the pencil about P, and thus, on c. The lines joining corresponding points on c do no longer pass through a single point and envelop a conic f which can be seen as the generalization of the Frégier point and shall be called a generalized Frégier conic. By varying the angle, we obtain a pencil of generalized Frégier conics which is a pencil of the third kind. We shall study the thus defined conics and discover, among other objects, general Poncelet triangle families.
Ključne riječi
conic; angle; projective mapping; Frégier point; Frégier conic; Poncelet porism; envelope
Hrčak ID:
288261
URI
Datum izdavanja:
28.12.2022.
Posjeta: 516 *