Original scientific paper

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

Abstract

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.

Keywords

conic; angle; projective mapping; Frégier point; Frégier conic; Poncelet porism; envelope

Hrčak ID:

288261

URI

https://hrcak.srce.hr/288261

Publication date:

28.12.2022.

Article data in other languages: croatian

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