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- Title
Pencils of Frégier Conics.
- Authors
ODEHNAL, BORIS
- 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 Fregier point of P. Replacing the right angles at P between assigned pairs of lines with an arbitrary angle 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 Freegier point and shall be called a generalized Freegier conic. By varying the angle, we obtain a pencil of generalized Freegier 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.
- Subjects
ARBITRARY constants; TRIANGLES; CONIC sections; CARNOT cycle; PROOF theory
- Publication
KoG, 2022, Vol 26, Issue 26, p33
- ISSN
1331-1611
- Publication type
Article
- DOI
10.31896/k.26.3