Original scientific paper

https://doi.org/10.31896/k.28.3

Universal Porisms and Yff Conics

Boris Odehnal ; University of Applied Arts Vienna, Vienna, Austria *

* Corresponding author.

Abstract

The Yff circumellipse and the Yff inellipse of a triangle allow for a poristic family of triangles (henceforth called Yff porism), since the initial triangle is already an interscribed triangle. Surprisingly, the Yff porism can be parametrized by means of rational functions, and thus, it delivers a porism in Universal Geometry. This also allows us to give explicit examples of poristic triangle families over finite fields. Considering the Yff inellipse and Yff circumellipse as the basis of an exponential pencil of conics, we can iterate the construction of the porism and find an infinite sequence (and thus infinitely many) nested rational triangle porisms over
the real (and complex) number field or a finite closed chain of porisms in the case of a finite field.

Keywords

porism; inellipse; circumellipse; triangle; rational porism; rational parametrization; finite field; finite projective plane

Hrčak ID:

323821

URI

https://hrcak.srce.hr/323821

Publication date:

20.12.2024.

Article data in other languages: croatian

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