Original scientific paper

https://doi.org/10.31896/k.27.2

A Miquel-Steiner Transformation

Boris Odehnal orcid.org/0000-0002-7265-5132 ; University of Applied Arts Vienna, Vienna, Austria *

* Corresponding author.

Abstract

Each complete quadrilateral has three Miquel-Steiner points. Any triangle together with an arbitrarily chosen point not on a triangle side also defines a complete quadrilateral, and thus, this pivot point defines three Miquel-Steiner points. These three Miquel points form a triangle
which is perspective with the base triangle. The mapping that assigns to the pivot point the uniquely defined perspector is a quadratic and not involutive Cremona transformation and shall be called Miquel-Steiner transformation. We shall study the action of the Miquel-Steiner transformation and its inverse.

Keywords

Miquel points; quadrilateral; triangle; quadratic Cremona transformation

Hrčak ID:

311472

URI

https://hrcak.srce.hr/311472

Publication date:

21.12.2023.

Article data in other languages: croatian

Visits: 810 *