Original scientific paper

https://doi.org/10.31896/k.24.5

The Feuerbach Theorem and Cyclography in Universal Geometry

William Beare orcid.org/0000-0001-9127-5138 ; School of Mathematics and Statistics UNSW, Sydney, Australia
Norman J. Wildberger orcid.org/0000-0003-3503-6495 ; School of Mathematics and Statistics UNSW, Sydney, Australia

Abstract

We have another look at the Feuerbach theorem with a view to extending it in an oriented way to finite fields using the purely algebraic approach of rational trigonometry and universal geometry. Our approach starts with the tangent lines to three rational points on the unit circle, and all subsequent formulas involve the three parameters that define them. Tangency of incircles is treated in the oriented setting via a simplied form of cyclography. Some interesting features of the finite field case are discussed.

Keywords

Feuerbach theorem; incircles; universal geometry; cyclography; finite fields

Hrčak ID:

248417

URI

https://hrcak.srce.hr/248417

Publication date:

27.12.2020.

Article data in other languages: croatian

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