Original scientific paper

Universal Affine Triangle Geometry and Four-fold Incenter Symmetry

Nguyen Le ; School of Mathematics and Statistics UNSW, Sydney, Australia
Norman John Wildberger orcid.org/0000-0003-3503-6495 ; School of Mathematics and Statistics UNSW, Sydney, Australia

Abstract

We develop a generalized triangle geometry, using an arbitrary bilinear form in an affine plane over a general field. By introducing standardized coordinates we find canonical forms for some basic centers and lines. Strong concurrencies formed by quadruples of lines from the Incenter hierarchy are investigated, including joins of corresponding Incenters, Gergonne, Nagel, Spieker points, Mittenpunkts and the New points we introduce. The diagrams are taken from relativistic (green) geometry.

Keywords

Triangle geometry; affine geometry; Rational trigonometry; bilinear form; incenter hierarchy; Euler line; Gergonne; Nagel; Mittenpunkt; chromogeometry

Hrčak ID:

96195

URI

https://hrcak.srce.hr/96195

Publication date:

30.1.2013.

Article data in other languages: croatian

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