Original scientific paper

Universal Hyperbolic Geometry III: First Steps in Projective Triangle Geometry

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

Abstract

We initiate a triangle geometry in the projective metrical setting, based on the purely algebraic approach of universal geometry, and yielding in particular a new form of hyperbolic triangle geometry. There are three main strands: the Orthocenter, Incenter and Circumcenter hierarchies, with the last two dual. Formulas using ortholinear coordinates are a main objective. Prominent are five particular points, the b, z, x, h and s points, all lying on the Orthoaxis A. A rich kaleidoscopic aspect colours the subject.

Keywords

universal hyperbolic geometry; triangle geometry; projective geometry; bilinear form; ortholinear coordinates; incenter; circumcenter; orthoaxis

Hrčak ID:

77080

URI

https://hrcak.srce.hr/77080

Publication date:

29.12.2011.

Article data in other languages: croatian

Visits: 4.225 *