Original scientific paper

Universal Hyperbolic Geometry IV: Sydpoints and Twin Circumcircles

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

Abstract

We introduce the new notion of sydpoints into projective triangle geometry with respect to a general bilinear form. These are analogs of midpoints, and allow us to extend hyperbolic triangle geometry to non-classical triangles with points inside and outside of the null conic. Surprising analogs of circumcircles may be defined, involving the appearance of pairs of twin circles, yielding in general eight circles with interesting intersection properties.

Keywords

universal hyperbolic geometry; triangle geometry; projective geometry; bilinear form; sydpoints; twin circumcircles

Hrčak ID:

96187

URI

https://hrcak.srce.hr/96187

Publication date:

30.1.2013.

Article data in other languages: croatian

Visits: 1.910 *