Original scientific paper

Quadrangle Centroids in Universal Hyperbolic Geometry

Sebastian Blefari ; 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 study relations between the eight projective quadrangle centroids of a quadrangle in universal hyperbolic geometry which are analogs of the barycentric centre of a Euclidean quadrangle. We investigate the number theoretical conditions for such centres to exist, and show that the eight
centroids naturally form two quadrangles which together with the original one have three-fold perspective symmetries. The diagonal triangles of these three quadrangles are also triply perspective.

Keywords

Universal hyperbolic geometry; projective geometry; centroids quadrangles; diagonal triangles; perspectivities

Hrčak ID:

174102

URI

https://hrcak.srce.hr/174102

Publication date:

16.1.2017.

Article data in other languages: croatian

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