The Australian Journal of Mathematical Analysis and Applications

Home News Editors Volumes RGMIA Subscriptions Authors Contact

ISSN 1449-5910  


Paper Information

Paper Title:

Hyperbolic Barycentric Coordinates


Abraham A. Ungar

Department of Mathematics, North Dakota State University,
Fargo, ND 58105,


A powerful and novel way to study Einstein's special theory of relativity and its underlying geometry, the hyperbolic geometry of Bolyai and Lobachevsky, by analogies with classical mechanics and its underlying Euclidean geometry is demonstrated. The demonstration sets the stage for the extension of the notion of barycentric coordinates in Euclidean geometry, first conceived by Mbius in 1827, into hyperbolic geometry. As an example for the application of hyperbolic barycentric coordinates, the hyperbolic midpoint of any hyperbolic segment, and the centroid and orthocenter of any hyperbolic triangle are determined.

Full Text PDF:

2004-2023 Austral Internet Publishing