Non-Euclidean Triangle Centers

Abstract

Non-Euclidean triangle centers can be described using homogeneous coordinates that are proportional to the generalized sines of the directed distances of a given center from the edges of the reference triangle. Identical homogeneous coordinates of a specific triangle center may be used for all spaces of uniform Gaussian curvature. We also define the median point for a set of points in non-Euclidean space and a planar center of rotation for a set of points in a non-Euclidean plane.

29 pages, 12 figures; added three additional centers

References in corpus (2)

• On some classical constructions extended to hyperbolic geometry
• Mass in the Hyperbolic Plane

Cited by in corpus (2)

• On The Geometry of a Triangle in the Elliptic and in the Extended Hyperbolic Plane
• On Centers and Central Lines of Triangles in the Elliptic Plane