Invariant Quadrea of Orthocenter Triangles from Four Null Points in Universal Hyperbolic Geometry

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Authors: Coady, John D.
Cited by: 0

Abstract

We consider four distinct null points in the projective plane of Universal Hyperbolic Geometry over a field of characteristic not two. For each triple of points, the associated triply nil triangle admits a well-defined orthocenter via projective polarity. We prove that the quadrea of the projective triangle formed by any three of these four orthocenters is invariant under variation of the cross-ratio parameter, taking the universal value 16/27 . The result is established algebraically and verified by symbolic computation. This invariant extends known absolute constants in Universal Hyperbolic Geometry arising from null configurations, such as those appearing in the 48/64 theorem.

Fields of Study & Subjects

Mathematics and Applications Algebraic and Geometric Analysis Advanced Mathematical Theories and Applications

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
2 February 2026
Document type
Preprint