Orthocenters Exist - Universal Hyperbolic Geometry

Explore the fascinating world of universal hyperbolic geometry in this 44-minute lecture that challenges classical notions and introduces crucial concepts for triangle geometry. Learn about the existence of orthocenters in hyperbolic triangles, a concept not found in classical hyperbolic geometry. Discover key definitions such as side, vertex, couple, triangle, and trilateral. Delve into important theorems including the Altitude line theorem, Orthocenter theorem, and Desargues theorem. Investigate the polar of a point with respect to a triangle and explore the orthic line, orthostar, and ortho-axis - the most significant line in hyperbolic triangle geometry. Gain valuable insights into this advanced mathematical topic through clear explanations and visual aids.

Introduction
Definitions: couple, triangle, trilateral
Altitude line theorem
Altitude point theorem
Orthocenter theorem
Proof of Orthocenter theorem
Ortholine theorem
Desargues' theorem
Cevians and Desargues' polars
Orthic axis, orthostar and ortho-axis