Universal Hyperbolic Geometry
Universal Hyperbolic Geometry (UNSW). This is a collection of video lectures on Universal Hyperbolic Geometry given by Professor N. J. Wildberger. This course explains a new, simpler and more elegant theory of non-Euclidean geometry; in particular hyperbolic geometry. It is a purely algebraic approach which avoids transcendental functions like log, sin, tanh etc, relying instead on high school algebra and quadratic equations. The theory is more general, extending beyond the null circle, and connects naturally to Einstein's special theory of relativity.
| Lecture 10 - Orthocenters Exist! |
In classical hyperbolic geometry, orthocenters of triangles do not in general exist. Here in universal hyperbolic geometry, they do. This lecture introduces a number of basic important definitions: that of side, vertex, couple, triangle, trilateral. We also introduce Desargues theorem and use it to define the polar of a point with respect to a triangle. The lecture culminates in the definition of the orthic line, orthostar and ortho-axis of a triangle. The ortho-axis will prove to be the most important line in hyperbolic triangle geometry.
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