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 09 - Duality and Perpendicularity |
Perpendicularity in universal hyperbolic geometry is defined in terms of duality. One big difference with classical HG is that points can also be perpendicular, not just lines. Once we have perpendicularity, we can define altitudes. We also state the collinear points theorem and concurrent lines theorem, using homogeneous coordinates and determinants.
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