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 14 - Reflections in Hyperbolic Geometry |
Symmetries are crucial in studying geometry. In Euclidean geometry we have translations, rotations, reflections, dilations and also projections and perspectivities. This lecture introduces reflections into universal hyperbolic geometry. First we discuss the two different kinds of reflections (in a point or in a line) in Euclidean geometry. The hyperbolic version rests on some remarkable facts, also directly connected to the geometry of a circle.
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