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 15 - Reflections and Projective Linear Algebra |
Reflections are the fundamental symmetries in hyperbolic geometry. The reflection in a point interchanges any two null points on any line through the point. Using the projective parametrization of the circle, we associate to the reflecting point a 2x2 projective matrix. So we need to develop some basics about projective linear algebra: where we consider vectors and matrices but only up to scalars.
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