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 24 - Visualizing Quadrance with Circles|
To really understand the fundamental concept of quadrance between points in universal hyperbolic geometry, which replaces the more familiar notion of distance, it is useful to think about circles. Circles are conics, defined in terms of quadrance, and in our usual two dimensional picture they can appear as ellipses, parabolas or hyperbolas. We illustrate three different families, with three different centers. A careful study of these examples will give the student a good understanding of this crucial concept in geometry.
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