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 20 - Pure and Applied Geometry - Understanding the Continuum|
The distinction between pure and applied geometry is closely related to the difference between rational numbers and decimal numbers. Especially when we treat decimal numbers in an approximate way: specifying rather an interval or range rather than a particular value. This gives us a way of explaining the distinction between a line meeting a circle exactly or only roughly.
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