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 34 - Spherical and elliptic geometries (cont.) |
We continue our introduction to spherical and elliptic geometries, starting with a discussion of longitude and latitude on a sphere. We explain the relationship of spherical geometry and Euclid's 5 postulates. Elliptic geometry is the result of identifying antipodal points on the sphere. Measurement on the surface of a sphere uses angles to define spherical distances, but additional functions are required. We describe Ptolemy's tables of chords and later Indian and Arab work on tables of sines. The final result is Menelaus' theorem.
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