Rational Trigonometry in Three Dimensions - Universal Hyperbolic Geometry

Explore the extension of rational trigonometry to three dimensions in this 31-minute video lecture. Learn how to use vector approaches and dot products to define quadrance and spread in 3D space. Discover how fundamental trigonometric laws like Pythagoras' theorem, Triple quad formula, Cross law, Spread law, and Triple Spread formula apply in higher dimensions. Delve into new concepts such as solid spread and its relation to determinants. Gain insights into quadrance calculations, parallel vectors, scalar products, and the properties of spreads. Examine the connection between spreads and determinants in both 2D and 3D contexts, providing a comprehensive understanding of rational trigonometry in three-dimensional space.

Introduction quadrance
Quadrances of 3-vector
Parallel vectors
The scalar/inner/dot product
Elementary properties of a spread
Three main laws of trigonometry
Spreads and determinants in 2-dimensions
Determinants