Quadrance and Spread - Universal Hyperbolic Geometry

Explore the fundamental concepts of Universal Hyperbolic Geometry (UHG) in this 36-minute video lecture. Delve into the algebraic definitions of quadrance between points and spread between lines, the core metrical concepts in UHG. Review the basics of Rational Trigonometry in the Euclidean affine setting before transitioning to the hyperbolic projective framework. Compare the five main laws of Rational Trigonometry with the four primary laws of UHG. Examine exercises covering right triangles and dual laws, and gain insights into the lecturer's perspective on the importance of these mathematical concepts. Suitable for those with a background in geometry and trigonometry looking to expand their understanding of hyperbolic geometry.