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.

CONTENT SUMMARY: pg 1: @ Metrical notions over rational numbers!; measurements
pg 2: @ Affine geometry/Projective geometry compared
pg 3: @ Preliminary: Rational Trigonometry in Euclidean Geometry; WildTrig series mentioned
pg 4: @13:31 Further development in the Euclidean affine case; Main laws of Rational Trigonometry; 1st and 2nd most important results in mathematics @16:37 ; the most powerful law among the 5 @ ;
pg 5: @ Trigonometry in Universal Hyperbolic Geometry; In principle one could start the series here; the main definitions
pg 6: @25:45 Main laws of Hyperbolic trigonometry; njwildberger opinion @
pg 7: @ exercises 21-1:5
pg 8: @33:19 exercises 21-6:9; right triangle, dual laws; closing motivational remarks @ THANKS to EmptySpaceEnterprise!