Quadrance and spread | Universal Hyperbolic Geometry 21 | NJ Wildberger

This is the first video in the second part of this series on Universal Hyperbolic Geometry (UHG), introducing algebraic definitions of the main metrical concepts: quadrance between points and spread between lines. We first review the basics of Rational Trigonometry (RT) in the Euclidean affine setting, motivating the move to the hyperbolic projective setting. The five main laws of RT are laid out and compared with the four main laws of UHG.

Video Contents:
00:00 Metrical notions (over rational numbers!); measurements
03:40 Affine geometry/Projective geometry compared
07:50 Preliminary: Rational Trigonometry in Euclidean Geometry; WildTrig series mentioned
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 @18:30
20:02 Trigonometry in Universal Hyperbolic Geometry; In principle one could start the series here; the main definitions
25:45 Main laws of Hyperbolic trigonometry; njwildberger opinion @30:08
31:53 Exercises 21-(1:5)
33:19 Exercises 21-(6:9); right triangle, dual laws; closing motivational remarks @34:28 (THANKS to EmptySpaceEnterprise!)

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