Quadrance and Spread - Universal Hyperbolic Geometry

This course introduces quadrance and spread as algebraic metrical concepts, reviewing rational trigonometry in Euclidean affine geometry before developing their use in the hyperbolic projective setting. It compares the main laws of rational and universal hyperbolic trigonometry and includes exercises.

Syllabus

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!