### UnivHypGeom27: The Spread law in Universal Hyperbolic Geometry

The spread between two lines in hyperbolic geometry is exactly dual to the notion of the quadrance between two points. The Spread law is the third of the four main laws of trigonometry in universal hyperbolic geometry. Its proof also relies on a remarkable polynomial identity, just as did the proofs of Pythagoras' theorem and the Triple quad formula. In this video we review the definition of spread, give an example relating it to the spread between lines in Euclidean geometry, and give a proof.CONTENT SUMMARY: pg 1: @00:11 ; spread; quadrance spread duality;pg 2: @03:04 ; examplepg 3: @04:36 ; Spread law (hyperbolic version); proofpg 4: @06:49 ; proof continued; big expression resolution @08:52; observation on how to remember factors @11:41 ; the heart of the proof @12:49 ;? formula(*);pg 5: @13:15 ; proof continued; formula(***); "And that's a proof of the spread law." @17:05pg 6: @17:29 ; Harvesting consequences of proof of spread law; quadrea of the triangle introducedpg 7: @22:33 ; Exercises 27.1-3 (THANKS to EmptySpaceEnterprise)

Length:
24:21