The Spread Law in Universal Hyperbolic Geometry - Universal Hyperbolic Geometry

Explore the Spread law in Universal Hyperbolic Geometry in this 24-minute video lecture. Delve into the concept of spread between two lines in hyperbolic geometry, which is dual to the quadrance between two points. Learn about the Spread law, the third of four main laws of trigonometry in universal hyperbolic geometry, and its proof using a remarkable polynomial identity. Review the definition of spread, examine an example relating it to Euclidean geometry, and follow the detailed proof of the Spread law. Discover the consequences of the proof, including the introduction of the quadrea of a triangle. Conclude with exercises to reinforce your understanding of this fundamental concept in hyperbolic geometry.

CONTENT SUMMARY: pg 1: @ ; spread; quadrance spread duality;
pg 2: @ ; example
pg 3: @ ; Spread law hyperbolic version; proof
pg 4: @06:49 ; proof continued; big expression resolution @08:52; observation on how to remember factors @11:41 ; the heart of the proof @ ; formula*;
pg 5: @13:15 ; proof continued; formula***; "And that's a proof of the spread law." @
pg 6: @ ; Harvesting consequences of proof of spread law; quadrea of the triangle introduced
pg 7: @ ; Exercises 27.1-3 THANKS to EmptySpaceEnterprise