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.