First Steps in Hyperbolic Geometry - Universal Hyperbolic Geometry

This course introduces universal hyperbolic geometry as a projective study of a circle. It develops perpendicularity through duality and defines quadrance and spread before presenting Pythagorean, triple, spread, and cross laws.

Syllabus

CONTENT SUMMARY: notion of perpendicularity @04:48 Perpendicularity via duality @05:33 Do the altitudes of a triangle meet in a point? @10:54 Quadrance: m'ment between points @15:14 exercise @18:41 remark on Beltrami-Klein model @19:11 Pythagoras' theorem and Triple quad formula @20:30 Spread: m'ment between lines and quadrance spread duality theorem @23:29 Remark on Beltrami-Klein model @26:45 Pythagoras' dual theorem @28:43 Main formulas for triangles that involve both quadrances and preads @ THANKS to EmptySpaceEnterprise
Introduction
Perpendicularity via duality
Quadrance: measurement between points
Quadrance: measurement between lines
remark on Beltrami-Klein model
Spread: measurement between lines
Pythagoras' dual theorem
Spread law