First Steps in Hyperbolic Geometry - Universal Hyperbolic Geometry

Explore the fundamental concepts of universal hyperbolic geometry in this 37-minute video lecture. Delve into the projective study of a circle and relativistic geometry, focusing on key topics such as perpendicularity, duality, and the pole-polar correspondence. Learn about the orthocenter of a triangle and discover how quadrance and spread measurements arise from cross ratios. Examine essential formulas including Pythagoras' theorem, Triple quad formula, Pythagoras' dual theorem, Triple spread formula, Spread law, and Cross law. Compare these concepts to their counterparts in Rational Trigonometry and gain insights into the Beltrami-Klein model. Through a structured presentation, grasp the foundations of this geometric framework and its applications in mathematical analysis.

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