Explore the concept of perpendicularity in universal hyperbolic geometry through this in-depth video lecture. Discover how duality defines perpendicularity, distinguishing it from classical hyperbolic geometry by allowing points to be perpendicular, not just lines. Learn about altitudes and delve into the collinear points theorem and concurrent lines theorem using homogeneous coordinates and determinants. Examine various examples of viewing planes, perpendicular points, and lines to gain a comprehensive understanding of these advanced geometric concepts.
Overview
Syllabus
Introduction
Examples of viewing plane
Point and line duality theorems
Proof of point duality theorem
Perpendicularity
Examples of perpendicular points and lines
Altitudes
Concurrent lines theorem
Collinear points theorem
Taught by
Insights into Mathematics
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