Computations with Homogeneous Coordinates - Universal Hyperbolic Geometry
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Overview
Syllabus
CONTENT SUMMARY: Lines and planes through the origin as points and lines on the viewing plane @00:01 A projected line on the viewing plane @05:32 Official definitions: hyperbolic point, hyperbolic line @08:48 examples: plot points, plot lines @14:29 find a line given 2 points @21:55 A graphical illustration: @25:15 page change: solution to prob. on previous page @26:28 Join of two points theorem @28:50 Meet of two lines theorem @31:51 Duality rinciple @34:46 formulas have application to cartesian geometry 37:38 meet of lines app. to cartesian geom. @40:03 hyperbolic Geometry is a computational subject memorize j function @ THANKS to EmptySpaceEnterprise
Introduction
Three dimensional space V³
Definitions projective point and line
Problem 1: Plot points and linesp
Join of two points theorem
Meet of two lines theorem
Duality principle
Application to Cartesian geometry
Taught by
Insights into Mathematics