The Circle and Cartesian Coordinates in Universal Hyperbolic Geometry - Lecture 5

This introduction uses rational Cartesian coordinates to describe points, lines, and the unit circle. It develops theorems for joining points, testing collinearity and concurrency, parameterizing the circle, and finding line-circle intersections.

Syllabus

CONTENT SUMMARY: Line through two points theorem @04:31 Collinear points theorem @6:56 Determinants @08:09 Number system we will use @11:28 Concurrent lines theorem @15:10 Affinely parallel lines and Point on two lines theorem @16:42 Parameterization of unit circle theorem @19:33 experience with parameterization of unit circle @24:23 Meets of line and circle theorem @ THANKS to EmptySpaceEnterprise
Introduction
Line through two points theorem
Determinants
Concurrent lines theorem
Parametrization of unit circle theorem
Meets of line and circle theorem