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

Explore fundamental concepts of Cartesian geometry in this 36-minute video lecture from the Universal Hyperbolic Geometry series. Delve into the basics of points, lines, and the unit circle using Cartesian coordinates. Learn key theorems including the line through two points, collinear points, and concurrent lines. Discover the rational parametrization of the circle and examine how lines intersect with circles. Gain insights into applying Cartesian coordinates to both Euclidean and hyperbolic geometry. Follow along with detailed explanations, proofs, and practical examples to strengthen your understanding of these essential geometric principles.

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