Geometry With a General Dot Product - WildTrig: Intro to Rational Trigonometry - N J Wildberger

Explore the extension of metrical geometry beyond chromogeometry using rational trigonometry in this 23-minute video lecture. Learn about general dot products defined by arbitrary invertible symmetric 2x2 matrices and their corresponding notions of quadrance, perpendicularity, and spread. Examine a specific case where the unit circle appears as an ellipse in the usual view, demonstrating the power and versatility of this approach. Discover how this generalized perspective has significant applications in classical triangle geometry, providing a fresh and insightful look at fundamental geometric concepts.

Introduction
Bilinear quadratic form
Linear quadratic form
Spread between vectors
Examples