Affine One-Dimensional Geometry and the Triple Quad Formula - Math Foundations 123

Explore the fundamental concepts of affine one-dimensional geometry and discover the Triple Quad Formula in this 27-minute video lecture. Delve into the second most important theorem in mathematics, examining how to measure the separation between two points and the relationship between three collinear points. Learn about measuring in affine geometry, the symmetry of distance, and the derivation of the Triple Quad Formula. Engage with an interactive segment where you're encouraged to deduce the formula independently before it's revealed. Follow along as the lecturer provides examples and a proof of this crucial mathematical concept, gaining valuable insights into rational geometry and its foundations.

In this video, at a certain point I invite you to discover this crucial formula for yourself. It is highly recommended, especially if you are a serious student of mathematics, that you spend an hour or so to deduce the required result before I tell you what it is. This occurs around of the video.
Intro to the Triple Quad Formula
Measuring in affine geometry
Distance is symmetric
Measuring in affine geometry
Triple Quad Formula
Example of Triple Quad Formula
Proof of Triple Quad Formula