The Triple Spread Formula, Circumcircles and Curvature - Rational Geometry Math Foundations

Explore the projective Triple quad formula, also known as the Triple spread formula in Rational Trigonometry, and its relationship to curvature in this 24-minute mathematics lecture. Delve into the concept of a triangle's circumcircle and learn how to determine its size using the three side quadrances. Discover the connection between the fundamental Triple quad formula and its projective version. Examine the definition of quadratic curvature as the reciprocal of circumquadrance. Investigate the relationship between projective 1-points and the core circle to understand how the projective triple quad formula links one-dimensional and two-dimensional geometries. Topics covered include the core circle, dilation factors, circumquadrance calculations, and circle quadratic curvature.

Introduction
The Core Circle
Dilation by factor d
What dilation by factor d does to a core circle
Circumquadrance and diameter of quadrance
Calculating a circumquadrance
Curvature
Circle quadratic curvature