Brahmagupta's Formula and the Quadruple Quad Formula - Rational Geometry Math Foundations

Explore the connections between Brahmagupta's formula and the Quadruple Quad Formula in this 41-minute mathematics lecture. Delve into the classical area formula for cyclic quadrilaterals and its relationship with a one-dimensional result. Review Heron's formula and the Triple Quad Formula, leading to Archimedes' theorem. Examine Robbins' modern insights on non-convex cyclic quadrilateral areas and their link to the Quadruple Quad Formula's factorization. Work through practical examples demonstrating the superiority of rational number precision over real number approximations. Conclude with an exercise that unveils an overarching theorem encompassing both Brahmagupta's and Robbins' formulas, offering a rich learning experience in advanced geometry and algebraic manipulation.

Introduction
Quadruple Quad Function
Relation between Brahmagupta's formula and Quadruple Quad Formula
Brahmagupta's identity
Practicing Algebra
Factoring using a computer algebra package
Areas of Polygons
Oriented Quadrilateral
Unoriented Quadrilateral