Explore Brahmagupta's formula for cyclic quadrilateral areas and the Quadruple Quad Formula in this 41-minute mathematics lecture. Delve into the rational variant of Brahmagupta's formula, independent of real numbers and square roots. Examine the situation of four affine 1-points and discover the analog of the Triple Quad Formula. Investigate important manipulations for pairs of quadratic equations. Practice advanced algebraic skills through detailed proofs and formulas. Learn about Archimedes' function, quad triples, and the mysterious Quadruple Quad Formula. Gain valuable insights for teaching and understanding college-level mathematics, with a focus on foundational concepts in geometry and algebra.