Explore fundamental formulas in metrical algebraic geometry through this 50-minute seminar presented by N J Wildberger at the School of Mathematics and Statistics, UNSW. Delve into elementary yet powerful formulas in the affine setting, connecting to classical theorems by Heron, Brahmagupta, and Ptolemy, as well as David Robbins' modern discovery on cyclic pentagon areas. Gain insights into these results within a general framework, applicable across various fields and quadratic forms. Cover topics including the affine one-dimensional case, quadratic equations, cyclic quadrilaterals, algebraic geometry, Brahma Gupta's formula, and David Robbins' formula.