Seminar: Some Fundamental Formulas from Metrical Algebraic Geometry

A seminar presented to the School of Mathematics and Statistics, UNSW on June 9, 2015 by N J Wildberger. This talk discusses rather elementary but surprisingly powerful formulas which lie at the base of metrical algebraic geometry. They are presented here in the affine setting, although projective variants also exist and will be discussed at a later talk. We find that one-dimensional metrical formulas connect to the classical theorems of Heron, Brahmagupta and Ptolemy, as well as to the more modern discov