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Jun 15, 2014 at 18:54 comment added Dirk I would phrase the first reason for the usefulness of quadratics as "They imply a notion of positivity".
Jun 15, 2014 at 17:00 history made wiki Post Made Community Wiki by Todd Trimble
Jun 13, 2014 at 10:32 comment added Paul Siegel @GerryMyerson It would indeed have been news to him, but he would probably agree once he realized that $\mathbb{R}^2$ with the standard inner product is a model for the Euclidean axioms. I did not claim (or need to claim) that this is the historical starting point for geometry.
Jun 13, 2014 at 9:44 comment added Gerry Myerson "this is the starting point of nearly all of geometry" --- it would have been news to Euclid that he was equipping a vector space with a quadratic structure.
Jun 13, 2014 at 6:53 history answered Paul Siegel CC BY-SA 3.0