Mathematics Points
Axioms of Euclidean Plane Geometry The great advantage of expressing geometry as an axiomatic system was that it no longer was necessary to memorize long lists of independent facts about the nature of the universe--one only had to know a small set of axioms, and by applying to them the rules of inference, one could reconstruct the entire collection of geometric truths. Noncommutative Algebra a great many of thc most familiar algebraic relationships originated from real problems, some of them geometric and some from economics and physical science. Parabolas were familiar as conic sections and as the paths of projectiles, and the simple formula for a parabola could easily be graphed using the techniques of analytic geometry. Volume formulas suggested cubic equations, and they were also easy to graph and analyze. But it was not much harder to use the same techniques to analyze polynomials of degree four or five or higher. Few objected that this was not algebra, even though it no longer