The path from Euclid's geometry to differential geometry
University of Oregon
May 23, 2011
Refreshments will be served in Bailey 204 at 4:15
I'll review (a version of) Euclid's axioms (postulates) for plane geometry. We'll then discuss the end of the 2000 year search for a proof of the parallel postulate (by discovery of counterexamples in the 19th century). We'll describe these counterexamples explicitly and then introduce the basic idea of differential geometry. We'll end with a description of the Uniformization Theorem (which inspired an eventually successful approach to the Poincare Conjecture). The only prerequisite for this lecture is a basic familiarity with plane geometry. At one or two points, some calculus might also be helpful.
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