Mathematics Colloquia and Seminars

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For a general closed curve in R^3, the total curvature is bounded below by 2 pi with equality for convex planar curves. I will present a theorem of Milnor and Fary showing that if the curve is knotted the bound on total curvature can be increased to 4 pi. Milnor's method gives a sharp lower bound within any fixed isotopy class of knot. Everything here is elementary. No prerequisites.