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Explore rational curvature, winding, and turning in this 48-minute lecture on Algebraic Topology. Delve into the concept of turn-angle or tangle, a rescaled version of curvature using natural geometric units. Learn how to describe polygons, both convex and non-convex, using this approach. Discover winding numbers and the turning number of planar curves. Examine topics such as angle spread in Rational Trigonometry, turn angles for various polygons, total curvature of convex polygons, and the turning number of smooth curves. This lecture, part of a beginner's course on Algebraic Topology, provides a fresh perspective on fundamental geometric concepts and their applications in topology.
