Rational Curvature, Winding, and Turning in Algebraic Topology - Lecture 11

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.

Introduction
AngleSpread Rational Trigonometry- Overview
Q. How to describe the amount of turning?
Turn of the basics unit
Turn angles
Quadrilateral Turn angles
n-gon computation
Convex polygon
General n-gon
Alternate approach of the T angle
Total curvature of Convex Polygon
Winding numbers of a curve
The turning on different points of the curve
Turning number of a smooth curve