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Duality for Polygons and the Fundamental Theorem of Algebra - Algebraic Topology Lecture 12

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This lecture develops duality between a plane polygon and a cone with respect to the origin and unit circle. It then uses winding numbers of images of concentric circles to give a rational proof of the Fundamental Theorem of Algebra.

Syllabus

Introduction
Recall T=1 turn angle
Problem 14
Duality of Polygons and cones
Cone
Unit circle and a polygon
Dual polygon
Facts; Exercise on Duality
Applications of Winding numbers
Fundamental theorem of Algebra
Rotational Polynomial theorem
Proof of pictures and Winding numbers

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Insights into Mathematics

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