AlgTop12: Duality for polygons and the Fundamental Theorem of Algebra

We define the dual of a polygon in the plane with respect to a fixed origin and unit circle. This duality is related to the notion of the dual of a cone.

Then we give a purely rational formulation of the Fundamental Theorem of Algebra, and a proof which keeps track of the winding number of the image of concentric circles about the origin. This is an argument every undergraduate math student ought to know!

This is the 12th lecture in this beginner's course in Algebraic Topology, given by Assoc Prof N J Wildberger at UNSW.