"The Chord Theorem" as presented by our very own Will Kazez

The Chord Theorem is an elementary, fairly bizarre fact about subsets
of the plane. I will give an elementary, fairly bizarre proof of this
theorem, and then show how it can be applied to stalking*. It can be
used to give a completely useless characterization of the positive
integers. I will also discuss its implications for curves on a torus
which never cross themselves. The talk will be elementary and won't
assume any mathematics beyond pre-calculus.

*Stalking. The object of your attention starts at the math department
and walks along a circuitous route to a point 1000 ft due north* of
us. You follow along while maintaining a constant distance and
staying exactly south of the person being followed. The question is,
must your path cross the first person's path? Does the answer depend
on their path, your distance, or what?

*A point 1000 ft due north. That would be a point on the bridge
leading towards the bookstore.