Also, you can fit just about anything to two points.

Hey, that's an interesting question: is there anything you can't fit to two arbitrary points?

Seems like with compression, x/y offsets, and rotation you could fit just about curve.

In general on the plane, you can fit a polynomial of n-1 degree exactly to n distinct points (i.e. it will pass through those points)

This least to an easy way to demonstrate the evils of over-fitting :)

And there is exactly 1 polynomial of degree n-1 that will match n points ;)

It's true! I somehow missed a "unique" there, too late to edit.

A single point