Some Nifty Things

Here are some of my small discoveries and observations and demonstrations:

Inverted Pendulum

Riemann Mapping Theorem by Steepest Descent:

Gauss-Bonnet Theorem via a bike wheel: gauss-bonnet.bicycle.pdf

Theorem of cosines via energy conservation.

A puzzler: why does this nut spin?

A Puzzle of Floating Cork.

minperimeter.pdf

Minimal perimeter triangles:

Dot Product via energy conservation.