Pendulums are fascinating mathematical and physical objects.  We use them all the time, though we don't usually realize it.  Early clocks relied on the regularity of pendulums to keep time accurately.  Swings are pendulums.  Did you ever notice that the long rope swings swing farther and slower than the regular swings at the playground?  When I was a kid, we used to throw the swing over the bar to shorten the chains (at the disapproval of our teachers).  We figured out that this made the swing go really fast.

So I've got you thinking about pendulums and what you know about them... I now share with you one of the most beautiful mathematical videos I've ever seen: