A neat post on twitter today by Evelyn Lamb got me thinking about simple topology:

One of the people replying to her post pointed out the amazingly neat video here:

http://aperiodical.com/2012/05/torus/

These posts got me thinking about the fun square diagrams you can make for a torus, the Klein bottle, and the projective plane. I decided to play around with some of those ideas with my kids tonight and it turned out to be super fun. It is so great to have the chance to introduce them to math that isn’t usually part of the pre-college curriculum. Here’s what we did:

Since we were reminded of Vi Hart’s amazing “Wind and Mr. Ug” video in the middle of our video, here a quick link to it:

This video was actually the first Vi Hart video that I ever saw. It is one of the most amazing pieces of math for the masses that I’ve ever seen. Actually, I thought she deserved a MacArthur “Genius” grant after seeing it. Even today it is mesmerizing.

There are also a couple of other fun videos on youtube that give a little insight into the Klein bottle and projective plane. Riding a bike around a Klein bottle –

and neat visualization of the projective plane:

Though this wasn’t the field of math that I studied, I’ve always found it to be amazing. It has a particularly fond memories for me because of one of my former students, Ali Gilmore. She came to the University of Minnesota when she was in high school for a special math program. She wasn’t all that interested in the multi-variable calculus we were studying so I gave her a copy of Massey’s Algebraic Topology to read. She was hooked, and many years later is a post Doc at UCLA focusing on low dimensional topology and knot theory.