I have posted a few videos on this page.

The first one is approximately 3 minutes long. It’s called “A Bug Goes off on a Tangent.” It’s about an insect that can’t climb to the top of the white board, but wants to know the distance to the top of the white board. He discovers similar triangles. It was inspired by participation by elementary school students in a local mathematics club. Enjoy!

http://www.youtube.com/watch?v=PSK858OJYt4

This video also has an accompanying blogpost, found here.

Pi is defined as the ratio of the circumference of a circle, to its diameter. It follows (how?) that the same constant pi is also the number of r x r squares that have the same total area as a circle of radius r (and so the area of a circle is given as (pi) multiplied by r^2).

In this 5 minute video, young Squeaky the Square discovers pi in his own uniquely square way! Please enjoy!

The difference of squares formula is accessible to mathematicians at any age an any level. Here is a video inspired by a few sessions of math club for elementary school students.

The difference of squares formula has less elementary applications. This popular post gives uses it to prove the arithmetic-geometric mean inequality. (No extra videos go with that post).

The next video is a hilarious performance by Ján Mináč and Leslie Hallock at the University of Western Ontario. It answers an important question regarding the sum of two algebraic numbers. It also answers questions regarding the relative power of the chalk and the sword!

Can Mathematics save Romeo and Juliet?