In the heyday of analog computing, Vladimir Lukyanov designed an advanced computer that used water as the storage media. Various tubes, tanks, valves, pumps and sluices churned out solutions for the user based on variables such as changing tax rates or increasing money supply. From the Russian magazine Science and Life:
Our favorite mathemagician, Vi Hart, jams on Fibonacci.
A pentomino is like a domino, but with five connected squares instead of two. A set of all twelve can easily be cut from scraps of plywood.
There are many ways to calculate an approximation to pi, but rarely is math as delicious as in this idea from Davidson College professor Tim Chartier. Make a quarter circle in a square of graph paper and place chocolate chips on the squares that lie inside the circle. If you now count the chips and compute four times the number of chocolate chips divided by the total number of squares, that will be approximately pi.
If you are looking for a subject likely to inflame the hearts of mathematicians, make them slightly weak in the knees, and induce some distinctly poetical sentiments, Klein’s Quartic, first described by German mathematician Felix Klein in 1878, seems like a pretty good bet. Though the surface itself, per Wikipedia, “does not have a (non-trivial) 3-dimensional linear representation,” several prominent math-bloggers have produced models, projections, and plain-language written explanations attempting – and doing a pretty good job of it, IMHO – to communicate their passion for the construct…
In this vid, “mathemusician” Vi Hart and Sal Khan (of the amazing Khanacademy) discuss the difference between linear and logarithmic scales and human perception. I like their joking idea of a liner scaled piano where the keys would get fatter and fatter as you moved up the scale.
The diameters of US quarters and pennies are very close to the ratio needed to make a truncated icosahedron, i.e., a soccer ball in the US or a football elsewhere. Copper pennies take the place of the usually black pentagons and quarters take the place of the usually white hexagons, so even the colors work out.
