As most geeks know, playing with Lego is superb training in math and geometry. Indeed, many schools now explicity offer “Lego and math” classes. When you have to calculate the number and type of bricks necessary to make a weird shape, or when you try to create a curve out of square bricks, you quickly run into concepts like fractions, exponents, and squares, cubes and roots. When I first learned about the idea of logarithmic scale, it made immediate sense — because I’d once had the same idea while plotting out brick space on a big flat Lego pad.

Now, Andrew Lipson … this guy’s nuts. Though I mean that in a good way. He essentially performs Xtreme math using Lego bricks: He’s devoted the last few years to developing Lego models of famous geometric shapes, including the Moebius strip (pictured above), the Moebius-like “Klein Bottle”, and the incredibly weird, single-surfaced Bour’s surface. Want to build them yourself? Here’s how Lipson did it:

OK, I admit it — these weren’t constructed entirely without computer assistance. Usually I write some C code to generate whatever the shape is and figure out which cells in a grid made up of 1x1x1 LEGO bricks should be filled in. The code outputs this as an LDraw .DAT file, separated into construction steps adding one complete layer of the structure in each step. Then I use MLCad to view the .DAT file. I play around with the parameters and repeat until I have something that looks nice and which will probably be able to balance.