Why, build a level three Menger Sponge, of course! What the heck is a Menger Sponge? Glad you asked. It's a three-dimensional fractcal cube of sorts, first described by Austrian mathematician Karl Menger in 1926. When, some seventy years later, Dr. Jeannine Mosely found herself confronted with a gargantuan pile of business cards, rendered useless after the company she worked for changed addresses, she knew what she had to do with them: hand-make a real, live Menger Sponge -- creating an actual object from something that had previously been merely a mathematical abstraction -- a (sorta nerdy) feat of Guinness Book proportions. Before we show you how she made one in reality, a quickie guide to making them in the abstract:
1. Begin with a cube.
2. Divide every face of the cube into 9 squares. This will sub-divide the cube into 27 smaller cubes, like a Rubik's Cube
3. Remove the cube at the middle of every face, and remove the cube in the center, leaving 20 cubes (second image). This is a Level 1 Menger sponge.
4. Repeat steps 1-3 for each of the remaining smaller cubes.
66,048 business cards, 8,000 business card cubes (Menger subunits) and 150 pounds of cube later, it was finished. Figuring the whole project required about 600 hours to build, she recruited volunteers from around the country to build parts of it and then ship them to her. Construction photos after the jump!
First, you've got to make a cube from six business cards -- without staples, tape or glue -- which Dr. Mosely describes how to do:
To make a cube out of six business cards, first take two cards and place them across each other at right angles, centering them as nearly as possible. Fold the flaps of the bottom card down over the top card. Turn them over and repeat. Pull the two cards apart. Six of them can be assembled as shown below to make a cube. All flaps must be on the outside of the finished cube.
For a super-detailed (and kinda math-y) description of how Mosely accomplished the rest of her fractal feat, check out this page at the aptly-named Institute for Figuring. Meanwhile, we'll skip right to the pictures:
Photo by Ravi Ap