## THE spires scoop blog

Inspired by the Mega Menger project, the OSA “Baby Nerds” Club have decided to construct a level 3 Menger sponge out of folded business cards!

But what is a Menger Sponge?

This is a Menger Sponge:

Clear? Maybe jnot.

It was first described by mathematician Karl Menger in 1926. It is a cube, where each side has a hole of exactly one ninth of the surface. Each of those holes has a hole on each surface and the remaining surface is split into eight with a hole one ninth of the surface inside it.

For each iteration of the holes through the middle, the sponge is an additional level. For example, any normal cube is a level 0 Menger sponge, as it has no holes! A level 1 would be made up of 20 level 0 cubes, a level 2 made of 20 level 1 cubes, a level 3 made of 20 level 2 cubes etc. A level 5 Menger sponge is made up of over 3 million level 0s! Wow!

If you had a level infinity Menger Sponge, then it would have infinite surface area, even if it was only a millimetre wide! Cool, right? For a normal cube, it would have to be infinitely large to achieve this!

We, the baby nerds, just adore solving problems like this, and though it’s ambitious, we know we can do it! If you want to help out, come to M7 after school on Wednesday, and find out what we’re all about! (;

Our project will require hours of work sometime in the summer, probably near the anniversary of the domino calculator project that the club attempted last year! We also hope to receive a donation of business cards for the project, we will need over 48000! So if you have any, please donate them to our cause!