# Circles, Geomagic, and Marble Calculators

Welcome to this week’s Math Munch!

We gave you a taste of some of Vi Hart’s math art last week with her balloon creations.  This week, we’re featuring some of Vi’s doodling in math class art – her Apollonian gaskets!  An Apollonian gasket is a fractal made by drawing a big circle, drawing two or three (or more!) smaller circles inside of it so that they fit snugly, and then filling all of the left-over empty space with smaller and smaller circles.  Here’s the video in which Vi tells how she draws Apollonian gaskets with circles and other shapes (and how she makes other awesome things like an infinitely long caravan of camels fading into the distance).  And here are some more Apollonian gaskets made by filling other shapes with circles from Math Freeze.

Next, you may have seen a magic square before, a number puzzle in which you fill a square grid with numbers so that each row, column, and diagonal have the same sum.  (Play with one here.)  But have you ever seen a geomagic square?

Magic squares have been around for thousands of years, but in 2001, Lee Sallows started thinking about them in a new way.  Lee realized that you could think of the numbers in the square as sticks of particular lengths, and the number being added to as an amount of space you were trying to fill with those sticks.  That led him to try to make magic squares out of things like pentominoes and other polyominoes, butterflies,  and many other shapes!  Aren’t they beautiful?

Finally, what do marbles, binary, and wooden levers have in common?  Mathematical artist, designer, and wood-worker Matthias Wandel built a binary adding machine that uses marbles and wooden gates!  Here’s a video demonstrating how it works:

Matthias doesn’t only build calculators.  Here’s a marble elevator and a machine that you can take apart and reassemble to make a new track.

Bon Appetit!

### 11 responses »

1. That was a very intriguing machine to watch and like whenever he added something at the end it was showed the sum.I think Mathhias Wendal did an awesome job building it and it functioned perfectly. I think it was awesome that you guys put something like this on math munch because me and my brother have a lot of marbles and sometimes us pipes or tubes to make a marble machine,and i never thought you could use a marble contraption for math. It was a very creative video and also creative machine and thank you guys and you guys keep on inspiring me. 🙂

2. I love how this machine works, it is very simple mechanics with a some math intertwined in it. I enjoyed watching this machine work when he put in all of the marbles at the same time. He must have spent quite some time in building this machine. I wonder what goes on behind this machine when Matthias puts some marbles into the machine.

3. Would this math machine still work if you used different number beside 1,2,4,8,16,32?
What numbers would you have used instead?

4. Wow, apollonian gaskets look awesome, but seem like they’d take a long time to do because somewhere along the line you have to draw very, very small shapes. What makes an apollonian gasket a fractal, and what exactly is a fractal? Are triangles and circles the best shape to use when drawing apollonian gaskets?

5. Wow! That marble machine was very interesting! Since it runs in binary, how would it handle numbers larger than 256/512? Would it be able to handle such numbers? These are the usual numbers that are converted to decimal, would you need a larger adding machine? This machine, from the video’s perspective, recreates the system in which a computer adds numbers. How neat!

• Hi, Jacob! I imagine you would need a larger machine to add beyond 256. I also love how this recreates more complicated computing. It’s always amazing to me to see “low-tech” versions of the crazy machines that make up our most complicated technology. Thanks for the comment!

6. That’s so cool that you can make an adding calculator with marbles i never knew that it was so simple to make, would you know how you would you be able to make a bigger version to calculate larger numbers?