# Bridges, Unfolding the Earth, and Juggling

Welcome to this week’s Math Munch – from the Netherlands!

I’m at the Bridges Mathematical Art Conference, which this year is being held in Enschede, a city in the Netherlands. I’ve seen so much beautiful mathematical artwork, met so many wonderful people, and learned so many interesting new things that I can’t wait to start sharing them with you! In the next few weeks, expect many more interviews and links to sites by some of the world’s best mathematical artists.

But first, have a look at some of the artwork from this year’s art gallery at Bridges.

 By Gabriele Meyer By Henry Segerman and Craig Kaplan

Here are three pieces that I really love. The first is a crocheted hyperbolic plane lampshade. I love to crochet hyperbolic planes (and we’ve posted about them before), and I think the stitching and lighting on this one is particularly good. The second is a bunny made out of the word bunny! (Look at it very closely and you’ll see!) It was made by one of my favorite mathematical artists, Henry Segerman. Check back soon for an interview with him!

By Francisco De Comite

This last is a curious sculpture. From afar, it looks like white arcs surrounding a metal ball, but up close you see the reflection of the arcs in the ball – which make a hexagonal flower! I love how this piece took me by surprise and played with the different ways objects look in different dimensions.

Mathematical artists also talk about their work at Bridges, and one of the talks I attended was by Jack van Wijk, a professor from Eindhoven University of Technology in the Netherlands. Jack works with data visualization and often uses a mixture of math and images to solve complicated problems.

One of the problems Jack tackled was the age-old problem of drawing an accurate flat map of the Earth. The Earth, as we all now know, is a sphere – so how do you make a map of it that fits on a rectangular piece of paper that shows accurate sizes and distances and is simple to read?

To do this, Jack makes what he calls a myriahedral projection. First, he draws many, many polygons onto the surface of the Earth – making what he calls a myriahedron, or a polyhedron with a myriad of faces. Then, he decides how to cut the myriahedron up. This can be done in many different ways depending on how he wants the map to look. If he wants the map to be a nice, normal rectangle, maybe he’ll cut many narrow, pointed slits at the North and South Poles to make a map much like one we’re used to. But, maybe he wants a map that groups all the continents together or does the opposite and emphasizes how the oceans are connected…

Jack made a short movie that he submitted to the Bridges gallery. He animates the transformation of the Earth to the map projections beautifully.

Jack’s short movie wasn’t the only great film I saw at Bridges. The usual suspects – Vi Hart and her father, George Hart – also submitted movies. George’s movie is about a math topic that I find particularly fascinating: juggling! The movie stars professional juggler Rod Kimball. Click on the picture below to watch:

This is only the tip of the iceberg that is the gorgeous and interesting artwork I saw at Bridges. Check out the gallery to see more (including artwork by our own Paul and a video by Paul and Justin!), or visit Math Munch again in the coming weeks to learn more about some of the artists.

Bon appetit!

# Folds, GIMPS, and More Billiards

Welcome to this week’s Math Munch!

First up, we’ve often featured mathematical constructions made of origami. (Here are some of those posts.) Origami has a careful and peaceful feel to it—a far cry from, say, the quick reflexes often associated with video games. I mean, can you imagine an origami video game?

One of Fold’s many origami puzzles.

Well, guess what—you don’t have to, because Folds is just that! Folds is the creation of Bryce Summer, a 21-year-old game designer from California. It’s so cool. The goal of each level of its levels is simple: to take a square piece of paper and fold it into a given shape. The catch is that you’re only allowed a limited number of folds, so you have to be creative and plan ahead so that there aren’t any loose ends sticking out. As I’ve noted before, my favorite games often require a combo of visual intuition and careful thinking, and Folds certainly fits the bill. Give it a go!

Once you’re hooked, you can find out more about Bryce and how he came to make Folds in this awesome Q&A. Thanks so much, Bryce!

Next up, did you know that a new largest prime number was discovered less than a month ago? It’s very large—over 17 million digits long! (How many pages would that take to print or write out?) That makes it way larger than the previous record holder, which was “only” about 13 million digits long. Here is an article published on the GIMPS website about the new prime number and about the GIMPS project in general.

What’s GIMPS you ask? GIMPS—the Great Internet Mersenne Primes Search—is an example of what’s called “distributed computing”. Testing whether a number is prime is a simple task that any computer can do, but to check many or large numbers can take a lot of computing time. Even a supercomputer would be overwhelmed by the task all on its own, and that’s if you could even get dedicated time on it. Distributed computing is the idea that a lot of processing can be accomplished by having a lot of computers each do a small amount of work. You can even sign up to help with the project on your own computer. What other tasks might distributed computing be useful for? Searching for aliens, perhaps?

GIMPS searches only for a special kind of prime called Mersenne primes. These primes are one less than a power of two. For instance, 7 is a Mersenne prime, because it’s one less that 8, which is the third power of 2. For more on Mersenne primes, check out this video by Numberphile.

Finally, we’ve previously shared some resources about the math of billiards on Math Munch. Below you’ll find another take on bouncing paths as Michael Moschen combines the math of billiards with the art of juggling.

So lovely. For more on this theme, here’s a second video to check out.

Bon appetit!

# Mike Naylor, Math Magic, and Mazes

Mathematical artist, Mike Naylor juggling 5 balls.

Welcome to this week’s Math Munch!

Last week, Justin told you about our time at Bridges 2012, the world’s largest conference of mathematics and art, and I must reiterate: this was one of the coolest things I’ve ever been a part of. The art was gorgeous. The people were great. I’m pretty sure I was beaming with excitement. At dinner we met, Mike Naylor, a mathematical artist and generally fantastic guy living in Norway. You can read his full artist’s statement and artwork from the Bridges exhibition, but here’s an excerpt:

“Much of my artwork focuses on the use of the human body to represent geometric concepts, but I also enjoy creating abstract works that capture mathematical ideas in ways that are pleasing, surprising and invite further reflection.”

Meeting Mike was especially exciting for me, because just days earlier, I’d fallen in love with Mike’s math blog. This week, I’ll be sharing some of the gems I’ve found there:

I didn’t even mention abacaba.org, yet another amazing Mike Naylor project.  It’s a site devoted entirely to one pattern: A, aBa, abaCaba, abacabaDabacaba,…

Since Justin introduced mathematical poetry last week, check out one of Mike’s mathematical poems called “Decision Tree.” What a clever idea! Like Mike, I’m a juggler, so I absolutely loved his Fractal Juggler animation, which shows a juggler juggling jugglers juggling jugglers… Clever idea #2! And for a third clever idea, check out the Knight Maze he designed. Wow!

 “Decision Tree” “Fractal Juggler” “Knight Maze”

The most squares of whole area that will fit in a square of area 17.

Speaking of mazes, I found a whole bunch of cool ones when I was poking around the Math Magic site hosted by Stetson University. Each month Math Magic poses a math question for readers to work on and then submit their solutions. This month’s question is about packing squares in squares. (Click to see the submissions so far.)  At the bottom of the page you can find links to many more cool math sites, but as promised, I’ll share some of the mazes I found.

A puzzle designer for over 40 years, here Andrea Gilbert lays across one of her step-over sequence mazes.

First there’s Andrea Gilbert’s site, Click Mazes, which has all sorts of online mazes and puzzles.  In the picture you can see Andrea laying in one of her step-over sequence mazes.  How do you figure they work?

Then there’s Logic Mazes, a website of mazes by Robert Abbott. I don’t know much about Robert, but his site caught my eye because it begins with Five Easy Mazes: 1 2 3 4 5, but there are better mazes after that. I really liked the number mazes. Play around, think your way through, and have some fun!

Bon appetit!

 Number Mazes Eyeball Mazes Alice Mazes