Tag Archives: mazes

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

Pennies, Knights, and Origami Mazes

Welcome to this week’s Math Munch!

How many pennies do you think this is? Click to find out.

Big numbers are sometimes hard to get a feel for.  A billion is a lot, but so is a million.  The MegaPenny Project is a cool attempt at making the difference between large numbers easier to grasp.  Would 1,000,000 pennies fill a football field or would you need a billion pennies for that?  MegaPenny can help you figure it out.

The first kixote puzzle

Next up, we have kixote, a puzzle in the spirit of Sudoku and Ken-Ken, but involving knight’s moves.  Dan Mackinnon–its creator–has a blog called mathrecreation that he says, “helps me go a little further in my mathematical recreations, helps me understand things better, and sometimes connects me to other people who share similar interests. I hope that it might encourage you to play with math too.”  I’m sure we’ll be linking to more of Dan’s posts in the future!

Finally, since the mazes and paper-folding were so popular last week, we thought that this week we would share some paper-folding mazes! Here is a clip of MIT professor Erik Demaine talking about how he has created origami mazes, preceded by a discussion of origami robots that fold themselves!  The clip is a part of a lecture about origami that Erik gave last spring in New York City for the Math Encounters series put on by the Museum of Mathematics.  You can watch Erik’s entire origami lecture from the beginning by clicking here.

frame from lecture video

Eric Demaine with a sheet of origami cubes

You can also check out Erik’s Maze Folder applet–but if you try it out, take his warning and start with a small maze!

Bon appetit!

Mazes, Spirals, and Paper Folding

Welcome to Math Munch!   Here you will find links to lots of cool mathy things on the internet.  We’ll post some new items each week for you to enjoy.  We hope you are as inspired and excited by these creations as we are!

Maze A Day is a blog where Warren Stokes publishes new mazes he has created.  Every day!  What a cool project.

A number spiral

Here’s another maze that was submitted by truff.

Number Spiral is a website that shares some cool number spirals and some deep patterns that have been found in prime numbers.  I like how the author Robert Stacks both gives a very simple introduction to his work and carries it through to very complex mathematics.

Finally, here is a short video about the work of paper engineer Matt Shlian at the University of Michigan.  A favorite quote: ” I think there’s this great crossover right now between science and art that the art students don’t know anything about and the scientists don’t know that artists are out there that exist that can help them figure out some of these things.”

Bon Appetit!

Paper Cuts from Michigan Daily on Vimeo.