Monthly Archives: October 2014

Scary-o-graphic Projection, Thinky the Dragon, and Martin Gardner

Welcome to this week’s Math Munch!

Halloween is quickly approaching, which is why last week, Anna shared some pumpkin polyhedra. It just so happens that Justin did some pumpkin-y math of his own last year. He created a must-watch video called “Scary-o’-graphic Projection,” which was shown in the 2014 Bridges Short Film Festival. Enjoy, but don’t get too scared.

A stereographic projection sculpture by Henry Segerman.

A stereographic projection sculpture by Henry Segerman.

To learn some more about stereographic projection, watch one of Henry Segerman’s videos. You’ll also get to see some of his 3D printed sculptures.  (1 2)

In other news, Oct. 21 marked the 100th anniversary of the birthday of Martin Gardner!! (previously featured here, here, and here, among others) Around this time every year people get together to do math in his honor as part of Celebration of Mind.

This year we’re featuring one of Gardner’s optical illusions. Let’s begin with a video. Meet Thinky the Dragon.

You can find printable make-your-own templates here. (There are other colors as well.) Thinky is an example of a “hollow face” illusion, many more of which can be found on mathaware.org. There you can also find this video explaining the geometry behind this illusion.

And look at this AMAZING movie trailer that one of our readers made.  Thank you Lily!!!

Can you fold this strip of 7 squares into a cube?

Can you fold this strip of 7 squares into a cube?

Whats special about this square?  More than you think!

Whats special about this square? More than you think!

Thank you to Colm Mulcahy for his recent post on the BBC website, where Colm put together a list of 10 really wonderful problems from the hundreds that Gardner wrote about and popularized during his career. Gardner helped show the world that thinking about problems and mathematics was a really fun way to spend time. Watch the video below to learn more about Celebration of Mind events, and click here to see if there’s an event near you.  Note: You can even host an event of your own.

BONUS: I just have to mention MoSAIC for any math art enthusiasts in our audience. Around the country, small mathematical art conferences and exhibitions will go on this year. Click to learn more or find an event near you.

Munch in honor of Martin Gardner. Bon appetit!

Picture from the MoSAIC website.

Picture from the MoSAIC website.

Weights, Crazy Geometry Game, and Pumpkin Polyhedra

Welcome to this week’s Math Munch!

Weighing puzzleHere’s a puzzle for you: You have 12 weights, 11 of which weigh the same amount and 1 of which is different. Luckily you also have a balance, but you’re only allowed to use it three times. Can you figure out which weight is the different weight?

You certainly can! I won’t tell you how, but you can figure it out for yourself while playing this interactive weight game. This puzzle is tricky, but definitely fun. If one weight puzzle isn’t enough for you, you’re in luck– there are many, many variations! Check out this site to try a similar puzzle with nine weights, ten weights, and 27 weights.

Circle two pack

My solution to the Circle Pack 2 challenge. Can you do it in only 5 moves?

Next up, if you like drawing challenges, this is the game for you. Check out this crazy geometry game, in which you have to draw different shapes (like perfect equilateral triangles, squares, pentagons, and groups of circles of particular sizes) using only circles and straight lines! Here’s my solution to one of the challenges, the Circle Pack 2. See the two smaller circles inside of the larger middle circle? That’s what I wanted to draw– but I had to make all of those other circles and lines to get there! I did the Circle Pack 2 challenge in 8 moves, but apparently there’s a way to do it in only 5…

Truncated icosahedron pumpkinFinally, it’s pumpkin season again! Every year I scour the internet for new math-y ways to carve pumpkins. We’re all in luck this year– because I found great instructions for how to carve pumpkin polyhedra from Math Craft!  Check out this site to learn how to carve all the basics– tetrahedra, cubes, octahedra, dodecahedra, and (my favorite) icosahedra– and a bonus polyhedron, the truncated icosahedron (also know as the soccer ball).

Pumpkin polyhedra

Pumpkin Platonic polyhedra!

 

Don’t forget to make pi with the leftover pumpkin! Oh, and, bon appetit!

 

 

Spheres, Gears, and Souvenirs

92GearSphere-20-24-16Welcome to this week’s Math Munch!

Whoa. What is that?

Is that even possible?

This gear sphere and many others are the creations of Paul Nylander. There are 92 gears in this gear sphere. Can you figure out how many there are of each color? Do you notice any familiar shapes in the gears’ layout?

What’s especially neat are the sizes of the gears—how many teeth each gear color has. You can see the ratios in the upper left corner. Paul describes some of the steps he took to find gears sizes that would work together. He wrote a computer program to do some searching. Then he did some precise calculating and some trial and error. And finally he made some choices about which possibilities he liked best. Sounds like doing math to me!

Along the way Paul figured out that the blue gears must have a number of teeth that is a multiple of five, while the yellow ones must have a multiple of three. I think that makes sense, looking at the number of red gears around each one. So much swirly symmetry!

Spiral shadows!

Spiral shadows!

Be sure to check out some of Paul’s other math art while you’re on his site. Plus, you can read about a related gear sphere in this post by mathematician John Baez.

I figured there had to be a good math game that involves gears. I didn’t find quite what I expected, but I did find something I like. It’s a game that’s called—surprise, surprise—Gears! It isn’t an online game, but it’s easy to download.

Can you find the moves to make all the gears point downwards?

Can you find the moves to make all the gears point downwards?

This Wuzzit is in trouble!

Wuzzit Trouble!

And if you’re in the mood for some more gear gaming and you have access to a tablet or smartphone, you should check out Wuzzit Trouble. It’s another free download game, brought to you by “The Math Guy” Keith Devlin. Keith discusses the math ideas behind Wuzzit Trouble in this article on his blog and in this video.

Poster2

Last up this week, I’d like to share with you some souvenirs. If you went on a math vacation or a math tour, where would you go? One of the great things about math is that you can do it anywhere at all. Still, there are some mathy places in the world that would be especially neat to visit. And I don’t mean a place like the Hilbert Hotel (previously)—although you can get a t-shirt or coffee mug from there if you’d like! The mathematician David Hilbert actually spent much of his career in Göttingen, a town and university in Germany. It’s a place I’d love to visit one day. Carl Gauss lived in Göttingen, and so did Felix Klein and Emmy Noether—and lots more, too. A real math destination!

Lots of math has been inspired by or associated with particular places around the world. Just check out this fascinating list on Wikipedia.

Arctic Circle Theorem

The Arctic Circle Theorem

The Warsaw Circle

The Warsaw Circle

Cairo Pentagonal Tiling

The Cairo Pentagonal Tiling

Did you know that our word souvenir comes from the French word for “memory”? One thing that I like about math is that I don’t have to memorize very much—I can just work things out! But every once in a while, there is something totally arbitrary that I just have to remember. Here’s one memory-helper that has stuck with me for a long time.

May you, like our alligator friend, find some good math to munch on. Bon appetit!