Tag Archives: infinity

The Museum of Math, Shapes That Roll, and Mime-matics

Welcome to this week’s Math Munch!  We have so many exciting things to share with you this week – so let’s get started!

Something very exciting to math lovers all over the world happened on Saturday.  The Museum of Mathematics opened its doors to the public!

MoMath entranceThe Museum of Mathematics (affectionately called MoMath – and that’s certainly what you’ll get if you go there) is in the Math Munch team’s hometown, New York City.

human treeThere are so many awesome exhibits that I hardly know where to start.  But if you go, be sure to check out one of my favorite exhibits, Twist ‘n Roll.  In this exhibit, you roll some very interestingly shaped objects along a slanted table – and investigate the twisty paths that they take.  And you can’t leave without seeing the Human Tree, where you turn yourself into a fractal tree.

coaster rollersOr going for a ride on Coaster Rollers, one of the most surprising exhibits of all.  In this exhibit, you ride in a cart over a track covered with shapes that MoMath calls “acorns.”  The “acorns” aren’t spheres – and yet your ride over them is completely smooth!  That’s because these acorns, like spheres, are surfaces of constant width.  That means that if you pick two points on opposite ends of the acorn – with “opposite” meaning points that you could hold between your hands while your hands are parallel to each other – the distance between those points is the same regardless of the points you choose.  See some surfaces of constant width in action in this video:

Rouleaux_triangle_AnimationOne such surface of constant width is the shape swept out by rotating a shape called a Reuleaux triangle about one of its axes of symmetry.  Much as an acorn is similar to a sphere, a Reuleaux triangle is similar to a circle.  It has constant diameter, and therefore rolls nicely inside of a square.  The cart that you ride in on Coaster Rollers has the shape of a Reuleaux triangle – so you can spin around as you coast over the rollers!

Maybe you don’t live in New York, so you won’t be able to visit the museum anytime soon.  Or maybe you want a little sneak-peek of what you’ll see when you get there.  In any case, watch this video made by mathematician, artist, and video-maker George Hart on his first visit to the museum.  George also worked on planning and designing the exhibits in the museum.

We got the chance to interview Emily Vanderpol, the Outreach Exhibits coordinator for MoMath, and Melissa Budinic, the Assistant Exhibit Designer for MoMath.  As Cindy Lawrence, the Associate Director for MoMath says, “MoMath would not be open today if it were not for the efforts” of Emily and Melissa.  Check out Melissa and Emily‘s interviews to read about their favorite exhibits, how they use math in their jobs for MoMath, and what they’re most excited about now that the museum is open!

mimematicsLogo (1)Finally, meet Tim and Tanya Chartier.  Tim is a math professor at Davidson College in North Carolina, and Tanya is a language and literacy educator.  Even better, Tim and Tanya have combined their passion for math and teaching with their love of mime to create the art of Mime-matics!  Tim and Tanya have developed a mime show in which they mime about some important concepts in mathematics.  Tim says about their mime-matics, “Mime and math are a natural combination.  Many mathematical ideas fold into the arts like shape and space.  Further, other ideas in math are abstract themselves.  Mime visualizes the invisible world of math which is why I think math professor can sit next to a child and both get excited!”

One of my favorite skits, in which the mime really does help you to visualize the invisible world of math, is the Infinite Rope.  Check it out:

slinkyIn another of my favorite skits, Tanya interacts with a giant tube that twists itself in interesting topological ways.  Watch these videos and maybe you’ll see, as Tanya says, how a short time “of positive experiences with math, playing with abstract concepts, or seeing real live application of math in our world (like Google, soccer, music, NASCAR, or the movies)  can change the attitude of an audience member who previously identified him/herself as a “math-hater.””  You can also check out Tim’s blog, Math Movement.

Tim and Tanya kindly answered some questions we asked them about their mime-matics.  Check out their interview by following this link, or visit the Q&A page.

Bon appetit!

Rectangles, Explosions, and Surreals

Welcome to this week’s Math Munch!

What is 3 x 4?   3 x 4 is 12.

Well, yes. That’s true. But something that’s wonderful about mathematics is that seemingly simple objects and problems can contain immense and surprising wonders.

How many squares can you find in this diagram?

As I’ve mentioned before, the part of mathematics that works on counting problems is called combinatorics. Here are a few examples for you to chew on: How many ways can you scramble up the letters of SILENT? (LISTEN?) How many ways can you place two rooks on a chessboard so that they don’t attack each other? And how many squares can you count in a 3×4 grid?

Here’s one combinatorics problem that I ran across a while ago that results in some wonderful images. Instead of asking about squares in a 3×4 grid, a team at the Dubberly Design Office in San Francisco investigated the question: how many of ways can a 3×4 grid can be partitioned—or broken up—into rectangles? Here are a few examples:

How many different ways to do this do you think there are? Here’s the poster that they designed to show the answer that they found! You can also check out this video of their solution.

In their explanation of their project, the team states that “Design tools are becoming more computation-based; designers are working more closely with programmers; and designers are taking up programming.” Designing the layout of a magazine or website requires both structural and creative thinking. It’s useful to have an idea of what all the possible layouts are so that you can pick just the right one—and math can help you to do it!

If you’d like to try creating a few 3×4 rectangle partitions of your own, you can check out www.3x4grid.com. [Sadly, this page no longer works. See an archive of it here. -JL, 10/2016]

Next up, explosions! I could tell you about the math of the game Minesweeper (you can play it here), or about exploding dice. But the kind of explosion I want to share with you today is what’s called a “combinatorial explosion.” Sometimes a problem that appears to be an only slightly harder variation of an easy problem turns out to be way, way harder. Just how BIG and complicated even simple combinatorics problems can get is the subject of this compelling and also somewhat haunting video.

Donald Knuth

Finally, all of this counting got me thinking about big numbers. Previously we’ve linked to Math Cats, and Wendy has a page where you can learn how to say some really big numbers. But thinking about counting also made me remember an experience I had in middle school where I found out just how big numbers could be! I was in seventh grade when I read this article from the December 1995 issue of Discover Magazine. It’s called “Infinity Plus One, and Other Surreal Numbers” and was written by Polly Shulman. I remember my mind being blown by all of the talk of infinitely-spined aliens and up-arrow notation for naming numbers. Here’s an excerpt:

Mathematicians and precocious five-year-olds have long been fascinated by the endlessness of numbers, and they’ve named the endlessness infinity. Infinity isn’t a number like 1, 2, or 3; it’s hard to say what it is, exactly. It’s even harder to imagine what would happen if you tried to manipulate it using the arithmetic operations that work on numbers. For example, what if you divide it in half? What if you multiply it by 2? Is 1 plus infinity greater than, less than, or the same size as infinity plus 1? What happens if you subtract 1 from it?

After I read this article, John Conway and Donald Knuth became heros of mine. (In college, I had the amazing fortune to have breakfast with Conway one day when he was visiting to give a lecture!) Knuth has a book about surreals that’s the friendliest introduction to the surreal numbers that I know of, and in this video, Vi Hart briefly touches on surreal numbers in discussing proofs that .9 = 1. Boy, would I love to see a great video or online resource that simply and beautifully lays out the surreal numbers in all their glory!

It was fun for me to remember that Discover article. I hope that you, too, run across some mathematics that leaves a seventeen-year impression on you!

Bon appetit!

Noodles, Flowsnake, and Symmetry

Welcome to this week’s Math Munch!

Gemelli, by Sander Huisman

Gemelli, by Sander Huisman

How much do you like pasta?  Well, these mathematicians and scientists from around the world like pasta so much that they’ve been studying its shape mathematically!  Check out this New York Times article about Sander Huisman, a graduate student in physics from the Netherlands, and Marco Guarnieri and George L. Legendre, two architects from London, who have all taken up making graphs of and equations for pasta shapes.  Sander posts his pasta-graphs on his blog.  Legendre wrote this book about math and pasta, called Pasta By Design.  Legendre has even invented a new type of pasta, shaped like a Mobius strip (see last week’s Math Munch for lots of cool things with Mobius strips), which he named after his baby daughter, Ioli!

Some of Legendre’s pasta plots

Next, here comes the flowsnake.  Wait – don’t run away!  The flowsnake is not a terrifying monster, despite it’s ominous name.  It is a space-filing curve, meaning that the complete curve covers every single point in a part of two-dimensional space.  So if you were to try to draw a flowsnake on a piece of paper, you wouldn’t be able to see any white when you were done.  It’s named flowsnake because it resembles a snowflake.

The flowsnake curve

A single piece of the flowsnake curve.

Units of flowsnake fit together like puzzle pieces to fill the plane

Finally, check out this awesome online symmetry-sketcher, called Symmetry Artist!  Here, you can make doodles of all kinds and then choose how you want to reflect and rotate them.  Fun!

Bon appetit!