Tag Archives: video

Temari, Function Families, and Clapping Music

Welcome to this week’s Math Munch!

Carolyn Yackel

Carolyn Yackel

As Justin mentioned last week, the Math Munch team had a blast at the MOVES conference last week.  I met so many lovely mathematicians and learned a whole lot of cool math. Let me introduce you to Carolyn Yackel. She’s a math professor at Mercer University in Georgia, and she’s also a mathematical fiber artist who specializes in the beautiful Temari balls you can see below or by clicking the link. Carolyn has exhibited at the Bridges conference, naturally, and her 2012 Bridges page contains an artist statement and some explanation of her art.

temari15 temari3 temari16

Icosidodecahedron

Icosidodecahedron

Truncated Dodecahedron

Truncated Dodecahedron

Cuboctahedron

Cuboctahedron

Temari is an ancient form of japanese folk art. These embroidered balls feature various spherical symmetries, and part of Carolyn’s work has been figure out how to create and exploit these symmetries on the sphere.  I mean how do you actually make it that symmetric? Can you see in the pictures above how the symmetry of the Temari balls mimic the Archimedean solids? Carolyn has even written about using Temari to teach mathematics, some of which you can read here, if you like.

Read Carolyn Yackel’s Q&A with Math Munch.

 

Edmund Harriss

Edmund Harriss

Up next, you may remember Edmund Harriss from this post, and you might recall Desmos from this post. Well the two have come together! On his blog, Maxwell’s Demon, Edmund shared a whole bunch of interactive graphs from Desmos, in a post he called “Form Follows Function.” Click on the link to read the article, and click on the images to get graphs full of sliders you can move to alter the images. In fact, you can even alter the equations that generate them, so dig in, play some, and see what you can figure out.

graph2 graph1 graph3

Finally, I want to share a piece of music I really love. “Clapping Music” was written by Steve Reich in 1972. It is considered minimalist music, perhaps because it features two performers doing nothing but clapping. If you watch this performance of “Clapping Music” first (and I suggest you do) it might just sound like a bunch of jumbled clapping. But the clapping is actually built out of some very simple and lovely mathematical patterns. Watch the video below and you’ll see what I mean.

Did you see the symmetries in the video? I noticed that even though the pattern shifts, it’s always the same backwards as forwards. And I also noticed that the whole piece is kind of the same forwards and backwards, because of the way that the pattern lines back up with itself. Watch again and see if you get what I mean.

Bonus: Math teacher, Greg Hitt tweeted me about “Clapping Music” and shared this amazing performance by six bounce jugglers!!!  It’s cool how you can really see the patterns in the live performance.

I hope you find something you love and dig in. Bon appetit!

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.

Hyperbolic lampshade

By Gabriele Meyer

Bunny!

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!

Hexagonal flower

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.

Jack van WijkMathematical 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?

myriahedronTo 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. cylindrical mapThen, 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…crazy maps

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:

juggling

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!

Coasts, Clueless Puzzles, and Beach Math Art

summerAh, summertime. If it’s as hot where you are as it is here in New York, I bet this beach looks great to you, too. A huge expanse of beach all to myself sounds wonderful… And that makes me wonder – how much coastline is there in the whole world?

Interestingly, the length of the world’s coastline is very much up for debate. Just check out this Wikipedia page on coastlines, and you’ll notice that while the CIA calculates the total coastline of the world to be 356,000 kilometers, the World Resources Institute measures it to be 1,634,701! What???

Measuring the length of a coastline isn’t as simple as it might seem, because of something called the Coastline Paradox. This paradox states that as the ruler you use to measure a coastline gets shorter, the length of the coastline gets longer – so that if you used very, very tiny ruler, a coastline could be infinitely long! This excellent video by Veritasium explains the problem very well:

2000px-KochFlakeAs Vertitasium says, many coastlines are fractals, like the Koch snowflake shown at left – never-ending, infinitely complex patterns that are created by repeating a simple process over and over again. In this case, that simple process is the waves crashing against the shore and wearing away the sand and rock. If coastlines can be infinitely long when you measure them with the tiniest of rulers, how to geographers measure coastline? By choosing a unit of measurement, making some approximations, and deciding what is worth ignoring! And, sometimes, agreeing to disagree.

Need something to read at the beach, and maybe something puzzle-y to ponder? Check out this interesting article by four mathematicians and computer scientists, including James Henle, a professor in Massachusetts. They’ve invented a Sudoku-like puzzle they call a “Clueless Puzzle,” because, unlike Sudoku, their puzzle never gives any number clues.

Clueless puzzleHow does this work? These puzzles use shapes instead of numbers to provide clues. Here’s an example from the paper: Place the numbers 1 through 6 in the cells of the figure at right so that no digit appears more than once in a row or column AND so that the numbers in each region add to the same sum. The paper not only walks you through the solution to this problem, but also talks about how the mathematicians came up with the idea for the puzzles and studied them mathematically. It’s very interesting – I recommend you read it!

Finally, if you’re not much of a beach reader, maybe you’d like to make some geometrically-inspired beach art! Check out this land art by artist Andy Goldsworthy:

Andy Goldsworthy 1
Andy Goldsworthy 2

Or make one of these!

Happy summer, and bon appetit!