Monthly Archives: February 2015

SquareRoots, Concave States, and Sea Ice

Welcome to this week’s Math Munch!

The most epic Pi Day of the century will happen in just a few weeks: 3/14/15! I hope you’re getting ready. To help you get into the spirit, check out these quilts.

American Pi.

American Pi.

African American Pi.

African American Pi.

There’s an old joke that “pi is round, not square”—a punchline to the formula for the area of a circle. But in these quilts, we can see that pi really can be square! Each quilt shows the digits of pi in base 3. The quilts are a part of a project called SquareRoots by artist and mathematician John Sims.

John Sims.

John Sims.

There’s lots more to explore and enjoy on John’s website, including a musical interpretation of pi and some fractal trees that he has designed. John studied mathematics as an undergrad at Antioch College and has pursued graduate work at Wesleyan University. He even created a visual math course for artists when he taught at the Ringling College of Art and Design in Florida.

I enjoyed reading several articles (1, 2, 3, 4) about John and his quilts, as well as this interview with John. Here’s one of my favorite quotes from it, in response to “How do you begin a project?”

It can happen in two ways. I usually start with an object, which motivates an idea. That idea connects to other objects and so on, and, at some point, there is a convergence where idea meets form. Or sometimes I am fascinated by an object. Then I will seek to abstract the object into different spatial dimensions.

simstrees

Cellular Forest and Square Root of a Tree, by John Sims.

You can find more of John’s work on his YouTube channel. Check out this video, which features some of John’s music and an art exhibit he curated called Rhythm of Structure.

Next up: Some of our US states are nice and boxy—like Colorado. (Or is it?) Other states have very complicated, very dent-y shapes—way more complicated than the shapes we’re used to seeing in math class.

Which state is the most dent-y? How would you decide?

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West Virginia is pretty dent-y. By driving “across” it, you can pass through many other states along the way.

The mathematical term for dent-y is “concave”. One way you might try to measure the concavity of a state is to see how far outside of the state you can get by moving in a straight line from one point in it to another. For example, you can drive straight from one place in West Virginia to another, and along the way pass through four other states. That’s pretty crazy.

But is it craziest? Is another state even more concave? That’s what this study set out to investigate. Click through to find out their results. And remember that this is just one way to measure how concave a state is. A different way of measuring might give a different answer.

Awesome animal kingdom gerrymandering video!

Awesome animal kingdom gerrymandering video!

This puzzle about the concavity of states is silly and fun, but there’s more here, too. Thinking about the denty-ness of geographic regions is very important to our democracy. After all, someone has to decide where to draw the lines. When regions and districts are carved out in a way that’s unfair to the voters and their interests, that’s called gerrymandering.

Karen Saxe

Karen Saxe.

To find out more about the process of creating congressional districts, you can listen to a talk by Karen Saxe, a math professor at Macalester College. Karen was a part of a committee that worked to draw new congressional districts in Minnesota after the 2010 US Census. (Karen speaks about compactness measures starting here.)

Recently I ran across an announcement for a conference—a conference that was all about the math of sea ice! I never grow tired of learning new and exciting ways that math connects with the world. Check out this video featuring Kenneth Golden, a leading mathematician in the study of sea ice who works at the University of Utah. I love the line from the video: “People don’t usually think about mathematics as a daring occupation.” Ken and his team show that math can take you anywhere that you can imagine.

Bon appetit!

Reflection sheet – SquareRoots, Concave States, and Sea Ice

Braids, Hacktastic, and Rock Climbing

Welcome to this week’s Math Munch!

lym_angel

Math hair braiding art by So Yoon Lym, shown at the 2014 Joint Mathematics Meetings.

First up, a little about one of my favorite things to do (and part of what got me into math in the first place!): hair braiding. If you’ve ever done a complicated braid in someone’s hair before, you might have had an inkling that something mathematical was going on. Well, you’re right! Mathematicians Gloria Ford Gilmer and Ron Eglash have spent much of their careers studying and teaching about the math that goes into hair braiding.

SYL_Diosnedys_new1

See the tessellation?

In their research, Gloria and Ron investigate how math can improve hair braiding, how hair braiding can improve math, and how the overlap between the two can teach us about how different cultures use and understand math. As Gloria shows in her article on math and braids, tessellations are very important to braided designs.

braids

And so are fractals! Ron studies how fractals are used in African and African American designs, including in the layouts of towns, tile patterns, and cornrow braids. (Watch his TED Talk to learn more!) On his beautiful website dedicated to the math of cornrows, Ron shows how braiders use tools essential to making fractals to design their braids.

programmed braid

Just like when making a fractal, braid designers repeat the same shape while shifting, rotating, reflecting, and shrinking it. You can design your own mathematical cornrow braid using Ron’s braid programming app! If you’ve ever used Scratch, this app will look very familiar. I made the spiral braid on the right using the app. Next challenge: try to make your braid on a real head of hair…

trig bracelets Laura Taalman

Next up, a little about something I wish I could do: make awesome 3D-printed art! Here’s a blog that might help me (and you) get started. Mathematician Laura Taalman (who calls herself @mathgrrl on Twitter) writes a blog called Hacktastic all about making math designs, using a 3D-printer and many other tools. She has designs for all kinds of awesome things, from Menger sponges to trigonometric bracelets. One of the best things about Laura’s site is that she tells you the story behind how she came up with her designs, along with all the instructions and code you’ll ever need to make her designs yourself.

Rock climbing Skip

Skip Garibaldi, climbing

Finally, a little about something I’m trying to learn to do better: rock climbing! Mathematician Skip Garibaldi loves both math and rock climbing– so he decided to combine his interests for the better of each. In this video, Skip discusses some of the mathematical ideas important to rock climbing– including some essential to a type of climbing that I find most intimidating, lead climbing. Check it out!

Bon appetit!

Dearing, Edmark, and The Octothorpean Order

Welcome to this week’s Math Munch!

Dearing Wang

Dearing Wang

First up is a wonderful mathematical artist I found on instagram, under the name dearing_draws. Click to see the wonderful work of Dearing Wang. The instagram stream includes lots of timelapse videos showing the creation of the images, which is lovely, but even better is that Dearing has a youtube channel and a website devoted to teaching people how to make their own!! You should click over and follow a tutorial. Make something beautiful and send us a picture.

3 Fish in a Pond

3 Fish in a Pond

Tutorial Video

The Diamond Wedge Pattern

The Diamond Wedge Pattern

Tutorial Video

Impossible Octagon

Impossible Octagon

Tutorial Video

Another great thing about Dearing’s website is that he has a page where you can print out blank sheets to color, if that’s your thing. Not quite as mathematical, maybe, but it is nice. I like to color sometimes, and if you color systematically, maybe symmetrically, then it’s fairly mathematical after all. UPDATE: Dearing has agreed to let us host some some of his coloring sheets on Math Munch.  Click here for easily downloadable sheets to color.

John Edmark

John Edmark

Up next is another mathematical artist, John Edmark, a designer and adjunct professor at Stanford University. I was introduced to John’s incredible work through the following video. Just watch and let your jaw hit the floor in amazement.

This is a video of a zoetrope. The pieces spin and the camera shutter is timed to only show certain points in their rotation. What we see is sort of like a little loop of film showing us several frames of the animation. It’s impressive that John put all those frames together into sculptures that are beautiful, even when they’re not spinning.

PatTurn

PatTurn

But that isn’t all, there’s lots more to see on John’s website. I found his spiral videos pretty mesmerizing and fantastic. I also really like his artist statement, which begins “If change is the only constant in nature, it is written in the language of geometry.” I also just really like hearing artists talk about their work, because it’s a sort of behind the scenes look into their creative process and thinking.

(3D printable files are also available here for the incredibly fortunate among us with access to a 3D printer.)

An octothorpe

An Octothorpe

Finally, if you like solving riddles and puzzles, check out The Octothorpean Order. This is sort of an online puzzle hunt, with clues and tips on the website. You can read about it, but the best thing to do is dive in and start solving puzzles. You probably have to create a user name, but it’s good fun. I recommend it.

By the way,  “octothorpe” is the technical word for the “hashtag” or “pound” or “number sign.” It means eight fields, and I think it represents a farmers house in the middle and eight fields arround it. Cool right?

Here’s to having a mathematical week.  Bon appetit!