George Washington, Tessellation Kit, and Langton’s Ant

Welcome to this week’s Math Munch!

What will you do with your math notebook at the end of the school year? Keep it as a reference for the future? Save it as a keepsake? Toss it out? Turn it into confetti? Find your favorite math bits and doodles and make a collage?

Lucky for us, our first president kept his math notebooks from when he was a young teenager. And though it’s passed through many hands over the years—including those of Chief Justice John Marshall and the State Department—it has survived to this day. That’s right. You can check out math problems and definitions copied out by George Washington over 250 years ago. They’re all available online at the Library of Congress website.

Or at least most of them. They seem to be out of order, with a few pages missing!

That’s what mathematician and math history detective Fred Rickey has figured out. Fred has long been a fan of math history. Since he retired from the US Military Academy in 2011, Fred has been able to pursue his historical interests more actively. Fred is currently studying the Washington cypher books to help prepare a biography about Washington’s boyhood years. You can see two papers that Fred has co-authored about Washington’s mathematics here.

Fred writes:

Washington valued his cyphering books and kept them as a ready source of reference for the rest of his life. This would seem to be particularly true of his surveying studies.

Surveying played a big role in Washington’s career, and math is important for today’s surveyors, too.

Do you have a question for Fred about the math that George Washington learned? Send it to us and we’ll try to include it in our upcoming Q&A with Fred!

A tessellation, by me!

Next up, check out this Tessellation Kit. It was made by Nico Disseldorp, who also made the geometry construction game we featured recently. The kit is a lot of fun to play with!

One thing I like about this Tessellation Kit is how it’s discrete—it deals with large chunks of the screen at a time. This restriction make me want to explore, because it give me the feeling that there are only so many possible combinations.

I’m also curious about the URL for this applet—the web address for it. Notice how it changes whenever you make a change in your tessellation? What happens when you change some of those letters and numbers—like bababaaaa to bababcccc? Interesting…

For another fun applet, check out this doodling ant:

Langton’s Ant.

Langton’s Ant is following a simple set of rules. In a white square? Turn right. In a black square? Turn left. And switch the color of the square that you leave. This ant is an example of a cellular automaton, and we’ve seen several of these here on Math Munch before. This one is different from others because it changes just one square at a time, and not the whole screen at once.

Breaking out of chaos.

There’s a lot that is unknown about Langton’s ant, and it has some mysterious behavior. For example, after thousands of steps of seeming randomness, the ant goes into a steady pattern, paving a highway out to infinity. What gives? Well, you can try out some patterns of your own in the applets on the Serendip website. (previously). And you can read some amusing tales—ant-ecdotes?—about Langton’s ant in this lovely article.

I learned about Langton’s Ant from Richard Evan Schwartz in our new Q&A. In the interview, Rich shares his thoughts about computers, art, what to pursue in life, and of course: Really Big Numbers.

Check it out, and bon appetit!

Fields Medal, Favorite Numbers, and The Grapes of Math

Welcome to this week’s Math Munch! And, if you’re a student or teacher, welcome to a new school year!

One of the most exciting events in the world of math happened this August– the awarding of the Fields Medal! This award honors young mathematicians who have already done awesome mathematical work and who show great promise for the future. It also only happens every four years, at the beginning of an important math conference called the International Congress of Mathematicians, so it’s a very special occasion when it does!

Maryam Mirzakhani, first woman ever to win a Fields Medal

This year’s award was even more special than usual, though. Not only were there four winners (more than the usual two or three), but one of the winners was a woman!

Now, if you’re like me, you probably heard about the Fields Medal and thought, “There’s no way I’ll understand the math that these Field Medalists do.” But this couldn’t be more wrong! Thanks to these great articles from Quanta Magazine, you can learn a lot about the super-interesting math that the Fields Medalists study– and why they study it.

Manjul Bhargava

One thing you’ll immediately notice is that each Fields Medalist has non-math interests that inspire their mathematical work. Take Manjul, for instance. When he was a kid, his grandfather introduced him to Sanskrit poetry. He was fascinated by the patterns in the rhythms of the poems, and the number patterns that he found inspired him to study the mathematics of number patterns– number theory!

But, don’t just take my word for it– you can read all about Manjul and the others in these great articles! And did I mention that they come with videos about each mathematician?

… What’s your favorite number? Is it 7? If it is, then you’re in good company! Alex polled more than 30,000 people about their favorite number, and the most popular was 7. But why? What’s so special about 7? Here’s why Alex thinks 7 is such a favorite:

Why do you like your favorite number? People gave Alex all kinds of different reasons. One woman said about 3, her favorite number, “3 wishes. On the count of 3. 3 little pigs… great triumvirates!” Alex made these questions the topic of the first chapter of his new book, The Grapes of Math. (Get the reference?) In this book, Alex shares many curious ways that math appears in our world. Did you know that a weird pattern in numbers can be used to catch criminals? Or that the Game of Life, a simple computer program, shares surprisingly many characteristics with real life? These are only a few of the hundreds of topics Alex covers in his book. Whether you’re a math whiz or a newbie, you’ll learn something new on every page.

Alex currently writes about math for The Guardian in a blog called, “Alex’s Adventures in Numberland”— but he also loves and writes about soccer (or futbol, as it’s called in his native Brazil)! He even wrote a few articles for his blog about math and soccer.

Do you have any questions for Alex? (About math, soccer, or their intersection?) Write them here and you might find them featured in our interview with Alex!

Good writing about math is hard to find. If you’ve ever picked up a standard math textbook, you’ll know what I mean. But reading something fascinating, that grabs your interest from the first page and leads you through the most complex ideas like they’re as natural as anything you’ve observed, is a great way to learn. The Grapes of Math and “Alex’s Adventures in Numberland” do just that. Give them a go!

Bon appetit!

Math Awareness Month, Hexapawn, and Plane Puzzles

Welcome to this week’s Math Munch!

April is Mathematics Awareness Month. So happy Mathematics Awareness Month! This year’s theme is “Mathematics, Magic, and Mystery”. It’s inspired by the fact that 2014 would have marked Martin Gardner’s 100th birthday.

A few of the mathy morsels that await you this month on mathaware.org!

Each day this month a new piece of magical or mysterious math will be revealed on the MAM site. The mathematical offering for today is a card trick that’s based on the Fibonacci numbers. Dipping into this site from time to time would be a great way for you to have a mathy month.

It is white’s turn to move. Who will win this Hexapawn game?

Speaking of Martin Gardner, I recently ran across a version of Hexapawn made in the programming language Scratch. Hexapawn is a chess mini-game involving—you guessed it—six pawns. Martin invented it and shared it in his Mathematical Games column in 1962. (Here’s the original column.) The object of the game is to get one of your pawns to the other side of the board or to “lock” the position so that your opponent cannot move. The pawns can move by stepping forward one square or capturing diagonally forward. Simple rules, but winning is trickier than you might think!

The program I found was created by a new Scratcher who goes by the handle “puttering”. On the site he explains:

I’m a dad. I was looking for a good way for my daughters to learn programming and I found Scratch. It turns out to be so much fun that I’ve made some projects myself, when I can get the computer…

puttering’s Scratch version of Conway’s Game of Life

Something that’s super cool about puttering’s Hexapawn game is that the program learns from its stratetgy errors and gradually becomes a stronger player as you play more! It’s well worth playing a bunch of games just to see this happen. puttering has other Scratch creations on his page, too—like a solver for the Eight Queens puzzle and a Secret Code Machine. Be sure to check those out, too!

Last up, our friend Nalini Joshi recently travelled to a meeting of the Australian Academy of Science, which led to a little number puzzle.

What unusual ways of describing a number! Trying to learn about these terms led me to an equally unusual calculator, hosted on the Math Celebrity website. The calculator will show you calculations about the factors of a numbers, as well as lots of categories that your number fits into. Derek Orr of Math Year-Round and I figured out that Nalini’s clues fit with multiple numbers, including 185, 191, and 205. So we needed more clues!

Can you find another number that fits Nalini’s clues? What do you think would be some good additional questions we could ask Nalini? Leave your thoughts in the comments!

A result from the Number Property Calculator

I hope this post helps you to kick off a great Mathematics Awareness Month. Bon appetit!