# Pi Digit, Pi Patterns, and Pi Day Anthem

Painting by Renée Othot for Simon Plouffe’s birthday.

Welcome to this week’s Math Munch!

It’s here—the Pi Day of the Century happens on Saturday: 3-14-15!

How will you celebrate? You might check to see if there are any festivities happening in your area. There might be an event at a library, museum, school, or university near you.

(Here are some pi day events in NYC, Baltimore, San Francisco, Philadelphia, Houston, and Charlotte.)

John Conway at the pi recitation contest in Princeton.

There’s a huge celebration here in Princeton—in part because Pi Day is also Albert Einstein’s birthday, and Albert lived in Princeton for the last 22 years of his life. One event involves kids reciting digits of pi and and is hosted by John Conway and his son, a two-time winner of the contest. I’m looking forward to attending! But as has been noted, memorizing digits of pi isn’t the most mathematical of activities. As Evelyn Lamb relays,

I do feel compelled to point out that besides base 10 being an arbitrary way of representing pi, one of the reasons I’m not fond of digit reciting contests is that, to steal an analogy I read somewhere, memorizing digits of pi is to math as memorizing the order of letters in Robert Frost’s poems is to literature. It’s not an intellectually meaningful activity.

I haven’t memorized very many digits of pi, but I have memorized a digit of pi that no one else has. Ever. In the history of the world. Probably no one has ever even thought about this digit of pi.

And you can have your own secret digit, too—all thanks to Simon Plouffe‘s amazing formula.

Simon’s formula shows that pi can be calculated chunk by chunk in base 16 (or hexadecimal). A single digit of pi can be plucked out of the number without calculating the ones that come before it.

Wikipedia observes:

The discovery of this formula came as a surprise. For centuries it had been assumed that there was no way to compute the nth digit of π without calculating all of the preceding n − 1 digits.

Check out some of Simon’s math art!

Simon is a mathematician who was born in Quebec. In addition to his work on the digits of irrational numbers, he also helped Neil Sloane with his Encyclopedia of Integer Sequences, which soon online and became the OEIS (previously). Simon is currently a Trustee of the OEIS Foundation.

There is a wonderful article by Simon and his colleagues David Bailey, Jonathan Borwein, and Peter Borwein called The Quest for Pi. They describe the history of the computation of digits of pi, as well as a description of the discovery of their digit-plucking formula.

According to the Guinness Book of World Records, the most digits that someone has memorized and recited is 67,890. Unofficial records go up to 100,000 digit. So just to be safe, I’ve used an algorithm by Fabrice Bellard based on Simon’s formula to calculate the 314159th digit of pi. (Details here and here.) No one in the world has this digit of pi memorized except for me.

Ready to hear my secret digit of pi? Lean in and I’ll whisper it to you.

The 314159th digit of pi is…7. But let’s keep that just between you and me!

And just to be sure, I used this website to verify the 314159th digit. You can use the site to try to find any digit sequence in the first 200 million digits of pi.

Aziz & Peter’s patterns.

Next up: we met Aziz Inan in last week’s post. This week, in honor of Pi Day, check out some of the numerical coincidences Aziz has discovered in the early digits in pi. Aziz and his colleague Peter Osterberg wrote an article about their findings. By themselves, these observations are nifty little patterns. Maybe you’ll find some more of your own. (This kind of thing reminds me of the Strong Law of Small Numbers.) As Aziz and Peter note at the end of the article, perhaps the study of such little patterns will one day help to show that pi is a normal number.

And last up this week, to get your jam on as Saturday approaches, here’s the brand new Pi Day Anthem by the recently featured John Sims and the inimitable Vi Hart.

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!

# Numenko, Turning Square, and Toilet Paper

Welcome to this week’s Math Munch!

Have you ever played Scrabble or Bananagrams? Can you imagine versions of these games that would use numbers instead of letters?

Meet Tom Lennett, who imagined them and then made them!

Tom playing Numenko with his grandkids.

Numemko is a crossnumber game. Players build up number sentences, like 4×3+8=20, that cross each other like in a crossword puzzle. There is both a board game version of Numenko (like Scrabble) and a bag game version (like Banagrams). Tom invented the board game years ago to help his daughter get over her fear of math. He more recently invented the bag game for his grandkids because they wanted a game to play where they didn’t have to wait their turn!

The Multichoice tile.

One important feature of Numenko is the Multichoice tile. Can you see how it can represent addition, subtraction, multiplication, division, or equality?

How would you like to have a Numenko set of your own? Well, guess what—Tom holds weekly Numenko puzzle competitions with prizes! You can see the current puzzle on this page, as well as the rules. Here’s the puzzle at the time of this post—the week of November 3, 2013.

Challenge: replace the Multichoice tiles to create a true number sentence.

I can assure you that it’s possible to win Tom’s competitions, because one of my students and I won Competition 3! I played my first games of Numenko today and really enjoyed them. I also tried making some Numenko puzzles of my own; see the sheet at the bottom of this post to see some of them.

Tom in 1972.

In emailing with Tom I’ve found that he’s had a really interesting life. He grew up in Scotland and left school before he turned 15. He’s been a football-stitcher, a barber, a soldier, a distribution manager, a paintball site operator, a horticulturist, a property developer, and more. And, of course, also a game developer!

Do you have a question you’d like to ask Tom? Send it in through the form below, and we’ll try to include it in our upcoming Q&A!

The level editor.

Say, do you like Bloxorz? I sure do—it’s one of my favorite games! So imagine my delight when I discovered that a fan of the game—who goes by the handle Jz Pan—created an extension of it where you can make your own levels. Awesome, right? It’s called Turning Square, and you can download it here.

(You’ll need to uncompress the file after downloading, then open TurningSquare.exe. This is a little more involved than what’s usual here on Math Munch, but I promise it’s worth it! Also, Turning Square has only been developed for PC. Sorry, Mac fans.)

But wait, there’s more! Turning Square also introduces new elements to Bloxorz, like slippery ice and pyramids you can trip over. It has a random level generator that can challenge you with different levels of difficulty. Finally, Turning Square includes a level solver—it can determine whether a level that you create is possible or not and how many steps it takes to complete.

Jz Pan is from China and is now a graduate student at the Chinese Academy of Sciences, majoring in mathematics and studying number theory. Jz Pan made Turning Square in high school, back in 2008.

Jz Pan has agreed to answer some of your questions! Use the form below to send us some.

If you make a level in Turning Square that you really like, email us the .box file and we can share it with everyone through our new Readers’ Gallery! Here is my level from above, if you want to try it out.

Jz Pan has also worked on an even more ambitious extension of Bloxorz called Turning Polyhedron. The goal is the same, but like the game Dublox, the shape that you maneuver around is different. Turning Polyhderon features several different shapes. Check out this video of it being played with a u-polyhedron!

And if you think that’s wild, check out this video with multiple moving blocks!

Last up this week, have you ever heard that it’s impossible to fold a piece of paper in half more than eight times? Or maybe it’s seven…? Either way, it’s a “fact” that seems to be common knowledge, and it sure seems like it’s true when you try to fold up a standard sheet of paper—or even a jumbo sheet of paper. The stack sure gets thick quickly!

Britney and her 11th fold.

Well, here’s a great story about a teenager who decided to debunk this “fact” with the help of some math and some VERY big rolls of toilet paper. Her name is Britney Gallivan. Back in 2001, when she was a junior in high school, Britney figured out a formula for how much paper she’d need in order to fold it in half twelve times. Then she got that amount of paper and actually did it!

Due to her work, Britney has a citation in MathWorld’s article on folding and even her own Wikipedia article. After high school, Britney went on to UC Berkeley where she majored in Environmental Science. I’m trying to get in touch with Britney for an interview—if you have a question for her, hold onto it, and I’ll keep you posted!

EDIT: I got in touch with Britney, and she’s going to do an interview!

A diagram that illustrates how Britney derived her equation.

The best place to read more about Britney’s story in this article at pomonahistorical.org—the historical website of Britney’s hometown. Britney’s story shows that even when everyone else says that something’s impossible, that doesn’t mean you can’t be the one to do it. Awesome.

I hope you enjoy trying some Numenko puzzles, tinkering with Turning Square, and reading about Britney’s toilet paper adventure.

Bon appetit!

PS Want to see a video of some toilet-paper folding? Check out the very first “family math” video by Mike Lawler and his kids.

Reflection Sheet – Numenko, Turning Square, and Toilet Paper