Tag Archives: fractals

TED, Bridges, and Silk

Welcome to this week’s Math Munch!

The Math Munch team at TEDxNYED

Marjorie Rice | click to watch her interview video

On Saturday, the Math Munch team gave a 16-minute presentation at TEDxNYED about Math Munch! (Eventually there will be a video, and we’ll be sure to share it with you right away, but you’ll have to wait a month, maybe.)

We started with the story of Marjorie Rice, and in searching for a good picture of her, we came across this wonderful interview in a documentary about Martin Gardner. It’s so neat to hear her speak about her discoveries. You can see how proud she is and how much she truly loves math. Feel free to watch the whole documentary if you like. I haven’t gotten a chance yet, but I know it’s full of incredible stuff.

In the spirit of TED, I decided to share a few mathematical TED talks. This one is absolutely fascinating. In it, mathematician Ron Eglash describes how fractals underly the african designs. You know how we love fractals.

If you’re hungry for another TED talk, here’s one about connections between music, mathematics, and sonar.

Up next, remember when we wrote about attending last year’s Bridges conference? Well it happens every year, of course, and this year’s gallery of mathematical art is available online! Click on one of those images and you get to more of the artists work. I could easily spend hours staring at this art, trying to understand them, and reading the descriptions and artist statements. Seriously, there is just way too much cool stuff there, so I’ve picked out a few of my favorites. Also, I have great news to announce: Chloé Worthington (previously featured) had some of her art accepted to the exhibition! Congratulations, Chloe! If you look closely, you’ll see some of my art in there too. 🙂

Bjarne Jespersen

Marc Chamberland

Bob Rollings

Chloé Worthington

Mehrdad Garousi

By the way, if you ever create any mathematical art of your own, we’d love to see it! Send us an email at mathmunchteam@gmail.com, and maybe we’ll feature your work in an upcoming Math Munch. (Only if you want us too, of course.)

Silk creator Yuri Vishnevsky

Finally, I know many of you like playing around with Symmetry Artist, which can be found on our page of Math Art Tools. If you like that, then you’ll love Silk! It’s much the same, but generates a certain kind of whispiness as you draw that looks really cool. It also lets you spiral your designs toward the center, a feature which Symmetry Artist lacks. You can download the Silk app for iPad or iPhone, if you like. Silk was designed by Yuri Vishnevsky, with sound design by Mat Jarvis. Yuri has agreed to do a Q&A for us, but we haven’t quite finished it just yet. I’ll upload it as soon as possible, but for now, you can read an interview Mat and Yuri did with a website called Giant Fire Breathing Dragon.

Bon appetit!

Posted by Paul Salomon. Categories: Math Munch. Tags: Bridges, fractals, marjorie rice, Martin Gardner, mathematical art, Silk, TED talks. 8 Comments

Mar. ’13

Maths Ninja, Folding Fractals, and Pi Fun

Welcome to this week’s Math Munch!

First up, have you ever been stuck on a gnarly math problem and wished that a math ninja would swoop in and solve the problem before it knew what hit it? Have you ever wished that you had a math dojo who would impart wisdom to you in cryptic but, ultimately, extremely timely and useful ways? Well, meet Colin Beverige, a math (or, as he would say, maths) tutor from England who writes a fun blog called Flying Colours Maths. On his blog, he publishes a weekly series called, “Secrets of the Mathematical Ninja,” in which the mathematical ninja (maybe Colin himself? He’s too stealthy to tell) imparts nuggets of sneaky wisdom to help you take down your staunchest math opponent.

For example, you probably know the trick for multiplying by 9 using your fingers – but did you know that there’s a simple trick for dividing by 9, too? Ever wondered how to express thirteenths as decimals, in your head? (Probably not, but maybe you’re wondering now!) Want to know how to simplify fractions like a ninja? Well, the mathematical ninja has the answers – and some cute stories, too. Check it out!

A picture of a Julia set.

Next, I find fractals fascinating, but – I’ll admit it – I don’t know much about them. I do know a little about the number line and graphing, though. And that was enough to learn a lot more about fractals from this excellent post on the blog Hackery, Math, and Design by Steven Wittens. In the post How to Fold a Julia Fractal, Steven describes how the key to understanding fractals is understanding complex numbers, which are the numbers we get when we combine our normal numbers with imaginary numbers.

Now, I think imaginary numbers are some of the most interesting numbers in mathematics – not only because they have the enticing name “imaginary,” but because they do really cool things and have some fascinating history behind them. Steven does a really great job of telling their history and showing the cool things they do in this post. One of the awesome things that imaginary numbers do is rotate. Normal numbers can be drawn on a line – and multiplying by a negative number can be thought of as changing directions along the number line. Steven uses pictures and videos to show how multiplying by an imaginary number can be thought of as rotating around a point on a plane.

A Julia set in the making.

The Julia set fractal is generated by taking complex number points and applying a function to them that squares each point and adds some number to it. The fractal is the set of points that don’t get infinitely larger and larger as the function is applied again and again. Steven shows how this works in a series of images. You can watch the complex plane twist around on itself to make the cool curves and figures of the Julia set fractal.

Steven’s blog has many more interesting posts. Check out another of my favorites, To Infinity… and Beyond! for an exploration of another fascinating, but confusing, topic – infinity.

Finally, a Pi Day doesn’t go by without the mathematicians and mathematical artists of the world putting out some new Pi Day videos! Pi Day was last Thursday (3/14, of course). Here’s a video from Numberphile in which Matt Parker calculates pi using pies!

In this video, also from Numberphile, shows how you only need 39 digits of pi to make really, really accurate measurements for the circumference of the observable universe:

Finally, it wouldn’t be Pi Day without a pi video from Vi Hart. Here’s her contribution for this year:

Bon appetit!

Posted by Anna Weltman. Categories: Math Munch. Tags: computers, fractals, imaginary numbers, infinity, math help, numbers, pi, Vi Hart, video. 18 Comments

Mar. ’13

Dots-and-Boxes, Choppy Waves, and Psi Day

Welcome to this week’s Math Munch!

And happy Psi Day! But more on that later.

Click to play Dots-and-Boxes!

Recently I got to thinking about the game Dots-and-Boxes. You may already know how to play; when I was growing up, I can only remember tic-tac-toe and hangman as being more common paper and pencil games. If you know how to play, maybe you’d like to try a quick game against a computer opponent? Or maybe you could play a low-tech round with a friend? If you don’t know how to play or need a refresher, here’s a quick video lesson:

In 1946, a first grader in Ohio learned these very same rules. His name was Elwyn Berlekamp, and he went on to become a mathematician and an expert about Dots-and-Boxes. He’s now retired from being a professor at UC Berkeley, but he continues to be very active in mathematical endeavors, as I learned this week when I interviewed him.

Elwyn Berlekamp

In his book The Dots and Boxes Game: Sophisticated Child’s Play, Elwyn shares: “Ever since [I learned Dots-and-Boxes], I have enjoyed recurrent spurts of fascination with this game. During several of these burst of interest, my playing proficiency broke through to a new and higher plateau. This phenomenon seems to be common among humans trying to master any of a wide variety of skills. In Dots-and-Boxes, however, each advance can be associated with a new mathematical insight!”

Elwyn’s booklet about
Dots-and-Boxes

In his career, Elywen has studied many mathematical games, as well as ideas in coding. He has worked in finance and has been involved in mathematical outreach and community building, including involvement with Gathering for Gardner (previously).

Elywn generously took the time to answer some questions about Dots-and-Boxes and about his career as a mathematician. Thanks, Elywn! Again, you should totally check out our Q&A session. I especially enjoyed hearing about Elwyn’s mathematical heros and his closing recommendations to young people.

As I poked around the web for Dots-and-Boxes resources, I enjoyed listening to the commentary of Phil Carmody (aka “FatPhil”) on this high-level game of Dots-and-Boxes. It was a part of a tournament held on a great games website called Little Golem where mathematical game enthusiasts from around the world can challenge each other in tournaments.

What's the best move?A Sam Loyd Dots-and-Boxes Puzzle

What’s the best move?
A Dots-and-Boxes puzzle by Sam Loyd.

And before I move on, here are two Dots-and-Boxes puzzles for you to try out. The first asks you to use the fewest lines to saturate or “max out” a Dots-and-Boxes board without making any boxes. The second is by the famous puzzler Sam Loyd (previously). Can you help find the winning move in The Boxer’s Puzzle?

Next up, check out these fantastic “waves” traced out by “circling” these shapes:

Click the picture to see the animation!

Lucas Vieira—who goes by LucasVB—is 27 years old and is from Brazil. He makes some amazing mathematical illustrations, many of them to illustrate articles on Wikipedia. He’s been sharing them on his Tumblr for just over a month. I’ll let his images and animations speak for themselves—here are a few to get you started!

A colored-by-arc-length Archimedean spiral.

A sphere-like degenerate torus.

A Koch cube.

There’s a great write-up about Lucas over at The Daily Dot, which includes this choice quote from him: “I think this sort of animated illustration should be mandatory in every math class. Hopefully, they will be some day.” I couldn’t agree more. Also, Lucas mentioned to me that one of his big influences in making mathematical imagery has always been Paul Nylander. More on Paul in a future post!

Psi is the 23rd letter in the Greek alphabet.

Finally, today—March 11—is Psi Day! Psi is an irrational number that begins 3.35988… And since March is the 3rd month and today is .35988… of the way through it–11 out of 31 days—it’s the perfect day to celebrate this wonderful number!

What’s psi you ask? It’s the Reciprocal Fibonacci Constant. If you take the reciprocals of the Fibonnaci numbers and add them add up—all infinity of them—psi is what you get.

Psi was proven irrational not too long ago—in 1989! The ancient irrational number phi—the golden ratio—is about 1.61, so maybe Phi Day should be January 6. Or perhaps the 8th of May—8/5—for our European readers. And e Day—after Euler’s number—is of course celebrated on February 7.

That seems like a pretty good list at the moment, but maybe you can think of other irrational constants that would be fun to have a “Day” for!

And finally, I’m sure I’m not the only one who’d love to see a psi or Fibonacci-themed “Gangham Style” video. Get it?

Bon appetit!

******

EDIT (3/14/13): Today is Pi Day! I sure wish I had thought of that when I was making my list of irrational number Days…

Posted by Justin Lanier. Categories: Math Munch. Tags: art, dots-and-boxes, Fibonacci, fractals, games, interview, irrational, Martin Gardner, numbers, pi, psi, spirals, video, waves. 24 Comments