Tag Archives: topology

4 Million Digits, Fifteen Furlongs, and 5 Eames Vids

Welcome to this week’s Math Munch!

We’ve written about Pi before, but when I found this new way of visualizing the number, Pi, I knew I’d have to share it with you. In 2011, Shigeru Kondo and Alex Yee concluded an incredible project – to design and execute a program to calculate digits in the decimal expansion of Pi. What makes their attempt so remarkable is that the program ran for over a year (371 days), during which time it calculated precisely the first 10 trillion digits of Pi! (1 with 13 zeroes!)

A New York design firm, called Two-N, built a wonderful website using the first 4 million digits to help us see the patterns in the digits (or lack thereof). Each digit was assigned a color, and included in the image as a single pixel. What we see is a long (really long) string of colored digits. You can drag across the screen to zoom in on rows. There’s even a search bar so that you can find where your birthday appears, or any other 6-digit string for that matter.

If you’re having a hard time wrapping your head around 4,000,000 digits, check out Fifteen Furlongs. It’s a website designed by Kevin Wang, a college student at the University of Chicago, and it’s designed to help us understand different sizes and units of measurements. Try it.

Fifteen Furlongs? – “That’s about two minutes on the highway.” Didn’t help me  much, but 1 Furlong? – “That’s just under one Empire State Building tall.” Which is really interesting. So, if we laid down several empire state buildings in a row to make a highway, then I could drive over 15 of them in about 2 minutes. Cool! How can I understand 4 million?

  • 4 million pounds is the weight of 1,000 cars.  hmmmm.
  • 4 million cups is about one Olympic-sized pool.  whoa.
  • 4 million seconds is just over forty-six day’s time.  so cool.

Maybe you can play around and figure out just how big 10 trillion is. After each answer there’s a place for you to say whether or not the information was useful, which I assume they use that to improve the responses. Have fun.

Kevin agreed to answer a few questions for us, which you can read in our Q&A section.  If you have ideas for how to improve the site, Kevin wants to hear them. Just leave it in the comments, and he’ll see what he can do.

Finally, some mathematical videos by the well-known 20th century design team of Charles and Ray Eames. In 1961 they worked on an exhibition for IBM called “Mathematica: A World of Numbers and Beyond,” which included a huge timeline with descriptions of famous mathematicians and mathematical discoveries from antiquity to modern times. It also included a “mathematics peepshow,” a collection of fantastic short math films, some of which can be seen on YouTube:

Actually my favorites aren’t even available online! There are 5 more videos available in a new fantastic, free iPad app called Minds of Modern Mathematics. If you donwload the app, check out “Symmetry” and “Exponents.” They’re simply stunning.

The best-known Eames vid is probably Powers of Ten, (embedded below) their 1977 film meant to illustrate the incredible scale of the universe, big and small, and how exponents can help us keep track of the different “levels.” It surely inspired the Huang Twins when they designed The Scale of the Universe.

You know, we typically feature at least one video a week, and they’re starting to pile up! Good news, though: we’ve been keeping track on a YouTube playlist of every video ever Featured on Math Munch. You can also use the Videos link at the top of any page.

Have a great week. Bon appetit!

Faces, Blackboards, and Dancing PhDs

Welcome to this week’s Math Munch!

What does a mathematician look like? What does a mathematician do? Here are a couple of things I ran across recently that give a window into what it’s like to be a professional research mathematician—someone who works on figuring out new math as their job.

Gary Davis, who blogs over at Republic of Mathematics, recently posted a short piece that challenges stereotypes about mathematicians. It’s called What does a mathematician look like?

Who here is a mathematician? Click through to find out!

Gary’s point is that you can’t tell who is or isn’t a mathematician just by looking at them. Mathematicians come from every background and heritage. Gary followed up on this idea in another post where he highlighted some notable mathematicians who are black women. Here’s a website called Black Women in Mathematics that shares some biographies and history. And here’s a link to the Infinite Possibilities Conference, a yearly gathering “designed to promote, educate, encourage and support minority women interested in mathematics and statistics.” Suzanne Weekes, one of the five mathematicians pictured above, was a speaker at this conference in 2010.

Richard Tapia, another of the mathematicians above, is featured in the following video. His life story both inspires and delights.

And what does this diversity of mathematicians do all day? Well, one thing they do is talk to each other about math! And though there are many new technologies that help people to do and share and collaborate on mathematics (like blogs!), it’s hard to beat a handy chalkboard as a scribble pad for sharing ideas.

At Blackboard of the Day, Mathieu Rémy and Sylvain Lumbroso share the results of these impromptu math jam sessions. Every day they post a photograph of a blackboard covered in doodles and calculations and sketches of ideas. The website is in French, but the mathematical pictures are a universal language.

Diana Davis, putting the finishing touches on a blackboard masterpiece

Sharing mathematical ideas can take many forms, and sometimes choosing the right medium can make all the difference. Mathematicians use pictures, words, symbols, sculptures, movies, songs—even dances! Let me point you to the “Dance your Ph.D.” Contest. It’s exactly what it sounds like—people sharing the ideas of their dissertations (their first big piece of original work) through dance. Entries come in from physicists, chemists, biologists, and more.  Below you’ll find an entry by Diana Davis, a mathematician who completed her dissertation at Brown University this past spring. Diana often studies regular polgyons and especially ways of “dissecting” them—breaking them up into pieces in interesting ways.

Thanks to The Aperiodical—a great math blog—for sharing Diana’s wonderful video!

Some pages from Diana’s notebooks

All kinds of mathematicians study math and share it in so many ways. It’s like a never-ending math buffet!

Bon appetit!

Number Gossip, Travels, and Topology

Thanksgiving was great, but I hope you saved room for this week’s Math Munch!

First up, meet Tanya Khovonova, a mathematician and blogger who works at MIT.  Number Gossip is a website of hers where you can find the mysterious facts behind your favorite numbers.  For instance, did you know that the opposite sides of a die add to 7, or that 7 is the only prime number followed by a cube (8=23)? Speaking of 7, I also found this cool test for divisibility by 7 on Tanya’s website.

Tanya Khovonova

Is that divisible by 7? Let's take a walk.

Read about how to use it here, but basically you follow that diagram a certain way, and if you land back at the white dot, then you’re number is divisible by 7. I’m amazed and trying to figure out how it works!

Infographic - Holiday Travel Patterns

Next up, I wanted to share this incredible picture I found today.  It’s an infographic showing travel patterns in the US during the holiday season.  The picture must represent millions of little pieces of data, so I’ve spent a lot of time staring and analyzing it.  Did you notice the bumps in the bottom?  Why is that happening?  Why are the blue lines different from the white lines? There are so many good things to be seen.

Finally, take a look at these pictures!  They’re from Kenneth Baker’s Sketches of Topology blog.  Kenneth makes images demonstrating ideas in topology, one of the most visually appealing branches of mathematics.  Some of it is tough to understand, but the pictures certainly are fascinating.

On a related point, have you taken a look at the Math Munch page of math games? (You can always find the link at the top of the column to the right.)  I just added a topology game, the Four Color Game, and I’m kind of loving it.  It’s based on a famous math result about only needing 4 colors to nicely color any flat map.  This is called the Four Color Theorem, and it’s a part of topology.

Bon appetit!