Tag Archives: pi

Mayans, Calendars, and Ramanujan

Welcome to this week’s Math Munch!

There’s been a lot of fuss recently about the Mayan calendar and the “end of the world.” You’ll be relieved to hear that the world continues to hang in there. In fact, no less an authority than NASA put out a video to help clear up the misinformation surrounding the rolling over of the Mayan calendar.

mayanAll of the doomsday talk did get me researching the Mayan calendar and number system. Check out this page that discusses Mayan numerals and will even count and skip-count for you. Once you’ve got the knack of how to count in the Mayan system, maybe you’ll want to try to decipher the numbers on a Mayan ballcourt marker in this interactive applet.

A cool fact that I learned from that first page is that the Mayans also had another and fancier way of writing down numbers: face glyphs. I found a really comprehensive article by Mark Pitts that describes both face glyphs and the ordinary system, too.

glyphs

The Mayan face glyphs for 0, 1, 2, and 3:
mih, jun, cha’, and ux.

There are many interesting kinds of calendars that human being have developed over the centuries, all with different styles, different mathematical patterns, and different connections to the natural and human worlds. We’ve featured the Cloctal before, but how about some links to some other fun mathy calendars as the new year approaches?

Thursday-January-1

Thursday, January 1—in pennies.

I’m always amazed by what the internet produces when I dream up a search term like “binary calendar.” Perhaps you’ve seen a binary clock before—if not, check out this one—but I was delighted to find several different takes on a binary calendar served up by Google. Juan Osborne designed a binary calendar with all of the dates written out it a big colorful loop. Next, can you figure out the secret to this wooden binary calendar by Ken and Bobbie Ralphs? (It’s a lot like a marble calculator.) And third, here’s a binary calendar that you can make using just twelve pennies, courtesy of exploringbinary.com!

aztec-calendar-wheels

The Aztec tonalpohualli calendar.

There are many more amazing calendars to explore. Maybe you’ll check out Aztec calendar wheels, or find out about anniversaries of mathematicians from this calendar. (Isaac Newton was born on Christmas!) There are even more great calendars to explore at the Calendar Wiki, including some new calendars that have been proposed to “fix” our calendar—the Gregorian calendar—to get rid of traits like uneven months and leap years.

RamanujanSpeaking of anniversaries, this past Saturday was the 125th anniversary of the birth of the great Indian mathematician Srinivasa Ramanujan. Google celebrated the occasion with this doodle on the Indian Google homepage.

srinivasa_ramanujans_125th_birthday-992007-hp

Ramanujan’s story is inspiring and also in some ways tragic. There’s plenty of information about Ramanujan on the web, but you might particularly enjoy reading this recent tribute to him by Dilip D’Souza. One surprising fact I ran across is that one of Ramanujan’s formulas involving pi appeared in (of all places) the movie High School Musical.

formula

One of Ramanujan’s infinite series, which made an appearance in High School Musical.

Ramanujan’s 125th birthday this year became the occasion for India’s first National Mathematics Day. What a cool holiday! Here is a clip from Indian television that shows some Indian students honoring Ramanujan and doing some math.

I can’t understand everything that’s happening in the video, but it’s simply amazing to catch a glimpse of students on the other side of the world being excited about math. Also, you might notice that some of the students are figuring out cube roots of large numbers, while some others are shown figuring out what day of the week certain dates fell on. That’s a neat calendar-related feat that you can read more about here.

And just because it made me giggle, here’s a little bonus video.

Bon appetit!

Harmonious Sum, Continuous Life, and Pumpkins

Welcome to this week’s Math Munch!

We’ve posted a lot about pi on Math Munch – because it’s such a mathematically fascinating little number.  But here’s something remarkable about pi that we haven’t yet talked about. Did you know that pi is equal to four times this? Yup.  If you were to add and subtract fractions like this, for ever and ever, you’d get pi divided by 4.  This remarkable fact was uncovered by the great mathematician Gottfried Wilhelm Leibniz, who is most famous for developing the calculus.  Check out this interactive demonstration from the Wolfram Demonstrations Project to see how adding more and more terms moves the sum closer to pi divided by four.  (We’ve written about Wolfram before.)

I think this is amazing for a couple of reasons.  First of all, how can an infinite number of numbers add together to make something that isn’t infinite???  Infinitely long sums, or series, that add to a finite number have a special name in mathematics: convergent series.  Another famous convergent series is this one:

The second reason why I think this sum is amazing is that it adds to pi divided by four.  Pi is an irrational number – meaning it cannot be written as a fraction, with whole numbers in the numerator and denominator.  And yet, it’s the sum of an infinite number of rational numbers.

In this video, mathematician Keith Devlin talks about this amazing series and a group of mathematical musicians (or mathemusicians) puts the mathematics to music.

This video is part of a larger work called Harmonious Equations written by Keith and the vocal group Zambra.  Watch the rest of them, if you have the chance – they’re both interesting and beautiful.

Next up, Conway’s Game of Life is a cellular automaton created by mathematician John Conway.  (It’s pretty fun: check out this to download the game, and this Munch where we introduce it.)  It’s discrete – each little unit of life is represented by a tiny square.  What if the rules that determine whether a new cell is formed or the cell dies were applied to a continuous domain?  Then, it would look like this:

Looks like a bunch of cells under a microscope, doesn’t it?  Well, it’s also a cellular automaton, devised by mathematician Stephan Rafler from Nurnberg, Germany.  In this paper, Stephan describes the mathematics behind the model.  If you’re curious about how it works, check out these slides that compare the new continuous version to Conway’s model.

Finally, I just got a pumpkin.  What should I carve in it?  I spent some time browsing the web for great mathematical pumpkin carvings.  Here’s what I found.

A pumpkin carved with a portion of Escher’s Circle Limit.

A pumpkin tiled with a portion of Penrose tiling.

A dodecapumpkin from Vi Hart.

I’d love to hear any suggestions you have for how I should make my own mathematical pumpkin carving!  And, if you carve a pumpkin in a cool math-y way, send a picture over to MathMunchTeam@gmail.com!

Bon appetit!

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!