Monthly Archives: March 2012

Origami, Games, and the Huang Twins

Welcome to this week’s Math Munch!

Origami Whale

We’ve had a few posts (like this, this, and this) that included paper folding, but this week we really focus on doing it yourself.  Check out Origamiplayer.com, a terrific website that doesn’t just show you origami models.  It has an animator that folds them in front of you and waits for you to fold along with it.  I really like this origami pentagon, but there’s lots of designs and you can even sort them by type or difficulty.  You can change the speed or click around to different steps, so find a model you like and get folding!

Up next, meet the Huang Twins, 14-year old brothers from California.  Mike and Cary have been working as a team to design and program all kinds of great web stuff.  They actually have their own orgami animator to fold polyhedra.  But my favorite thing of theirs is The Scale of the Universe 2, an incredible applet that let’s you compare the sizes of all kinds of things big and small.  It uses scientific notation to describe the sizes, so if you’ve never seen that before, you might want to read up.  It’s genius.

They’ve also written several excellent games, which we’ve added to our Math Games page.  Cube Roll has a familiar format with a twist; The cube has to land on the correct side.  I really like that one.  No Walking, No Problem is another neat little puzzler.  Use the objects to move side to side, because you can’t walk!  Lastly, (though the Huangs didn’t write it) we’ve added Morpion Solitaire, a tough little game you can play online or on paper.

Bon appetit!

Cube Roll

No Walking, No Problem

Morpion Solitaire

(Beat, Beat, Beat…)

Welcome to this week’s Math Munch!

What could techno rhythms, square-pieces dissections, and windshield wipers have in common?

Animation in which progressively smaller square tiles are added to cover a rectangle completely.

The Euclidean Algorithm!

Say what?  The Euclidean Algorithm is all about our good friend long division and is a great way of finding the greatest common factor of two numbers. It relies on the fact that if a number goes into two other numbers evenly, then it also goes into their difference evenly.  For example, 5 goes into both 60 and 85–so it also goes into their difference, 25.  Breaking up big objects into smaller common pieces is a big idea in mathematics, and the way this plays out with numbers has lots of awesome aural and visual consequences.

Here’s the link that prompted this post: a cool applet where you can create your own unique rhythms by playing different beats against each other.  It’s called “Euclidean Rhythms” and was created by Wouter Hisschemöller, a computer and audio programmer from the Netherlands.

(Something that I like about Wouter’s post is that it’s actually a correction to his original posting of his applet.  He explains the mistake he made, gives credit to the person who pointed it out to him, and then gives a thorough account of how he fixed it.  That’s a really cool and helpful way that he shared his ideas and experiences.  Think about that the next time you’re writing up some math!)

For your listening pleasure, here’s a techno piece that Wouter composed (not using his applet, but with clear influences!)

Breathing Pavement

Here’s an applet that demonstrates the geometry of the Euclidean Algorithm.  If you make a rectangle with whole-number length sides and continue to chop off the biggest (non-slanty) square that you can, you’ll eventually finish.  The smallest square that you’ll chop will be the greatest common factor of the two original numbers.  See it in action in the applet for any number pair from 1 to 100, with thanks to Brown mathematics professor Richard Evan Schwartz, who maintains a great website.

Holyhedron, layer three

One more thing, on an entirely different note: Holyhedron! A polyhedron where every face contains a hole. The story is given briefly here. Pictures and further details can be found on the website of Don Hatch, finder of the smallest known holyhedron.  It’s a mathematical discovery less than a decade old–in fact, no one had even asked the question until John Conway did so in the 1990s!

Have a great week! Bon appétit!

Pi Digits, Pi-oetry, and Anti-Pi

This week’s Math Munch is brought to you by the number pi, because Wednesday (March 14th) is Pi Day!
 

Pi is an irrational number – meaning that it cannot be written as a ratio of integers.  Consequently, it’s decimal expansion goes on and on forever without any repeats.  But, that doesn’t mean people haven’t tried to list as many digits of pi as they can!  This site lists the first million digits of pi.  This site sings many of them – the tune is rather catchy.  And here you can search for strings of numbers in the decimal expansion for pi!  I searched for my birthday, 10/01/87 – it occurs 885,826 digits after the decimal point!

Remember the alphametics puzzle creator, Mike Keith?  Well, he writes poems and short stories in what he calls “Pilish,” in which the lengths of successive words represent successive digits of pi.  Here’s an explanation of the different forms of Pilish.  Mike holds the world record for the longest and second longest texts written in Pilish – they are his book, Not A Wake, and a short story, “Cadaeic Cadenza.”

Finally, as we celebrate pi on Wednesday, we should do so with some skepticism.  In the opinion of some mathematicians, pi is the wrong constant.  Inspired by this article by mathematician Bob Palais, some people have been speaking up in favor of the constant tau, which is double pi.  Here’s our favorite Vi Hart on the issue of pi:

You’ve heard what pi sounds like.  Want to know what tau sounds like?

Bon appetit!

Numberphile, Cube Snakes, and the Hypercube.

Welcome to this week’s Math Munch!

Each one of those pictures takes you to a math video.  Numberphile is a YouTube channel full of fantastic math videos by Brady Haran, each one about a different number.  Is one Googolplex bigger than the universe?  Why does Pac Man end after level 255?  Is 1 a prime number?  Click the numbers to watch the related video.  They also feature James Grime, one of my favorite math people on the internet.

Next up, let’s work on the Saint Ann’s School Problem of the Week.  You can read the fully worded question by following the link, but here it is in short:  If we start in the center, we can snake our way through the 9 small squares of a 3×3 square.  Can we snake our way through the 27 small cubes a 3x3x3 cube?  Can we do it if we start in the middle?

Can we snake our way through the 3x3x3 cube starting in the center?

There’s a new question posted every week (obviously), and if you check the Problem of the Week Archives, you can find more than 4 years of previous questions!  How many do you think we could solve if we did a 24 hour math marathon?

Finally, let’s have a mind-blowing look at higher dimensions.  The problem above is about whether a property of the square (a 2-dimensional object) can be carried over to the cube (its 3D counterpart).  So what is the 4-dimensional version of a cube?  The Hypercube!

The "cube" idea, from 1D to 4D

I’ve heard a lot of people say the 4th dimension is “time” or “duration,” but what would the 5th dimension be?  Well, here’s a video called “Imagining the Tenth Dimension.”  And if you’re hungry for more, there’s a series of 9 math videos called “Dimesions.”  All together it’s 2 amazing hours of math.  You can watch the first chapter online by clicking here.

Bon appetit!