Facebook Formulas

peak breakup timesThis graph on the right represents break ups per day, as determined by an analysis of Facebook status changes.  The data suggests that break-ups seem to occur most frequently in mid-February and late November.

Drawing conclusions from data is always dicey, and there are probably a lot of holes to poke in the methodology here, but it certainly is fun trying to attach meaning to these numbers!

This graph was featured in a TED Talk given by David McCandless, who runs the wonderful website www.informationisbeautiful.net.

The whole talk can be found here; this chart comes up at around the 6:50 mark.

The amount of data available through social networking sites is mindblowing, and it can’t be long before it will be used in some significant way.  Indeed, a group of MIT students has already devised a system, cleverly titled Project Gaydar, that, with some accuracy, identifies the sexual orientation of a Facebook user based on friends, likes, and other connections.

What will they compute about us next?

The Perfect Parallelepiped

In general, it’s unusual for a rectangle to have sides and diagonals whose lengths are all integers (i.e., whole numbers).  Consider the following three rectangles, all of width 3:

diagonals

Looking at the different lengths, we see one place where the diagonal length is an integer, but in the other cases, the diagonal length happens to be a non-terminating, non-repeating decimal (i.e., irrational).  Indeed, the diagonal length will be an integer exactly when the length and width are part of a Pythagorean triple, but compared to the alternative, this is uncommon.  (While there are infinitely many occurrences of this, we can still meaningfully consider it uncommon).

Now, imagine the situation in three dimensions.  A rectangular prism (think of a cardboard box) has 12 sides, 12 face diagonals, and four space diagonals.  It would be extremely unusual for all of those 28 lengths to be integers.  Even if we didn’t limit ourselves to rectangular prisms, but we allowed for the box to be slanted in all directions (that is, a parallelepiped), it would still be a numerical miracle for all those lengths to be integers.

Well, meet the perfect parallelepiped!

a perfect parallelepiped

This was discovered by a couple of mathematicians at Lafayette College in Pennsylvania, using brute-force computer trials.  It looks like they found some others, too.   So thank you, Clifford Reiter and Jorge Sawyer, for giving me an extra credit problem for my next exam!

Related Posts

Look Around You — Maths

funjy's mathsThis is a thoughtful and hilarious satire of old-school, British public television-style educational videos.

http://www.youtube.com/watch?v=Pj2NOTanzWI

I laughed repeatedly throughout.  Watch the video, and give it a minute or so to win to you over.  It’s worth it.

P.S.  Students–please do not bring razor blades, Garry Gum, or Anti-Garry Gum to class in your pencil case.

Thanks to Ivan R. for showing me this! 

I, RuBot

RuBotThis is a great video of RuBot, the Rubik’s cube solving robot!

http://www.youtube.com/watch?v=pOhU3WP7zXw

This video was shot at the Maker Faire, a sort of do-it-yourself science fair recently held in NYC.

Apparently you can scramble up the cube any way you like, and set it on RuBot’s platform.  RuBot picks it up, inspects the sides to determine the configuration, and then solves the cube!  RuBot must have been happy when it was recently announced that every position of the Rubik’s cube can be solved in 20 moves or less.

I’m not sure if Rubot can solve 4×4’s or 5×5’s cubes.  And I’m not sure why they made him look so creepy.

The Levytator

LevytatorFrom the “Why Didn’t I Think of This?” files comes the Levytator,

http://www.youtube.com/watch?v=iC_se2zrmLM

The Levytator is a more efficient and flexible take on the escalator.  It runs in a circuit, instead of conveyor-belt style, so you don’t lose half your steps to the useless, upside-down underground path, like in a traditional escalator.  Thus, you get more transportation per square foot of step.

In addition, the interlocking steps are curved and not rectangular, meaning that not only can the Levytator turn around corners, but essentially it can be designed to follow any kind of path a planner might need.

Be sure to check out the video for some cool demonstrations (which remind me a lot of closed-loop integrals).

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