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Raise your hand if you’ve heard of M.C. Escher.  Now raise your hand if you know what tessellations are.

Surprise!  If you know of M.S. Escher’s work, you are also familiar with tessellations — even if you don’t recognize the term.  In fact, if you have or have seen a tiled floor, tessellations are familiar to you.

A tessellation is a pattern of identical, interlocking shapes.  There can be no space between the shapes and none of the shapes can overlap.  Escher created complex tessellations of birds, lizards and fish. But even simple, square tiles are tessellations.

This video shows how they are made.  Don’t watch it expecting a tutorial.  Just look at how the shapes are formed and then replicated and rotated to form the tessellation.  A design like this one is pretty complex, but it’s interesting to see it in motion.

(There is no sound with this video, so there’s no need to crank up your speakers.)

Bonus!  I found this really great video that shows how to make a tessellation.  Check it out.

Where have you seen tessellations?  When do you think they’re useful or interesting to see?  Leave your comment!

Photo courtesy of andreas.rodler

So, I’ve seen an abacus (or the plural, abaci), but until this video, I’d never seen one in action.

Now, I’m not a big fan of speed in math, but I have to admit this is pretty darned cool — especially when the kids imagine the abacus to solve problems without it.

But how does an abacus work?

There’s a great (though complex) explanation here.  But here’s the really cool thing: to use an abacus, you have to have a really strong, knee-jerk sense of numeracy.  So, it’s not so much a shortcut as a demonstration of a great understanding of math basics.

I’m not sure I could live with Ursus Wehrli.  A Swiss artist and comedian, his ideas of order are a bit extreme.  You’ve probably seen his carefully arranged bowl of alphabet soup:

This is basic set theory — and we started learning how to do it in kindergarten.  But take a closer look.  While Wehrli decided to put his letter-shaped pasta in alphabetical order with the carrots at the bottom, he could have chosen something different — say vowels first or grouping all of the letters with curves.  (Psst… this is one of those times when math is neither right nor wrong.)

While it’s easy to see how he arranged elements in sets for this picture, some of his other endeavors are a bit more complex.  See for yourself in this week’s Film Friday clip:

Now, what do you think?  What is the criterion for each set?  Give me your take in the comments section.

Over the last year, I’ve come across lots of great math-related videos, and now that my blog is up and book is out, people are sending me links to many more.  I thought Fridays would be a great time to share them.  So, welcome to the first edition of Film Fridays!

Today’s little clip comes courtesy of my mother-in-law, who majored in math and then went on to have a seriously incredible career as a sales representative for American Greetings.  She uses math like it’s a second language — no big deal, thankyouverymuch.  (She also makes the most amazing pies ever.)

Still, this clip is a bit geeky — as many math videos are.  What I encourage you to do, though, is find the artistry and magic.  There will be no quiz.  This is just for fun. (Details are below the clip.)

So while this looks absolutely magical, it really does boil down to some very simple math.  The length of the pendulum determines how far it swings, and that in turn determines how many swings (or oscillations) it can complete in a given period of time.  In plain English: a short pendulum swings faster than a long one.  So the smarty-pants at Harvard built this pendulum based on the design of University of Maryland physics professor, Richard Berg.  Here’s the nitty gritty, if you’re interested:

The period of one complete cycle of the dance is 60 seconds. The length of the longest pendulum has been adjusted so that it executes 51 oscillations in this 60 second period. The length of each successive shorter pendulum is carefully adjusted so that it executes one additional oscillation in this period. Thus, the 15th pendulum (shortest) undergoes 65 oscillations.

In other words: Pretty.

I am so excited to show you more videos!  I especially can’t wait to introduce you to Vi Hart, who does the most captivating math doodles you can imagine.  (Wait a minute, who else does math doodles?)  So check in next week. And if you have a video that you want to share, please send me the link: llaing-at-comcast-dot-net.

OMGoodness!  Two posts within the hour!

I can’t resist sharing this terrific video.  If you’re as addicted to Twitter as I am — or as I was two weeks ago, just not getting it — take a look.  This guy is funny, and, wow, can he draw!