Tuesday, December 25, 2012

Six pointed stars -- just in time for the holidays!

So I'm on vacation in Maine where it was snowing today, and we took my little one for a walk in the snow.  A perfectly formed little snowflake fell on his eyelash, and we all just stood around and stared at him for a few minutes while it melted.  It was so beautiful!  I'd never been able to see that symmetry so well with my naked eye.  We took a picture, but it just didn't do it justice.
   Anyway, it reminded me of a book I'd seen once that would make a great gift.  The book contains snowflake photos taken and explanations by Caltech physicist Kenneth Libbrecht.  Apparently photographing snow is an expensive hobby, costing over a thousand dollars, not to mention you need to keep your camera warm!
   Then I just happened to see this wonderful video made by George Hart, Vi Hart's father and also one of the designers of many of MoMath's new exhibits.  The key in understanding what is obtained when you slice the Menger sponge in half along its diagonal is that we can view a star of David as being the union of three Rhombi, not just two equilateral triangles.  This different way of constructing the Star of David was exploited by an artist I recently saw at Tucson's 4th Avenue Street Fair.  Unfortunately, I can't find his site!  But the general idea can be seen in this basic picture I made.
It's just amazing to me how the things I see in everyday life sometimes link together in these nice ways... Anyway, there's a lot of six fold symmetry going on just in time for the holidays.

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