Sphere Transformations

Posted by Isaac M. McPhee Mar 14, 2008

I was browsing the Scientific American website this evening when I came across a link to a video on youtube - a computer generated piece from 1994 - which claimed to do the impossible: To turn a sphere inside out without tearing or creasing it.

The video can be found here.

Be warned, unlike many other videos online, this one is somewhat lengthy (just over 20 minutes), but it remains interesting throughout. Apart from simply showing the transformation and leaving it at that, it takes great pains to explain just how it is that such a conclusion can come to, beginning with an explanation of turning a simple rubber band inside out, and following by showing each section individually as it solves the problem one step at a time.

Is it just me or does this problem feel eerily similar to one of those "coffee table" brain teasers with the rings that you have to pull apart or the pile of large nails that have to be balanced on just a single nail? It's a good thing that this problem cannot truly be performed in any "real" sense (apart from on a computer or on paper as mathematics), because I can imagine that it would drive me absolutely crazy if I actually attempted it.

In truth, this is one of those problems that may or may not have any direct relevence as far as applied math goes (though I could very well be wrong in this - having not done any research as of yet, it very well might have found some pragmatic value somewhere), but at the very least lends itself to helping one to appreciate some of the subtle nuances of mathematics.