

I am not a math expert; I never even took calculus. From reading the article, originally the question three centuries ago was whether or not a cube could be rotated in such a way that another identically sized cube could pass through it (like if a tunnel was cut in it). The answer turned out to be yes, although it’s very close. Then as mathematicians started investigating other shapes the answer kept being yes. Eventually the question became, “are there any shapes that can’t pass through themselves?” It’s hard to prove because there are so many angles that have to be checked. Recently mathematicians were able to prove that if you can rule out one angle, you can also then rule out a certain (varying) percentage of adjacent angles. Using that makes it easier to rule out more rotations and they’ve now found the first shape where they can definitively say it can’t pass through itself.




























Oh wow, that’s pretty decent pay in Knoxville! Tough to add 90 minutes of round trip travel on top of that, though. I wish you the best in that, and hope you’re able to find some steadier work as well. I kind of enjoyed it but being away from my wife and kid in the evening weighed on me after a while.