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.
Math idiot here. What’s the significance of a shape not being able to pass through itself?
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.
Thank you so much for the explanation. So, not necessarily for a practical reason, but as an exercise.
New kind of sewer cover? Shrugs.
That’s a physics question, not a maths question :)
Well, it’s definitely a maths question. Significance in mathematics may be mere curiosity, but is significance nonetheless.