Members’ Seminar

You can make a paper Moebius band by starting with a $1$ by $L$ rectangle, giving it a twist, and then gluing the ends together. The question is: How short can you make $L$ and still succeed in making the thing? This question goes back to B. Halpern and C. Weaver in 1977. The previously known lower bound was $\pi/2$ and the previously known upper bound, conjectured to be the true answer, is $\sqrt{3}$. In my talk I will explain how to get the lower bound up to about $\sqrt{3}-1/26$, which is an improvement on $\pi/2$, and I will also explain show to reduce the question about the sharp upper bound to showing, a finite number of times, that some explicit piecewise algebraic function is non-negative on the unit cube in $14$ dimensions. (I'm working on the calculations...) These calculations have to do with geometrical properties of finite tensetrigies.