1 Sep
2009
1 Sep
'09
10:23 a.m.
On Aug 31, 2009, at 6:25 PM, Fred lunnon wrote:
Looks like we're the only two left, Mike --- did we miss Armageddon? WFL
Yes, and it's called "start-of-the-semester". But here's something for torus fans: Can the Minkowski sum of two smooth closed curves in R^3 ever be a smooth torus? If you don't know what a Minkowski sum is, let x(s) and y(t) be smooth closed curves in R^3 parameterized on the unit interval. Now consider the set z(s,t) = x(s) + y(t), (s,t) in [0,1]^2. Question: can you find an x(s) and y(t) so z(s,t) is a smooth surface for all (s,t) in [0,1]^2 ?