Museum of Maths opening in NYC http://momath.org/ 11 East 26th Street in Manhattan video: http://www.youtube.com/watch?v=jK7xPo1YXzY The video gives the impression this math museum is really more of a giant work of art than math per se. Two errors: 0:43 "a minimum spanning tree, the shortest possible way to ensure everyone is connected." Actually, the Steiner Minimum Tree is the shortest, and is in general shorter than the MST. Which incidentally is a highly interesting unfinished story. In any metric space, the SMT can be at most a constant factor shorter than the MST. The constant factor was exactly determined by F.Hwang & D.Z.Du in the plane; it is achieved for 3 sites forming equilateral triangle. However, many years later, it was pointed out that their proof is broken. Their result is probably true but remains conjectural. In 3-space yours truly made the conjecture the constant factor is achieved by a certain helical point set I call the "d-sausage" with d=3. This conjecture is also open. If d>=3 Du and I disproved the conjecture the constant arises from d+1 points in d-space forming a regular simplex, and our paper gave 3 disproofs. It was just recently pointed out that 2 out of our 3 disproofs are wrong. My disproof based on the d-sausage is the correct one; Du's disproofs were based on a "packing principle" which was refuted. It now might be conjectured if you are brave, that the d-sausage is optimal in d-space for every d>=3; Du had given an argument this should stop being true for large-enough d, but his argument is wrong since based on packing principle. 3:42 the Reuleaux triangle has constant WIDTH ("constant diameter" is a triviality, every shape has constant diameter). It can be used to drill an almost-square hole. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)