Seven, eight, and nine mutually touching infinitely long straight round cylinders: Entanglement in Euclidean space · HackerPapers discussions

Seven, eight, and nine mutually touching infinitely long straight round cylinders: Entanglement in Euclidean space — mentioned by Someone

Sat, 05 Apr 2014 20:14:01 GMT

About "just cool" thing: that discussion has been done a zillion times. On the one hand, it's just one of those funny problems: easy to describe, but far from simple to solve. On the other hand, I would say that mathematicians have earned the right to work on such silly problems, given that, if hey hadn't worked on similar silly problems before, our technology would be quite a bit less advanced. Half the world is built on the hobbies of mathematicians. What surprised me is that http://arxiv.org/abs/1312.6207 (which gives solutions with 8 and 9 cylinders, if one let's go of the constraint that…

Paper and discussion history. A mention is not an endorsement.

Seven, eight, and nine mutually touching infinitely long straight round cylinders: Entanglement in Euclidean space — mentioned by lotharbot

Sat, 05 Apr 2014 19:25:29 GMT

There's an arrangement of 8 that's very close to touching, but has been proven to not actually touch: http://www.sciencedirect.com/science/article/pii/S0195669808... Others believe they have found both an 8 and a 9: http://arxiv.org/pdf/1312.6207.pdf though this may not be exactly the same problem. In particular, the 9 cylinder problem allows 3 radii to be selected and then the other 6 are calculated as a result (meaning the 9 are probably not all identical.) It appears the 7 result in the initial paper is 7 cylinders of equal radius.

Paper and discussion history. A mention is not an endorsement.