Mathematicians find way to put 7 cylinders in contact without using their ends
1–10 of 87 posts
Re: Mathematicians find way to put 7 cylinders in contact without using their ends
#2Something special about 7 cylinders or would this be equally hard/simple for 6 or 8 ?
Re: Mathematicians find way to put 7 cylinders in contact without using their ends
#3Don't they just have to not be parallel?
Re: Mathematicians find way to put 7 cylinders in contact without using their ends
#4Something special about 7 cylinders or would this be equally hard/simple for 6 or 8 ?
It gets harder and harder (and then impossible) the more cylinders you have.
Re: Mathematicians find way to put 7 cylinders in contact without using their ends
#5Don't they just have to not be parallel?
No, your thinking 2D lines, but this is 3D space. It's easy to arrange things so they all miss each other and not have them be parallel. The goal is to have them touch, but not intersect.
Re: Mathematicians find way to put 7 cylinders in contact without using their ends
#6Re: Mathematicians find way to put 7 cylinders in contact without using their ends
#7Don't they just have to not be parallel?
Nah, not quite. You want every cylinder touching all 6 other cylinders and not going through them.
Re: Mathematicians find way to put 7 cylinders in contact without using their ends
#8Manufacturing errors? I can't tell if this is plastic, but if it is, surely a machinist can do better with metal.
Re: Mathematicians find way to put 7 cylinders in contact without using their ends
#9Earlier quoted context omitted.
It gets harder and harder (and then impossible) the more cylinders you have.
Now I wonder if there's a proof that it's impossible for 8...
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.
Re: Mathematicians find way to put 7 cylinders in contact without using their ends
#10Never seen this sort of thing before. Does this hold for an arbitrary radius? What if these were just lines in 3 space?