3 ms·
Something special about 7 cylinders or would this be equally hard/simple for 6 or 8 ?
by Zitrax 13y ago
Something special about 7 cylinders or would this be equally hard/simple for 6 or 8 ?
- SamReidHughes 13y agoIt gets harder and harder (and then impossible) the more cylinders you have.
- cousin_it 13y agoNow I wonder if there's a proof that it's impossible for 8...
- lotharbot 13y agoThere'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/S019566980800022X 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 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.
- acchow 13y agoThey all touch each other - if you have a solution for 7, you already have a solution for 6 (just remove a cylinder).