Mathematicians find way to put 7 cylinders in contact without using their ends • Hacker News Board

Re: Mathematicians find way to put 7 cylinders in contact without using their ends

#11

Post by kenferry » Sat, Apr 05, 2014, 7:26 PM UTC

josh-wrale wrote: post #8

Manufacturing errors? I can't tell if this is plastic, but if it is, surely a machinist can do better with metal.

They're just saying that building it is not a proof - the computer simulation is more exact than the model, and even the simulation is subject to rounding errors in what is considered "touching".

Sounds like they used the computer to search for a proposed solution that _could_ have been a false positive due to rounding error, then verified it through exact mathematical methods.

Re: Mathematicians find way to put 7 cylinders in contact without using their ends

#12

Post by delinka » Sat, Apr 05, 2014, 7:27 PM UTC

josh-wrale wrote: post #8

Manufacturing errors? I can't tell if this is plastic, but if it is, surely a machinist can do better with metal.

By "errors" they mean "the minute imperfections created by molding, machining, carving, etc." The rounding errors in the computer model would produce smaller physical artifacts than the manufacturing method would.

Re: Mathematicians find way to put 7 cylinders in contact without using their ends

#13

Post by soneca » Sat, Apr 05, 2014, 7:29 PM UTC

Great design for a no-gravity space station.

Easy to go everywhere from everywhere.

Re: Mathematicians find way to put 7 cylinders in contact without using their ends

#14

Post by deckar01 » Sat, Apr 05, 2014, 7:31 PM UTC

laxatives wrote: post #10

Never seen this sort of thing before. Does this hold for an arbitrary radius? What if these were just lines in 3 space?

If lines are considered cylinders, they would have a radius of zero and cannot touch without intersecting.

Re: Mathematicians find way to put 7 cylinders in contact without using their ends

#15

Post by ColinWright » Sat, Apr 05, 2014, 7:32 PM UTC

laxatives wrote: post #10

Never seen this sort of thing before. Does this hold for an arbitrary radius? What if these were just lines in 3 space?

Arbitrary radius - just scale up and/or down as required.

Re: Mathematicians find way to put 7 cylinders in contact without using their ends

#16

Post by acchow » Sat, Apr 05, 2014, 7:34 PM UTC

Zitrax wrote: post #2

Something special about 7 cylinders or would this be equally hard/simple for 6 or 8 ?

They all touch each other - if you have a solution for 7, you already have a solution for 6 (just remove a cylinder).

Re: Mathematicians find way to put 7 cylinders in contact without using their ends

#17

Post by acchow » Sat, Apr 05, 2014, 7:35 PM UTC

laxatives wrote: post #10

Never seen this sort of thing before. Does this hold for an arbitrary radius? What if these were just lines in 3 space?

Intuitively, it seems that radius/length ratio is what's important here.

Re: Mathematicians find way to put 7 cylinders in contact without using their ends

#18

Post by saalweachter » Sat, Apr 05, 2014, 7:35 PM UTC

ebol4 wrote: post #3

Don't they just have to not be parallel?

In three dimensions, non-parallel lines do not necessarily intersect.

Re: Mathematicians find way to put 7 cylinders in contact without using their ends

#19

Post by aaronem » Sat, Apr 05, 2014, 7:36 PM UTC

soneca wrote: post #13

Great design for a no-gravity space station. Easy to go everywhere from everywhere.

I was going to make a vaguely snide comment about difficulty in routing and managing services (air, water, power, data, &c.), but the more I look at the model, the less firmly I'm convinced that there is an intractable topological problem involved.

I'm still going to go with calling it the Villa Straylight, though.

Re: Mathematicians find way to put 7 cylinders in contact without using their ends

#20

Post by 3rd3 » Sat, Apr 05, 2014, 7:36 PM UTC

soneca wrote: post #13

Great design for a no-gravity space station. Easy to go everywhere from everywhere.

I'd love to see a jungle gym in this shape. I would definitely climb it!