Links from one of the best riddle website : http://www.wuriddles.com/cigarettes.shtml
Cylinder Length | Max cylinders that can touch | Min cylinders that can touch
Infinite | 7 | 5
Actual | 9 | 7
L=D | 4 | 4
Mathematicians find way to put 7 cylinders in contact without using their ends
41–50 of 87 posts
Re: Mathematicians find way to put 7 cylinders in contact without using their ends
#42Question I've not found the answer to:
It's possible to have 7 arbitrarily long cylinders
mutually touching. Currently it's not possible to
have more than 5 coins (which are short cylinders)
mutually touching. As the cylinder's aspect ratio
decreases, where are the thresholds: 7 -> 6 -> 5 ?Re: Mathematicians find way to put 7 cylinders in contact without using their ends
#43This sort of reminds me of: http://en.wikipedia.org/wiki/G%C3%B6mb%C3%B6c Because it is a 3D object that was found using mathematics. Any other examples? I think there are lots of new objects discovered in higher dimensions, but I like when there is something you can actually build and see. I also like how it appears to be very asymmetrical.
The Klein bottle is sort of like that, only it's supposed to be in 4 dimensions, but the 3d version is still pretty cool and quite famous!
http://en.wikipedia.org/wiki/Klein_bottle
Never heard about the gomboc before, thanks!
Re: Mathematicians find way to put 7 cylinders in contact without using their ends
#44This is going to sound like trolling, but it's not - I'm honestly curious. Why is this important? Is it just cool, or is there some real world application? Was someone paying for this research for some reason, or was it just a mathematician's hobby? EDIT: For the record, I don't have any problem with "just cool" research. I do that kind of research often (albeit, not as smart), and totally understand the value in it.…
I believe this result has important applications in cylindrical stack encryption; it's very difficult to produce a solution, but very easy to verify a given solution.
Brb, I'm gonna create CylinderCoin.
Re: Mathematicians find way to put 7 cylinders in contact without using their ends
#45Earlier quoted context omitted.
Surely mathematicians would use rationals[1] rather than floating point numbers, thus eliminating rounding errors at the expense of performance? [1] https://gmplib.org/
It is not a matter of rational numbers, since the solution is likely to be an irrational number. The paper [1] describes a system of 20 polynomial equations with 20 variables (Equations 10--12) and solving them is no trivial task. To the end, authors first numerically found candidate solutions up to some ten decimal digits [2] and used specialized tools to prove (!) that there exists a real solution sufficiently clos…
Interesting. I would have thought that one could solve such things exactly by representing each unique known irrational that arises (root 2, pi, etc) by its own rational multiplier, and then overloading the relevant equality checks. Of course, you'd need to anticipate/implement each irrational type that might arise (roots, the geometric transcendental pi, and so on.)
[Leaving the next sentence in, for comedy value. I typed it and then realised how ridiculous it is - apologies!]
Essentially it's just teaching the computer to do the algebra for you, isn't it?
Re: Mathematicians find way to put 7 cylinders in contact without using their ends
#46This is going to sound like trolling, but it's not - I'm honestly curious. Why is this important? Is it just cool, or is there some real world application? Was someone paying for this research for some reason, or was it just a mathematician's hobby? EDIT: For the record, I don't have any problem with "just cool" research. I do that kind of research often (albeit, not as smart), and totally understand the value in it.…
I believe this result has important applications in cylindrical stack encryption; it's very difficult to produce a solution, but very easy to verify a given solution.
You jest, but your comment made me think of what an impressive Enigma machine [1] such an arrangement of rotors could make. The tubes are slipping in contact, so it'd have to be electrical linkage rather than mechanical to conduct the flow of the data.
Re: Mathematicians find way to put 7 cylinders in contact without using their ends
#47 they built a wooden model to demonstrate their answer — although Bozóki notes
that the model doesn’t verify the result because manufacturing errors
are much greater than any errors the computer could have made.
Re: Mathematicians find way to put 7 cylinders in contact without using their ends
#48Links from one of the best riddle website : http://www.wuriddles.com/cigarettes.shtml Cylinder Length | Max cylinders that can touch | Min cylinders that can touch Infinite | 7 | 5 Actual | 9 | 7 L=D | 4 | 4
Those "max" values are speculation, while the "Min" values are for definite because there are constructions. So that table is of less value than you might think.
Re: Mathematicians find way to put 7 cylinders in contact without using their ends
#49they built a wooden model to demonstrate their answer — although Bozóki notes that the model doesn’t verify the result because manufacturing errors are much greater than any errors the computer could have made. What's the point, when its not practically possible?
The wooden model "works", eg they all touch. But it could be slightly less than perfect and you wouldn't be able to tell, mathematicians care about these things :)
Re: Mathematicians find way to put 7 cylinders in contact without using their ends
#50[deleted]