# Cylinder placing...

royalchicken
Posers and Puzzles 20 Mar '03 22:24
1. royalchicken
CHAOS GHOST!!!
20 Mar '03 22:24
Suppose you wish to place 7 equally-sized cylinders of length l and diameter d in such a way that they all touch each other. What is the largest value of l/d such that this is impossible?
2. richjohnson
TANSTAAFL
21 Mar '03 18:12
Originally posted by royalchicken
Suppose you wish to place 7 equally-sized cylinders of length l and diameter d in such a way that they all touch each other. What is the largest value of l/d such that this is impossible?
Do you mean that they all touch at least one other cylinder? or that they each touch every other cylinder?
3. royalchicken
CHAOS GHOST!!!
21 Mar '03 18:25
Each touches every other. I haven't even tried this puzzle yet, and I don't know the answer, but I think I'll give it a go.
4. royalchicken
CHAOS GHOST!!!
22 Mar '03 15:09
I've solved it. Anyone else? Ideas...?
5. 24 Mar '03 21:07
20
6. royalchicken
CHAOS GHOST!!!
24 Mar '03 21:54
Erm...no. How did you arrive at that?
7. bbarr
Chief Justice
24 Mar '03 22:08
Originally posted by royalchicken
Erm...no. How did you arrive at that?
Perhaps Fregean 'flash-grasping' of necessary truths?
8. royalchicken
CHAOS GHOST!!!
25 Mar '03 01:151 edit
Actually, ingenuity and trigonometry suffice. Are you guys going to give it a go, or wait around for Acolyte ðŸ˜‰?
9. bbarr
Chief Justice
25 Mar '03 02:09
Originally posted by royalchicken
Actually, ingenuity and trigonometry suffice. Are you guys going to give it a go, or wait around for Acolyte ðŸ˜‰?
Not me, the only interest I have in mathematics consists in its reduction to first-order logic with identity and set-theory. I'm a foundational type of guy.ðŸ˜€
10. royalchicken
CHAOS GHOST!!!
25 Mar '03 21:50
Ah. Pity. You'd be good at it. My chief interest in mathematics is currently analytic number theory. They don't teach THAT in school ðŸ˜‰.
11. royalchicken
CHAOS GHOST!!!
28 Mar '03 19:33
No takers? Acolyte?
12. Acolyte
29 Mar '03 09:05
Originally posted by royalchicken
No takers? Acolyte?
Erm... I don't have the dexterity to construct a physical model with biros, and I can't really picture how the 7 cylinders are arranged, much less prove that they have to be arranged in a particular way. ðŸ˜•
13. royalchicken
CHAOS GHOST!!!
30 Mar '03 02:081 edit
A wee hintie: 7 cylinders is the largest number for which this can be done (easy to prove), and there is only one configuration (consider that as fact; it is). To visualize it, use unsharpened pencils, or cigarettes, or just draw them (that's what I did-probably the easiest). Figure out 3, then 4, etc. Then look at limiting positions.

What is a biro?
14. 06 Apr '03 17:55
Originally posted by royalchicken
A wee hintie: 7 cylinders is the largest number for which this can be done (easy to prove), and there is only one configuration (consider that as fact; it is). To visualize it, use unsharpened pencils, or cigarettes, or just draw them (that's what I did-probably the easiest). Figure out 3, then 4, etc. Then look at limiting positions.

What is a biro?
A biro is a very cheap pen, a ballpoint oen
15. randomperson
Ruler of Insanity
06 Apr '03 18:05
can't u just fit them into a hexagon and let them be any size?