Timeline for How do I arrange pencils so they all touch each other?
Current License: CC BY-SA 3.0
12 events
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| Aug 15, 2015 at 4:20 | comment | added | Deusovi♦ | @chaslyfromUK: If the pairs aren't parallel, then they cannot touch each other. I'm not assuming that they're placed on a surface at all. If one of the pencils up there is not parallel to the one next to it, then it can't be touching the other ones because it'd be above or below them! And if two of the planes defined by the pairs of pencils are not parallel, then we have the same problem that I originally mentioned. | |
| Aug 14, 2015 at 21:39 | comment | added | chasly - supports Monica | @Deusovi - Okay. The problem for me with that is that you have added your own constraint - that the pairs have to be parallel. Again I say that that's only necessarily true on a perfectly flat table with frictionless pencils. If the table was even slightly bumpy then you could arrange it so certain pencils were lifted up slightly at the ends. The desired result is achieved by adjusting just one of each pair. Seen from above the non-parallel status of the pencils and the non-flatness of the table wouldn't show. Alternatively my suggestion of inter-pencil force would achieve the same thing. | |
| Aug 13, 2015 at 18:44 | comment | added | Deusovi♦ | @chaslyfromUK Sorry for being unclear - a bundle is just two pencils next to each other. Two parallel lines define a plane, so each "bundle" has its own plane defined by the centers (where the lead is in the pencils). Because the pencils are touching, the lead between two touching bundles has a consistent vertical distance, meaning the planes defined by touching bundles are parallel. The three planes are parallel and a fixed distance apart (because the pencil widths are constant), so the outer bundles cannot touch. | |
| Aug 13, 2015 at 15:36 | comment | added | chasly - supports Monica | @How do you define a 'bundle'? I still can't get what you mean. I cannot understand 'four pencils in two bundles'. | |
| Aug 13, 2015 at 15:33 | comment | added | Deusovi♦ | @chaslyfromUK By that I just mean that all four pencils in two bundles are touching all the others. | |
| Aug 13, 2015 at 15:32 | comment | added | chasly - supports Monica | @Deusovi - There is no requirement in the question that the pencils 'fully touch'. In fact I cannot imagine what that could mean. Can you define the term? | |
| Aug 13, 2015 at 15:17 | comment | added | Deusovi♦ | @ChaslyfromUK: Actually, yes. I can prove my objection. For two 'bundles' of two pencils to fully touch, they must be on parallel planes. But if all three planes are parallel, the two not in the middle must not be touching because they're too far apart. | |
| Aug 13, 2015 at 10:52 | comment | added | chasly - supports Monica | @Deusovi - That's only an accident of the shape of the underlying surface. There was no restriction on that in the question. Assume that pencils have an inter-pencil force that securely holds them together yet allows you to manipulate them. Suppose you do the problem in orbit with no underlying surface. Can you prove your objection then? I think not. :-) | |
| Aug 13, 2015 at 7:39 | review | Late answers | |||
| Aug 13, 2015 at 8:45 | |||||
| Aug 13, 2015 at 7:32 | comment | added | Deusovi♦ | They don't touch exactly. There would be a bit of space between the two pencils going diagonally like this [/] and the far right pencil that's almost vertical. | |
| Aug 13, 2015 at 7:24 | review | First posts | |||
| Aug 13, 2015 at 7:36 | |||||
| Aug 13, 2015 at 7:23 | history | answered | Reuven | CC BY-SA 3.0 |