Originally posted by royalchickenDo you mean that they all touch at least one other cylinder? or that they each touch every other cylinder?
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?
Originally posted by royalchickenNot 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.😀
Actually, ingenuity and trigonometry suffice. Are you guys going to give it a go, or wait around for Acolyte 😉?
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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?
Originally posted by royalchickenA biro is a very cheap pen, a ballpoint oen
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?