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How to divide a cylinder

  1. Mar 23, 2015 #1
    hello

    I have a cylinder

    which and how many lines will I have to draw in its base to delimit holes that will run through it, so that I will maximize its internal surface?

    thanks!
     
  2. jcsd
  3. Mar 23, 2015 #2

    Mark44

    Staff: Mentor

    Your question is too vague to answer.
     
  4. Mar 23, 2015 #3
    why you say so?
    what else you need to know?
    you can take a cylinder 10cm diameter, if that's what you need to know
    I need to find the optimum diameter of the holes and the highest number of holes
    but holes may not be circular, they can be any shape

    you can do it for a circle, how many shapes you can draw in it to maximize the length of the lines in it
    and then we can integrate it
     
  5. Mar 23, 2015 #4

    Mark44

    Staff: Mentor

    How is the cylinder oriented? Is it horizontal or vertical?

    I don't understand what this means. How do lines drawn in its base delimit holes running through it? What does this have to do with maximizing its internal surface?

    These are some of the questions that came to mind when I said that your question was too vague to answer.
     
  6. Mar 23, 2015 #5
    what you mean how the cylinder is oriented? it doesn't matter, you just have a cylinder

    when you draw lines in the cylinder's base, you delimit holes, right? do you understand this? holes that run the cylinder across its length
     
  7. Mar 23, 2015 #6

    Mark44

    Staff: Mentor

    This would make a difference if you filled the cylinder with some liquid. I thought that might be what you were after.
    No, I don't understand this. If I have a circular cardboard cylinder, with circular top and bottom caps, I can use a pen to draw lines on the end caps. I don't see how these lines have anything to do with holes in the cylinder wall.

    A picture would be most helpful...
     
  8. Mar 23, 2015 #7
    yes, I may fill the cylinder with some liquid, but the orientation will have no effect at all, as the whole cylinder will be filled and not part of it, so that gravity and orientation could play a role, this is what you are saying? no, orientation doesn't matter

    well it's simple
    the lines you will draw are the walls of the holes, I said the lines delimit holes, isn't it simple to understand?

    here it is:

    upload_2015-3-23_20-25-33.png

    just imagine holes across the cylinder with walls as the lines you draw on the base
     
  9. Mar 23, 2015 #8

    mathman

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    Gold Member

  10. Mar 23, 2015 #9
    ok, then, something more realistic please
     
  11. Mar 23, 2015 #10
    The lines you have in post 7 are strange. I do not see where the holes are.
     
  12. Mar 23, 2015 #11
    yes, they are strange
    aren't there holes with strange lines?
    the holes are the white beween closed loops of these lines and the lines are the walls of the holes
    the holes as I numerous times said, are running through the cylinder across its length
    geez
     
  13. Mar 23, 2015 #12

    jbriggs444

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    I see only three closed loops in that picture. They overlap.
     
  14. Mar 23, 2015 #13
    you must not be serious...
    check again there are many more...
    closed is a loop if it closes with the external margins of the cylinder base too
     
  15. Mar 23, 2015 #14

    jbriggs444

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    No. A line that touches the wall is not a hole. That's a gap on the exterior of the cylinder.

    Edit: In any case, if you count the walls as possible boundaries for loops then the "holes" you have include the entirety of the cylinder. There would be nothing left.
     
  16. Mar 23, 2015 #15
    is this some kind of joke?

    anyway, here is what I am after:
    see below these square areas in the circle
    NjXtG.jpg
    how can I maximise the total perimeter of these sub-areas of the circle?
    simple question
    can anyone do it?
    what's the maths behind it?
     
  17. Mar 23, 2015 #16

    jbriggs444

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    Which sub areas? Just the square ones? Do we get to double-count the perimeter of four unit squares plus the perimeter of the two by two square that contains them? What about a 2 by 3 rectangular area? What constraints do we have on the number of lines that can be used?
     
  18. Mar 23, 2015 #17
    no constrains
    don't overlap areas
    do you even have the slightest idea of how to do the maths?
     
  19. Mar 23, 2015 #18

    jbriggs444

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    Subject to no constraints... there is no maximum total perimeter. Just draw lines in a grid as fine as you please.

    The personal attacks are not appreciated.
     
  20. Mar 23, 2015 #19
    ok then is there a preference of how the lines should be drawn to maximize the perimeter of the areas for a 10cm diameter cylinder and minimum 0.01mm space of area?
     
  21. Mar 23, 2015 #20

    jbriggs444

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    Still restricting our attention to a rectangular grid with straight lines but requiring a separation of 0.01 mm between each line? That's rather trivial. You are after an approximate formula for the achievable perimeter or a prescription for how to achieve it?
     
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