- #1

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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!

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- Thread starter physior
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- #1

- 182

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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

Mark44

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Your question is too vague to answer.

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!

- #3

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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

- #4

Mark44

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How is the cylinder oriented? Is it horizontal or vertical?why you say so?

what else you need to know?

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?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?

These are some of the questions that came to mind when I said that your question was too vague to answer.

- #5

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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

- #6

Mark44

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This would make a difference if you filled the cylinder with some liquid. I thought that might be what you were after.what you mean how the cylinder is oriented? it doesn't matter, you just have a cylinder

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.physior said: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

A picture would be most helpful...

- #7

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This would make a difference if you filled the cylinder with some liquid. I thought that might be what you were after.

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

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.

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?

A picture would be most helpful...

here it is:

just imagine holes across the cylinder with walls as the lines you draw on the base

- #8

mathman

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http://en.wikipedia.org/wiki/Fractal

- #9

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ok, then, something more realistic please

- #10

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The lines you have in post 7 are strange. I do not see where the holes are.

- #11

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The lines you have in post 7 are strange. I do not see where the holes are.

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

- #12

jbriggs444

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I see only three closed loops in that picture. They overlap.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

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you must not be serious...I see only three closed loops in that picture. They overlap.

check again there are many more...

closed is a loop if it closes with the external margins of the cylinder base too

- #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.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

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.

- #15

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is this some kind of joke?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.

anyway, here is what I am after:

see below these square areas in the circle

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?

- #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?is this some kind of joke?

anyway, here is what I am after:

see below these square areas in the circle

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

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no constrains

don't overlap areas

do you even have the slightest idea of how to do the maths?

don't overlap areas

do you even have the slightest idea of how to do the maths?

- #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.no constrains

don't overlap areas

do you even have the slightest idea of how to do the maths?

The personal attacks are not appreciated.

- #19

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- #20

jbriggs444

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- #21

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can that be done?

- #22

jbriggs444

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You have to clarify the constraints we are operating under. For a rectangular grid, you were willing to offer the constraint that the lines could be no closer the 0.01 mm apart. But that constraint does not translate directly to a different tessellation.

can that be done?

To come up with an "optimum" you need two things:

1. A valuation function so that one can compare possible solutions. Apparently we are taking total perimeter of the individual figures in a tessellation as our valuation function.

2. The constraints or rules that must be adhered to. That would include things like a requirement to use straight lines, convex figures, minimum line spacing and the like. If one is not told the rules of the game, it is difficult to come up with the best strategy.

- #23

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there are no constrains basically, apart from the fact that the small areas must be 0.01mm^2

- #24

jbriggs444

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What stops me from dividing the cylinder into approximately 785,000 spiral slices each with 0.01mm

there are no constrains basically, apart from the fact that the small areas must be 0.01mm^2

- #25

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you cannot have spiral holes, I told you the holes are linear across the cylinder length

but let the cylinder thing, we were talking about the circle

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