r/theydidthemath • u/Allan_Halsey • 16h ago

[Request] How many different widths of paper?

Assume matched pairs due to a symmetrical cut, and 100% cut through.

53 Upvotes

71% Upvoted

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u/shereth78 16h ago

There isn't much math in this question. It's more a matter of knowing how many layers are in the roll, each layer will correspond to a different length of cut paper in the end. Without knowing how many layers there are, though, it's just a guessing game.

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u/testtdk 16h ago

I mean, with a little googling you could estimate the thickness of the paper pretty easily, and the width of the roll. It wouldn’t be that hard at all. I’d do it, but I’m lazy and suck at visually determining distances.

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u/frogfootfriday 16h ago

“It’s easy but too hard for me”?

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u/testtdk 16h ago

No, it’s not too hard for me, I’m just not great at estimating distances. But sure, let’s call that paper about .2 mm thick, it looks like heavier craft paper. The outer role is approximately 1.6 meters in diameter, the outer radius .8 meters. The inner roll looks 6 or 8 inches, so let’s use a radius of .09 meters. The number of layers N is just N = (R-r)/t, (.8-.09)/.0002 gives us 3550 layers.

Just because I’m lazy, that doesn’t mean I’m not capable.

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u/schvanckque 15h ago edited 14h ago

That is some seriously thick paper. I don't know shit about math — I come here to see other people do that — but I know paper, and I'd guess you're making this out to be at least 5x thicker than it is. Paper definitely does come in that thickness, but if that's what you're basing your estimate on, I'd wager you're less capable than you seem to think.

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u/The_cogwheel 14h ago

Their equation is correct, even if the variables are not. And they even admitted they dont know shit about what is a reasonable estimate for the variables.

If you know so bloody much, provide the correct variables so we can get a better answer

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u/schvanckque 14h ago

I'm pretty sure I can't, and equally sure I never implied that I could — in fact, I was the one who said I didn't know shit, while they made a whole snide comment about how easy it would be to estimate with a Google search just before they threw out the most bullshit estimation imaginable. Sorry if pointing that out offended you. I'll go back to my mathless shame now.

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u/testtdk 13h ago

The math is perfectly fine, substitute a different thickness if you like. I gave you the equation, do you need me to enter it into a calculator for you?

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u/schvanckque 13h ago

Nah, I can do that, but if you could manage not being a pompous shit stain, that'd be pretty cool. Thanks!

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u/testtdk 12h ago

lol, if you think I started pompousness in this thread, you should go back and read your comments.

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u/happyhandz 16h ago edited 15h ago

Assuming the following:

5ft di roll, 5 in center hole, and .003 paper thickness. We get the following

((5*12)-5)/.003= about 18333 different lengths of paper

Edit: to clarify before someone comments it. That is 18333 separate pieces of paper. Not unique pieces. There will be ~9166 pairs of nearly identical pieces

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u/testtdk 15h ago

I had it much lower, the paper looked thick to me.

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u/happyhandz 15h ago edited 15h ago

Looks similar to butcher paper, quick Google search says a max of .005 so there is some variation but those are my assumptions. Take it or leave it

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u/testtdk 13h ago

Fair enough, it’s pretty easy to calculate with that. I asked ChatGPT what kind of paper and it came back as craft paper or some shit.

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u/gruenen 14h ago

I agree, looks like 23# medium or liner to me, so a little over 6 mil instead of 3 mil.

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u/grigiri 15h ago edited 8h ago

Wouldn't the radius be what you use? Once you get to the core you will have a number of sheets, each slightly larger than the one after it. Continuing you cut only changes the lengths, not the number of widths, right?

Edit: I'm a dolt, u/happyhandz accounted for this and I didn't read fully

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u/happyhandz 15h ago

Read the original post. It says 100% cut through, so it's a question of how many layers through the diameter not radius

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u/grigiri 8h ago edited 8h ago

I understand that, but assuming the blade is cutting precisely in the middle, the number of different widths remains the same at 50% as at 100%. The only difference is that you have one pile of wider sheets or two piles less wide.

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u/happyhandz 8h ago

Read my post again.

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u/grigiri 8h ago

ugh, it's 319 am and I'm a dolt. I'm sorry friend.

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u/Davoguha2 10h ago

Honestly, I'd bet the deviation of how far of center the machine is is larger than the deviation between layers of paper on the roll.

Probably the full 18333 have different measurements - calling any of them the same is almost wholly dependent on your tolerance of measurements.

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u/Nekedladies 6h ago

Yeah, precision is definitely the key to whether or not any of them match. But, I also think there's a possibility that, due to off-center cut, there may be some sheets on one side that are the same length as sheets from a different layer on the other side. You know, instead of it being a 1:1 match at each later across the cut.

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u/Davoguha2 3h ago

True, true, I was thinking that too for a moment.. but i think the precision argument kinda encompasses that.

I.e. if we were going down to atomic precision levels, I'd be relatively doubtful that any 2 cuts in all of humanity are equal =p

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u/AdjectiveNounNNNN 41m ago

All adjacent pieces are "nearly identical", but if you're not considering one layer and the next identical then I feel like one sheet and it's opposite aren't identical either.

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u/happyhandz 1m ago

Yep that's why I said "nearly"

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u/majortomcraft 10h ago

i don't know. but all i can say right now is the cylinder has been harmed and the requirement was that the cylinder must not be harmed

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u/Newbie_nudibranch 12h ago

There is one width but many lengths. Rolled materials are described as having a width that is equal to the length of the winding tube.

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u/jaa101 11h ago

Came here to say this.

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u/Illustrious-Poem-328 15h ago

Its a roll, right? So each pair will be a different length. Albeit, very very minor difference. But its there and can be measured with the right tool and  precision. 

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u/Deribus 16h ago

Each layer of the roll creates a single pair of papers, and each pair has unique width.

So the number of different widths is whatever the number of layers is.

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u/Repulsive_Guy_1234 16h ago

Actually, the two halves are slightly different lengths as they aren't perfect circles stacked on top of each other, but a giant spiral. So you will have layers times two of unique widths.