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Thread: 7 Folds

  1. #1 7 Folds 
    Moderator Moderator AlexP's Avatar
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    I've read that you can never fold a piece of paper in half more than 7 times. I've tried it, and it's true. Mathematical reason for this?


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    The mathematical answer is that it is not impossible.

    Go here

    http://pomonahistorical.org/12times.htm

    to know the truth.


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    Everything the laws of the universe do not prohibit must finally happen.
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    I've read that you can never fold a piece of paper in half more than 7 times. I've tried it, and it's true. Mathematical reason for this?

    This is good. Let me understand this. You have tried this how many times, starting with how many different sizes of paper, of how many different thicknesses, and with how much determination and skill?


    The pure experimental approach to proving that something *NEVER* works is just fascinating to me.
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    I remember a tv programme heard this one- I thought it was true as I couldnt get more than folds either. So they took a huge sheet if thin paper and managed to fold it 9/10 times, so more is possible but not much more!
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    The Mythbusters dealt with this one. They managed it. You'd have to watch the episode to get all the details though.
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    HA HA i managed an 11fold with tissue paper though xP
    cause tramps like us, baby, we were born to run
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    It depends on what type of paper you are using, or how you are folding it. If you are using a typical piece of paper (8" X 11"), then it is not possible to fold it in half more than seven times because every time you fold it, it becomes much thicker and smaller. It's thickness rises exponentially, thereby making it that much harder to fold. Folding it adds extra layers. If you fold it in half twice, it has 2^2 layers, which is 4. If you fold it 7 times, you then have to fold 2^7 layers, which is 128 layers thick!

    Mythbusters is not necessarily the best source. The piece of paper they used was the size of a aircraft hangar, and even then they had to use machines to fold it more than 7 times.
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  9. #8  
    Forum Ph.D. Nevyn's Avatar
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    Size doesn't matter when folding a peice of paper. Mythbusters has proven it by use of machines, no where was it said that you couldn't
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    Size and type of paper does matter. The smaller it is, it becomes much harder to fold, especially if it is very thick. After a certain point, it becomes so thick that it can't be folded no matter how much you try to squeeze it. Also, keep in mind that the height of the paper doubles each time it is folded.

    A regular sheet of paper, such as the standard 8" x 11", can't be folded any more than 7 times. What was debunked, first by Britney Gallivan and then later confirmed by others, was that paper of any size and any thickness cannot be folded more than 7 times. She managed to fold a long strip of toilet paper more than 12 times, and derived equations for it:



    where L is the minimum possible length, n is the number of folds possible, and t is material thickness.

    The other method that we are familiar with is the alternating one, which is:



    Where W is the width, and n is the number of folds.

    Source: http://pomonahistorical.org/12times.htm


    The Mythbusters cheated because they used an enormous sheet of very thin paper, and even then they had to use machines to do it.

    And the reasons it becomes so difficult is as I stated before, because the thickness increases exponentially with each fold.
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    Quote Originally Posted by Corona
    The Mythbusters cheated because they used an enormous sheet of very thin paper, and even then they had to use machines to do it.
    earlier in your post you put that size and thickness of the paper doesn't matter, pray tell which do you believe because you have just contradicted yourself
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    Quote Originally Posted by Nevyn
    Quote Originally Posted by Corona
    The Mythbusters cheated because they used an enormous sheet of very thin paper, and even then they had to use machines to do it.
    earlier in your post you put that size and thickness of the paper doesn't matter, pray tell which do you believe because you have just contradicted yourself
    No, what I said was:

    Quote Originally Posted by Corona
    It depends on what type of paper you are using, or how you are folding it. If you are using a typical piece of paper (8" X 11"), then it is not possible to fold it in half more than seven times because every time you fold it, it becomes much thicker and smaller. It's thickness rises exponentially, thereby making it that much harder to fold. Folding it adds extra layers. If you fold it in half twice, it has 2^2 layers, which is 4. If you fold it 7 times, you then have to fold 2^7 layers, which is 128 layers thick!
    I did not contradict myself, you just misinterpreted.
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    Quote Originally Posted by Corona
    Size and type of paper does matter.
    point proven?
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    Quote Originally Posted by Nevyn
    Quote Originally Posted by Corona
    Size and type of paper does matter.
    point proven?
    Not sure what you mean, but if you are asking whether or not I can prove that statement, then look at the equation.

    Also, as I said before, when you fold a piece of paper in half, you are adding height and decreasing its length and width. Each fold doubles the height, and makes it more difficult to fold layers in half. How much height is added depends on thickness of the paper. Eventually you reach a physical limit to how much it can be folded because of its proportions.
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    Well, this topic doesn't really belong in Math, in my opinion. There may be something I'm missing, but.....

    Let A be the area of an element in R<sup>2</sup>, call it a piece of paper if you like. Let n count the number of equal subdivisions of A. Then evidently, for some subset a of A, a = A/2<sup>n</sup> (remembering that 2<sup>0</sup> = 1 and 2<sup>1</sup> = 2, whereby for n = 0, a = A, for n = 1, a = A/2 and so on....)). There is no rule, as far as I can see, that says the sequence A/2<sup>n</sup> terminates on n = 7.

    Obviously there may be physical considerations, but these are not, or should not be, a consideration in a math sub-forum.
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    Quote Originally Posted by Corona
    Size and type of paper does matter.
    Quote Originally Posted by Corona
    The Mythbusters cheated because they used an enormous sheet of very thin paper, and even then they had to use machines to do it.
    The 'point' was that you contradicted yourself in the same post. (see above)
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    Quote Originally Posted by Nevyn
    Quote Originally Posted by Corona
    Size and type of paper does matter.
    Quote Originally Posted by Corona
    The Mythbusters cheated because they used an enormous sheet of very thin paper, and even then they had to use machines to do it.
    The 'point' was that you contradicted yourself in the same post. (see above)
    How is this a contradiction? I said they "cheated" because if you watched the show carefully, they originally set out to fold a regular sheet of paper in half, which they couldn't.

    You have to remember that the Mythbusters will sometimes create the conditions necessary if some "myth" is otherwise impossible, or if they screwed up, and even with these conditions it still may not be possible. Paper folding isn't the only one in which they did this.
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  18. #17  
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    *bashes head against keyboard* Can anyone else explain the contradiction that I have shown? :?
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  19. #18  
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    since the number of possible folds is dependant on the size and thickness of the paper, probably to a lesser extent how accurate and with what strength the folds were made, mythbusters didn't cheat. using a bigger and thinner piece of paper with a machine that could make accurate and good folds is just changing the variables.

    problem is myths seem to be told in many different ways.
    it could have been said that, "you can't fold a sheet of paper more than 7 times," or that "you can't fold an A4 sheet of printer paper/regular paper more than 7 times."

    ohh how silly it feels to write so much on folding paper.
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    Yeah, but the myth that they were trying to disprove was that you couldn't fold a normal sheet of paper, which was the standard 8" x 11", in half more than seven times. In fact, they weren't even able to fold a large sheet of paper in half more than 7 times.

    The sheet of paper they used was not a single sheet, rather it was a bunch of large sheets put together. Not only that, but it was much thinner than regular paper. That's how they cheated. I mean, come on, of course a sheet like that is going fold more than 7 times. However, as I stated before, the number of folds depends on the type of paper and its size, its dimensions and how you are folding it. I don't see where you are getting a contradiction out of this.

    Quote Originally Posted by wallaby
    problem is myths seem to be told in many different ways.
    it could have been said that, "you can't fold a sheet of paper more than 7 times," or that "you can't fold an A4 sheet of printer paper/regular paper more than 7 times."

    ohh how silly it feels to write so much on folding paper.
    Yeah thats true. But I think the question here was how many times you could fold paper in half.
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  21. #20  
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    Quote Originally Posted by Corona
    Yeah, but the myth that they were trying to disprove was that you couldn't fold a normal sheet of paper, which was the standard 8" x 11", in half more than seven times. In fact, they weren't even able to fold a large sheet of paper in half more than 7 times.The sheet of paper they used was not a single sheet, rather it was a bunch of large sheets put together.
    well that was silly of them, if they just connected a whole lot of regular sheets then they only achieved folding lots of regular sheets 7 times as opposed to 1 large sheet more than 7 times.

    Quote Originally Posted by Corona
    Not only that, but it was much thinner than regular paper. That's how they cheated. I mean, come on, of course a sheet like that is going fold more than 7 times. However, as I stated before, the number of folds depends on the type of paper and its size, its dimensions and how you are folding it. I don't see where you are getting a contradiction out of this.
    if the myth they were testing was that you can't fold a normal sheet of paper well then yea they cheated, i must of lost track of which phrasing of the myth they were testing. my mistake.
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    Hey mythbusters "cheats" all the time - when they fail to do the normal myth they massage it a bit until they can take a bite at it.
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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    Hang on, most of you are now suggesting that no matter what the size, technically something, a sheet, a film, a perfect surface area of something, can't be folded more than 7 times.

    In theory therefore an algorithm, an equation, "something" should exist that basically says that "7" halves-folds is the "envelope" of space-time.

    I wouldn't let that bug me for too long without having a good enough answer.
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