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It's a commonly stated belief that no one can fold a piece of paper in half after doing so seven times. Even I have been unable to fold a piece of normal paper for an 8th time.

Is this true for normal (A4/newspaper) sized-paper?

I would also be interested to know if this is this an absolute rule, or would a sufficiently large piece of paper be foldable more than seven times?

  • 1
    Define normal. Isn't newspaper paper normal? Airpost? – user unknown Aug 24 '11 at 3:30
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    mythbusters covered this one. However, the clip I found uses a massive sheet – Monkey Tuesday Aug 24 '11 at 3:46
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    I got to 9 (using extra thin A4 paper) so this is officially BUSTED. – Konrad Rudolph Aug 24 '11 at 15:32
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    You also need to define if all the folds have to be in the same direction. I have taken an 8.5" x 11" piece of paper, folded it 5-6 times in one direction (along the longer axis, i.e. left-to-right), then was able to fold it 3-4 more times along the shorter (although now longer) axis, i.e. up-to-down. – fred Aug 24 '11 at 18:17
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    People interested in origami find this statement outright hilarious :) – user288 Aug 24 '11 at 22:40
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No, it is not true for all scenarios.

This idea was examined by Britney Gallivan, who came up with a mathematical model for the limits, and used this knowledge to fold a large piece of paper twelve times in January 2002.

She was a junior in high school at the time.

Reference: Historical Society of Pomona Valley


According to the above reference, the upper-bound equation for "Alternate Direction Folding", which I understand to be the normal style, is

Formula

Without LaTeX, this looks like:

W = πt.2^(3(n-1)/2)

Solve for n, we get:

n = 1 + 2/3.log2 (W/πt)

Plugging in the values for standard A4 80 g/m² office copy paper (W=297mm, t=0.105mm) we get:

n = 1 + 2/3.log2(297/(0.105π))

n = 7.543

Notes:

  • The equation works with square paper, and I have used A4's longest side, perhaps overestimating the number of folds by a fraction.
  • The thickness of 80 g/m² was interpolated from the chart on cited page.
  • Pi looks like this, in this font: π

If the original formula calculated by Gallivan is correct, this shows that a standard piece of copy paper, even if it is extended a little, cannot be folded 8 times.

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    I particularly like this answer because a secondary school student figured it out and provided an answer that included a mathematical model. (I hope this helps encourage more younger people to engage in scientific thinking.) – Randolf Richardson Aug 24 '11 at 4:39
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    for A4 it may well be true, iirc to get more folds you need a very long thin piece of paper such as toilet paper – jk. Aug 24 '11 at 8:19
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    @jk - youtube.com/watch?v=kRAEBbotuIE here is supersized to 11 from mythbusters. – Daniel Iankov Aug 24 '11 at 8:51
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    It's important to note that Ms. Gallivan foled a very large sheet of paper. Since the OP asked for a A4 sized paper, your answer could be improved by saying how many times that sheet of paper can be folded by using the model you cite. – Borror0 Aug 24 '11 at 15:11
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    Questions also mentions "newspaper size". Newspapers are printed on much thinner paper ( between 40 g/m2 and 57 g/m2), full sized newspaper sheet is 24"x36" (already folded once, containing 4 pages of newspaper). Result for above formula for 40g/m2 24x36" sheet is 9.26 – vartec Aug 27 '11 at 21:44

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