Newspaper Fold
What would be the dimension of a single sheet of a newpaper, if it is folded by half upto 50 times.
Assume, the original size 600 mm by 380 mm !
Assume, the original size 600 mm by 380 mm !
Labels: mathemagic, thinktank
posted by Rajesh Lal at
8:49 AM
18 Comments:
1mm by 1mm? It's a bit of a guess
Folding it in half reduces one dimension by half, the other is unchanged. So assuming you folded each way evenly, each dimension gets halved 25 times.
By reapeadedly hitting the "=" button on the calculator, I get 1.78 x 10^-5 by 1.13 x 10^-5
Of course, the real question now is how thick is the paper at this impossible fold level.
it didn't say how thick the paper is.. Assuming you could fold the paper in half 50 times, the dimensions would be 24mm x 15.2mm x (orginal thickness * 2) ^ 50
assuming 1mm thickness, the first fold would be 2mm thick (2^1). The second fold would by 4mm think (2^2). the 3rd 8mm (2^3) and so on, until you get to the 50th fold (2^50) which is 1,125,899,906,842,624mm.
FYI, it's pretty much impossible to fold a sheet of paper more than 8 times.. regardless of the size of the sheet of paper. If the paper is extreamly thin and very very very large, you might get the 8th fold, but the 9th would be too think to fold.. it would just be an arc..
The dimensions of the sheet of paper are unchanged, it is still te same size albeit in a folded state. Why has the question been phrased 'up to 50 times'?
Although it is indeed impossible to fold a sheet of paper 50 times.
By a theoretical approach, I get gbusman's answer.
600/(2^25) X 380/(2^25)
The "up to" part makes me wonder if it could be a trick question where the answer is just the original dimensions: 600 mm by 380 mm
BTW, this reminds me of the Jurassic Park fractal that can be conceptualized by repeated foldings of a line and then unfolding at a right angle.
everytime a number gets halved 10x, it becomes 1024 times less. by 5x 32 times less. dimentions: .0000178 mm x 0.0000113 mm
Its a trick of mind... using a calculator would be too easy, but im pretty sure most people are use to these types of tricks. So I applaud everyone who took the time to pull out their calculater and hit /2 a bunch of times. But come on. Since when is it that easy. The 2 guys who had tho 10x formulas did better than me. But its apparent the answer the author is looking for is 600x380mm. Basic math isn't fun enough to to sound like it would be interesting on this board. Stuff like that would make most of us leave.
Hope they get better ladies and gents. A few weeks ago I was excited to get the new trick of the day. They haven't been so great latley.
It is a proven fact when folding paper in half--equal halves--it can only be folding prefectly in half seven times. This is true no matter how large the sheet of paper in to begin with.
At seven folds you have a rectangilar piece of folded paper measuring 37.5mm x 47.5mm.
If it were possible to continue folding in half, after sixteen folds you would have a folded piece of paper measuring 2.34375mm x 1.484375mm.
Since 25.4mm is equal to one inch, the paper after sixteen folds would measure approximately .09227" x .05843", or a piece way too tiny to continue folding anyway.
But the simplicity of this question shows that no matter how many times you fold a 600mm x 380mm piece of paper, the paper still measures 600mm x 380mm regardless of how many times it is folded.
Yeah, Rob is right, the paper's only ever 600mm x 380mm no matter how many times you folded it, however, if you cut it in half 500 times the dimensions would be quite smaller.
and I curse my friend, and his great idea, for dragging me away from my computer, otherwise, I probably would have said it earlier
Yes I agree no matter how many times folded it won't loose anything, even if folded 1 trillion times , which is impossible
argh i posted some long thing but my internet wouldn't process it or something so it didnt work so im trying again. I cant be bothered to write it all out again but this is the jist of it:
No piece of paper can be folded in half more than six times (it might be seven but im pretty sure it's six) no matter what size it is. Even if it was the size of a football pitch it wouldn't fold more times than a piece of paper as described in the question.
BUT the question says 'up to 50 times'(which is impossible) so it doesn't need to be exactly that number, so if i calculate the size after six folds (the maximum amount) then i would have the answer.
It's a shame that i can't be bothered with the maths part (even thought it's quite simple) but i just like the ideas part of an answer.
:)
sorry for double post
it seems other people have been saying the same thing before me, i should read them before posting next time but i didnt read them although i have a similar answer. sorry about that :P
I believe you can only fold any piece of paper up to 7 times before it becomes too thick to fold.
http://www.pomonahistorical.org/12times.htm
This girl managed to fold a piece of paper 12 times for extra credit in a math class.
Thanks for the link. WOW...! 12 times!!!!
A hottie with a brain.
A typical piece of paper is .004" thick.
In folding a square or rectagular piece of paper in half, you double its thickness with each fold.
1= .004"
2= .008"
3= .016"
4= .032"
5= .064"
6= .128"
7= .256"
8= .512"
9= 1.024"
10= 2.048"
11= 4.096"
12= 8.192"
ANSWER: 600 mm by 380 mm (SAME)
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Details
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Dimension of the actual newspaper will remain same, no matter how many times you fold it.
GOT RIGHT
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Rob, Eric
Thanks to the anonymous guy for sharing the great link
http://www.pomonahistorical.org/12times.htm
"This girl managed to fold a piece of paper 12 times for extra credit in a math class."
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