why is it hard/impossible to fold paper 7 times or more?
In: Physics
The number holds true for paper of typical thickness. With a thinner paper you can fold it more times.
It’s often difficult to appreciate the speed of exponential growth (where the value regularly doubles, triples, etc.) as the values typically start small and get big very quickly. The “rice on a chessboard” story is another good example.
When you fold paper once the thickness doubles. Two folds and it’s 2^2 = 4 times thicker. After only 7 folds the paper is now 2^7 = 128 times its original thickness. In fact, it would only take around 42 folds to (theoretically) make your folded paper the same distance to the moon.
I think I’ve seen a video where people took a very large sheet of paper and eventually folded it about 9/10 times but they still ran into the same problem eventually.
2^7 = 128
Now try to fold 128 pieces of paper that are each 128th the size of a normal piece of paper…
From a strictly mechanics point of view:
I am going to call the folded up piece of paper an “assembly” so it does not get confused with an unfolded piece of paper.
When you fold a piece of paper the over all thickness of the assembly is now two sheets of paper. When you fold it again its over all thickness is 4 sheets of paper. When you fold it again the assembly is now 8 sheets thick. This gets important at the fold/crease.
So when you fold the paper, the paper at the crease has to stretch all the way around the crease. On the first fold, the extra distance that has to be covered is zero, on the second fold the extra distance that has to be covered is the thickness of 2 sheets of paper, on the third fold you now have to cover an extra distance of 4 sheets of paper, and so on and so forth.
So paper that previously only had to cover a distance of 1 sheet of paper now have to be stretched to 3, 5, 9 or more sheets of paper so you can complete the fold. And each time this gets more and more difficult.
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