A piece of paper of non-zero thickness cannot be folded more than a specific number of times due to thickness constraints
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Reference discussions detail how material thickness and dimensions establish a mathematical and physical upper bound on the number of times paper can be folded.
# Why can't a piece of paper (of non-zero thickness) be folded more than $N$ times?
Tags: material-science, geometry, continuum-mechanics
- Score: 21
- Views: 10640
- Answers: 4
- Answered: yes
- Asked by: iamsid (313 rep)
- Asked: 2011-01-16
- Edited: 2013-07-19
- Site: physics
## Question
Updated:
In order to fold anything in half, it must be $\pi$ times longer than its thickness, and that depending on how something is folded, the amount its length decreases with each fold differs. – Britney Gallivan, the person who determined that the maximum number of times a paper or other finite thickness materials can be folded = 12.
Mathematics of paper folding explains the mathematical aspect of this.
I would like to know the physical explanation of this. Why is it not possible to fold a paper more than $N$ (=12) times?
## Answers
### Answer by Simon (score: 28 [ACCEPTED])
I remember that the question in your title was busted in Mythbusters episode 72.
A simple google search also gives many other examples.
As for single- vs alternate-direction folding, I'm guessing that the latter would allow for more folds. It is the thickness vs length along a fold that basically tells you
# How many times can a piece of paper be folded in half?
Tags: geometry
- Score: 4
- Views: 6227
- Answers: 3
- Answered: yes
- Asked by: iamsid (143 rep)
- Asked: 2011-01-16
- Edited: 2011-01-16
- Site: math
## Question
What is the maximum number of times a piece of paper (of non-zero thickness) can be folded in half (mathematically)?
Edit:
I totally forgot to mention the "non-zero thickness" part; I've now included it.
## Answers
### Answer by Qiaochu Yuan (score: 6 [ACCEPTED])
The zero thickness model is a bad model. For nonzero thickness the problem was studied by Britney Gallivan, who derived an upper bound on the number of folds based on the thickness and dimensions of the paper. The current world record for actual paper was set by her; it's $12$. There are some additional details and references at her Wikipedia article.
### Answer by user17762 (score: 4)
Theoretically you can fold the paper into half infinite number of times since $1 - (\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \cdots) = 0$. However, practically the number of times you can fold the paper into half will depend on the dimensions of the paper (length, breadth and thickness), the stiffness of the pap
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