Saturday, 9 April 2016

Folding a Paper

Folding of paper teaches us a lot, lets explore and try to make a simple theory..

1. This is known fact, If you fold a paper 100 times, the thickness of the paper will almost cover the entire observable universe..

Folding a paper 100 times, the thickness is T (100) = t * 2^100 = t * 1.268 * 10^30
                                                                               =0.05 mm * 1.268* 10^30
                                                                               = 6.34 * 10^22 kms
t is the thickness of the paper which is 0.05 mm
and T is thickness of paper after 100 folds

Observable Universe Diameter is 91 billion light years
Diameter in Kms = 91 billion * 9.461* 10^12 kms = 8.61* 10^23 kms

2. You cant fold a normal paper beyond 7/8 times, because the ratio of length to thickness will become less than two and further folding is difficult.. So what should be the optimum length of a paper to fold as many times as possible? There are formula available, here is a simple formula..

# Folding of a paper is limited to normal human ability
# Folding can only be done in breath and length -wise, it cannot be done on the thickness side, because it will cause damage to the paper itself
# Paper can be comfortably folded when the length to thickness ratio is more than than two.. Optimum length of a paper required to fold should have a length to thickness ratio of 2:1

Folding only on the length of the paper:

Optimal Length for folding n times L(n) = t * 2^n * 2^(n-1)

So if a paper need to be folded 13 times the paper length should be, L(13) = t * 2^13 * 2^12

Assuming paper thickness of 0.05 mm, the optimum length required to fold a paper 13 times on its length is L (13) = 0.05 *  2^13 * 2^12 = 1677 metres = 1.67 kms long Paper!!!

And the thickness of the paper after 13 folds is T (13) = t * 2^13 = 0.05 * 2^13 = 0.409 metres

Folding on Breadth and Length:

Assuming folding on breading first and then on length,

B (n) = t * 2^n * 2^(n-1)
Where t thickness, n is no. of folds done breath-wise

L (n) = T * 2^n * 2^(n-1)
where T is the thickness after the n folds Breadth-wise which is t*2^n and n is the no. of folds done length-wise

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