Bed sheet Problem

Bed Sheet Problem 

You have insomnia one night and decide to remove your bed sheet, which is only about 0.4 millimeter thick. You fold it up once. and it becomes 0.8 mm thick. How many times do you fold it if you want to make the bed sheet thickness equal to the distance between the Earth and the moon? The remarkable answer is that if you fold your sheet only 40 times. then you will sleep on the moon! In another version of the problem. you are handed a sheet of paper with a typical thickness of 0.1 millimeter. IT you could fold it 51 times. the stack would reach further than the sun! Alas. it is not physically possible to create many folds in physical objects like these. The prevailing wisdom throughout much of the 1900s was that a sheet of real paper could not be folded in half more than 7 or 8 times. even if the starting paper sheet was large. However. in 2002. high school student Britney Gallivan shocked the world by folding a sheet in half an unexpected 12 times. In 2001. Gallivan determined equations that characterize the limit on the number of times we can fold a sheet of paper of a given size in a single direction. For the case of a sheet with thickness t. we can estimate the initial minimal length L of a paper that is required in order to achieve n folds: L = [(1rt)/6] X (2n + 4) x (2n - I). We may study the behavior of (2n + 4) x (2n - I). Starting with n = O. we have the integer sequence O. 1.4.14.50.186.714. 2.794.11.050.43.946. 175.274. 700.074 .... This means that for the eleventh act of folding the paper in half. 700.074 times as much material has been lost to folding. at the curved edges along the folds. as waS lost on the first fold
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