Thursday, 3 April 2014

The Bedsheet Problem

The bedsheet problem is an urban legend that states the following: any piece of paper (no matter the dimensions) cannot fold more than 7 times . All who claimed the myth was valid could only cite empirical evidence. They could not explain or prove it mathematically. The puzzle was both mysterious and inexplicable.

Theoretically if we are given an infinitely long sheet of paper, then there would be no absolute folding limit. However, this result does not seem true when the experiment is conducted. In December 2001, Britney Gallivan created a mathematical representation of the bedsheet problem in which she described the interaction between the thickness, length, and number of folds that were possible. Gallivan's mathematical model describes the reality of the physical system. Her derivation gives the loss function for folding a piece of paper in half.

Britney Gallivan, who was at the time a junior in high school, solved this well-known problem. She was asked by her teacher to fold a sheet of paper 12 times and as an incentive she would get extra credit. She failed multiples times. Later she succeeded after using a thin gold sheet and proved the assumption wrong. Gallivan was able to achieve 12 folds by folding a roll of thin toilet paper that stretched over three-fourths of a mile. It took seven hours in a shopping mall with her parents, but Gallivan was able to bust a myth as well as derive a formula relating the width, thickness of a paper and the number of folds achievable. The urban legend of 7 folds was disproved in 2001. Gallivan wrote a 40 page pamphlet on her discovery in which she explained the mathematics, the story and other information about her project.

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