Mathemagic ??

I have posted my writings on many topics - TV, Newpapers, Culture, Nature. This time it is MATHEMATICS !!

Here are some interesting sayings about Folding paper in half.

• The fact : It is impossible to fold any piece of paper no matter how big, small, thin or thick more than 8 times
• You can't fold a paper more than five or six times. Dont believe? Try it. Thinner paper? Longer paper? It doesn't matter; you just can't do it.

All the above statements have been proved to be false in January 2002 by a high school student of Pomona, California by name - Britney Gallivan. She has been successful in folding the paper for 12 times !!!

All started when her Maths teacher told that She would get an extra maths credit, if she took up the option of solving the problem of folding a sheet in half 12 times. She tried and failed with reasonably-sized sheets of paper.

So she used something incredibly thin - gold foil and she succeeded in folding her gold foil in half 12 times. But her maths teacher said that ultra-thin gold foil was too easy - she had to fold paper 12 times. She studied the problem, and came with two mathematical solutions.

The first solution was for folding the paper in alternate directions. She derived a formula relating the number of folds possible (n) to the width (W, of the square sheet you start with) and the material's thickness (t):

The second solution was for folding the paper in a single direction. This is the case when you try to fold a long narrow sheet of paper. She derived another formula relating the number of folds possible in one direction (n) to the minimum possible length of material (l) and the material's thickness (t):

She derived from her formula that to successfully fold paper 12 times, she would need about 1.2 km of paper. After some searching she found a roll of special toilet paper that would suit her needs. She rolled out the jumbo toilet paper, marked the halfway point, and folded again and again. After seven hours, she folded her paper for the 11th time into a slab, about 80 cm wide and 40 cm high (in the photo above). She then folded it another time to get that 12th fold !!!!

Incredible isn't it ??