Nice site, with apt illustrations and mathematical explanations.
This reminds me of an interesting trivia:
For centuries, it was believed that paper could not be folded in half more than 8 times. Until one high school student broke that seemingly impossible limit. And she did so with a giant sheet of paper, and some interesting mathematics.
She won the Guiness World Record for that feat.
"It was an accepted belief that folding a piece of paper in half more than 8 times was impossible. On 27 January 2002, high school student, *Britney Gallivan*, of Pomona, California, USA, folded a single piece of paper in half 12 times and was the first person to fold a single piece paper in half 9, 10, 11, and 12 times. The tissue paper used was 4,000 ft (1,219 m; 0.75 miles) long.
In preparation for the challenge, Gallivan identified criteria for folding and the phenomenon that ultimately limits the geometric folding progression. She derived mathematical equations for single direction – L=πt/6(2ⁿ+4)(2ⁿ-1) – and alternate direction – W=πt23(ⁿ-1)/2 – folding. The equations establish the relationship between the length of paper required (L), the thickness of the paper (t), the minimum possible width of square material (W), and the number of possible folds (n). It is documented in her book *How to Fold Paper in Half Twelve Times*."
