Folding paper twelve times

Maybe you heard that it was impossible to fold a piece of paper in half 10 times(or eight). This Paper-Folding rule was broken at 2001 by a high school student, Britney Gallivan (of Pomona, California).

That year she was given a math problem and she can get extra credit if she solve the problem of folding a sheet in half 12 times.

 At first, she tried something incredibly thin - gold foil, it worked. But her teacher told her that she had to fold a paper. She moved on and came with two mathematical solutions, and 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)

One is  the single direction folding case, the exact limiting equation is: 

Another is the alternate direction folding:

You can visit Britney Gallivan's wikipedia for detail.