Well, the answer may surprise you. You would need to fold the
piece of paper 42 times for it to be thick enough to reach
the moon.
Reality:
It is impractical to get a long enough piece of paper to fold
it 42 times. Paper will not exceed its maximum dimension in
its unfolded state, clearly a good theory would not allow for
unbounded streching of paper, when the paper is simply
folded.
The correct mathematics of paper folding includes a term for
the initial length of the paper and how it folds. So a piece
of paper reaching the earth must be at least as long as that
distance before folding.
So you can, in theory , fold a long 1mm thick sheet of paper
in half 42 times to reach the moon by thickness, but the
length of the sheet to begin is with is: L = 1.012*10^21 m.
That's just under 107,000 light years. And our galaxy is
about 100,000 light years across.
Fact:
The current world paper-folding record belong to
California high school student Britney Gallivan, who in 2002
managed to fold a 1.2km-long piece of tissue paper 12 times.
