Q2.2.8Paper folding

How many times must a sheet of paper (thickness, $t=0.1\,\mathrm{mm}$ but otherwise any size required) be folded to reach the moon (distance from Earth, $d=384,400\;\mathrm{km}$ )?

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The thickness of the paper on the $$n$$ th fold is $$2^nt$$ , so we require $2^nt \ge d \Rightarrow n_\mathrm{min} = \lceil \log_2(d/t) \rceil$ :

>>> d = 384400 * 1.e3       # distance to moon, m
>>> t = 1.e-4               # paper thickness, m
>>> math.log(d / t, 2)      # base-2 logarithm
41.805745474760016

Hence the paper must be folded 42 times to reach to the moon ( $\lceil x \rceil$ denotes the ceiling of $$x$$ : the smallest integer not less than $$x$$ ).