Earth sized piece of paper

How big a piece of paper is needed to cover the entire Earth?

Size of A0 paper: a x b mm^2 where a = 1189 and b = 841

Size of A-n paper = a * (a/b)^n x b * (a/b)^n mm^2

Diameter of Earth = e ~ 12742000000 mm

To cover the Earth, need:

a * (a/b)^n > e

so

log(e/a) < n log(a/b) so n > log(e/a)/log(a/b)

need n > log(12742000000/1189)/log(1189/841) ~ 46.7

So A-47 paper would be sufficient.

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