Can a piece of A4 paper be folded so that it’s thick enough to reach the moon?

While procrastinating around the web I stumbled on a page that contained the image below, from cracked.com.

I can’t help but believe that this is false… Even though the article header says:

22 Statistics That Will Change The Way You See the World

My question: is what the image below implies a mathematical impossibility? (…Just for procrastination’s sake…)

mathematical-impossibility

If you could fold a piece of A4 paper just 42 times it would be thick enough to reach the moon

Answer

Even if the sheet of paper were infinitely foldable, the answer is that no, you can’t reach the moon by folding a sheet of A4 paper any number of times, for a reason that bears calling out (and in fact explains why a sheet of paper that size can only be folded a certain number of times — that is, why it’s impossible to fold it 42 times in the first place): consider the last fold and imagine looking at the sheet in a cross-section perpendicular to this fold. The ‘faces’ of the folded paper that are at the top and at the bottom after the last fold must be connected along the fold edge, since they were part of a single ‘face’ before the fold — but this means that the distance along the paper between the top and bottom must be at least as long as the distance ‘through’ the paper on a straight line between them. In other words, you need to start with a sheet of paper that’s at least 385,000km along at least one direction (using Sabyasachi’s numbers) to be able to reach that far, regardless of what sequence of folds you use.

Attribution
Source : Link , Question Author : blade19899 , Answer Author : Steven Stadnicki

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