“One small fold for man.…”

How many times can you fold a piece of paper in half?

The above question — one of our 365 Things To Make You Go “Hmmm…” questions — started off as a simple idea. How many times can you fold a piece of paper in half?

Unless your name is Britney Gallivan and you’ve developed your own formula for folding paper (which puts an end to the myth nicely, but spoils what we’re about to say), you have probably found that you can only fold it 7 or 8 times, no matter what size of paper you use.

Onto part two of the question…

If it were possible, how many times would you have to fold a piece of paper in half in order to reach the Moon?

To make it easier for you, here are some options: a) 42 times; b) 420 times; c) 4200 times; d) 42 million times; or e) 420 million million times;

Still unsure? Well, here’s the maths… And credit where credit’s due — this is based heavily on a piece that made fascinating reading in The Times by Anjana Ahuja (12.09.09)

Pieces of paper are pretty thin things. So thin, in fact, that most of you will have picked one of the larger numbers in answer to the question… From here to the Moon is 400,000 km away — a wad of A4 paper from your printer would have to be 4,000,000,000,000 pieces thick to get up there.

Clearly that’s no ecologically sensible way to explore space, so why not just use **one** piece of paper, but fold it lots of times. As Ahuja puts it, “a lunar landing through the art of origami”.

And here’s the interesting bit: If you fold the paper once, it doubles the thickness. The second fold will double *that* thickness (which means your paper is four times as thick as it was when it started). Obviously after you fold it the third time, you have a wad around about 8 times the thickness of the original.

Still a long way to go, but remember that each fold is *doubling* what you already have… To cut a long (but impressive?) story short, 20 folds would have you climbing up Everest on a **10km** thick mound of paper. You’d be over halfway to lunar landing after fold 41, which means that with just **42 folds** you could be bouncing on the Moon.

That’s 42 small folds for man, a giant piece of paper for mankind…

But of course you can only fold a piece of paper in half 8 times, so this has been a pointless exercise really.

Sorry for wasting your time…

NB. Our Game Show Maths resource features an investigation which looks at the effects of halving and doubling in more detail. Think exponential growth, but for primary schools.

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