Only on record has mankind yet completed glory, beauty, truth, knowledge, virtue, and abiding love.” -George young name Shaw

I gambling you think you pretty good at estimating things, don’t you? many of us do, after ~ all, from the number of piano tuners in a big city like Chicago come the number of gumballs in a container prefer the one below.

You are watching: Fold a piece of paper 42 times


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Image credit: Blogger user One Smoove Family, via http://onesmoovefamily.blogspot.com/2012/10/carnival-birthday-party-all-about-games.html.

But how great are you really at estimation? A problem was very first posed come me by a fellow professor when I to be at Lewis & Clark college, and I think the a wonderful exercise to share with students, teachers, and also the curious amongst us of all ages. Opportunities are, whether you’re at home, at work or in a classroom, the one thing everyone has access to is a item of paper.


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If girlfriend folded this piece of file in half, the would now be twice together thick together it to be before.


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So my concern is this: how many times would you need to fold this document onto chin to with the Moon?

How numerous times would certainly you expect? would certainly it be simply a few? In the hundreds? The thousands? The millions? The Moon is numerous thousands that miles/kilometers away, after ~ all.


Image credit: forum user Leofidus the Roberts room Industries, via https://forums.robertsspaceindustries.com/discussion/17470/scale-of-planets-and-stars.

You have the right to take a vote if you desire to guess, however let’s take a watch at how we’d number it out together. No fancy calculations, no measuring anything, just estimation!

I might not know just how thick one item of file is, yet I know it’s pretty thin. I can, however, calculation how huge those 500 web page reams are. You understand what I’m talking about: these guys.


Image credit: Simon McCoy at BBC News.

They’re about 2 inches high, i beg your pardon is maybe about 5 centimeters. If that’s a 500 web page ream we’re talk about, that way each individual web page is around 0.01 cm high.

And, an ext precisely, what the the Moon?


The average distance to the Moon native the earth is around 384,000 km, or — if we remember a page is 0.01 cm thick — about 3.84 x 10^12 pages away.

So you’d expect that you’ll need an awful most foldings to gain there, wouldn’t you?

Don’t be so hasty! once I begin with an unfolded page (zero foldings), the one web page thick. Once I wrinkles a page once, it will certainly be two sheets thick. Yet — and also this is vital — as soon as I fold it a second time on itself, it’s no three, however four sheets thick.


Image credit: designerd13 of Instructables, via http://www.instructables.com/id/Extension-of-the-paper-wallet/.

If i fold that a third time, I’ll see that that 8 sheets thick. Have the right to you see a pattern here? file folding is exponential, so the if i fold that a 4th time, it’ll it is in 16 pages thick, a 5th time will offer me 32 pages thick, a sixth will be 64, and also so on.


Image credit: Echo Romeo that Physics Buzz, via http://physicsbuzz.physicscentral.com/2011/04/folding-paper-how-hard-can-it-be.html.

Practically, v a standard-sized paper of paper, you’ll begin running into some challenges at approximately this point, however we can imagine an arbitrarily large item of paper, one that we have no trouble folding as many times as we like.

By time I’d acquire to 9 foldings, my folded file would it is in thicker than my initial ream the 500 sheets. By time I’d acquire to 20 foldings, my folded record is an ext than 10 kilometers high, i m sorry surpasses Mt. Everest. If you save going, you will do it be in outer an are after 24 foldings, you could record the Hubble an are telescope after ~ 28, and after 41 foldings, you’d finally be closer come the Moon than the Earth. So that means that 42 foldings is what the takes!


Image credit: Adrian Paenza.

The practical world record, for those of girlfriend wondering, goes come this group of students, who — through a 13,000 foot-long role of toilet paper — regulate to accomplish a chuck 13 folds!


http://www.youtube.com/watch?v=NNgxmyGPZls

Pretty incredible, no it? “Only” 29 an ext folds to do it come the Moon, but practically, that way you’d require a role of record many billions of times together long, i m sorry — as you might expect — is much longer than the Earth-Moon distance.

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But, still, 42 crease is a pretty small number! are you surprised? Well, that’s the strength of an exponential, the it allows you turn small things into huge things by merely compounding what you have actually over and over again. And also incredibly, it just takes 42 foldings of a file to get from the planet to the Moon, and only around 94 foldings of a record to do something the size of the whole visible Universe. And now you recognize how plenty of times you’d need to fold a item of file to reach the Moon!


An previously version the this write-up originally showed up on the old Starts through A Bang blog at Scienceblogs.