I bet you think she pretty good at estimating things, nothing you? most of us do, ~ all, native the variety of piano tuners in a large city choose Chicago come the number of gumballs in a container choose the one below.
You are watching: Fold over a piece of paper 42 times and it will reach the moon
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But how good are girlfriend really in ~ estimation? A difficulty was very first posed come me by a other professor once I to be at Lewis & Clark college, and also I think that a wonderful practice to share through students, teachers, and also the curious amongst us of all ages. Possibilities are, whether you’re at home, at job-related or in a classroom, the one point everyone has accessibility to is a item of paper.
If friend folded this piece of file in half, that would currently be twice as thick as it was before.
So my question is this: how many times would you need to fold this paper onto chin to reach the Moon?
How plenty of times would certainly you expect? would it be just a few? In the hundreds? The thousands? The millions? The Moon is hundreds of thousands of miles/kilometers away, after ~ all.
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You have the right to take a poll if you desire to guess, yet let’s take it a look at at exactly how we’d figure it the end together. No sophisticated calculations, no measuring anything, simply estimation!
I may not know just how thick one piece of document is, however I recognize it’s nice thin. Ns can, however, calculation how large those 500 page reams are. You recognize what I’m talking about: these guys.
Image credit: Simon McCoy in ~ BBC News.
They’re around 2 inch high, which is maybe around 5 centimeters. If that’s a 500 web page ream we’re talk about, that means each individual page is around 0.01 centimeter high.
And, an ext precisely, what that the Moon?
The typical distance to the Moon indigenous the planet is around 384,000 km, or — if us remember a page is 0.01 centimeter thick — around 3.84 x 10^12 pages away.
So you’d mean that you’ll need an awful lot of foldings to gain there, wouldn’t you?
Don’t it is in so hasty! once I begin with one unfolded web page (zero foldings), that one web page thick. When I fold a page once, it will certainly be two sheets thick. But — and this is crucial — when I wrinkles it a 2nd time on itself, it’s not three, but four sheets thick.
Image credit: designerd13 the Instructables, via http://www.instructables.com/id/Extension-of-the-paper-wallet/.
If i fold that a 3rd time, I’ll view that the 8 sheets thick. Can you watch a pattern here? document folding is exponential, so that if i fold it a 4th time, it’ll it is in 16 pages thick, a 5th time will offer me 32 pages thick, a 6th will it is in 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, with a standard-sized paper of paper, you’ll begin running right into some difficulties at around this point, but we can imagine one arbitrarily large item of paper, one that we have actually no problem folding as plenty of times together we like.
By time I’d acquire to 9 foldings, my folded file would it is in thicker 보다 my initial ream the 500 sheets. Through time I’d gain to 20 foldings, mine folded paper is an ext than 10 kilometers high, i beg your pardon surpasses Mt. Everest. If you keep going, you will do it be in outer space after 24 foldings, you could capture the Hubble an are telescope after 28, and also after 41 foldings, you’d lastly be closer to the Moon 보다 the Earth. For this reason that method that 42 foldings is what that takes!
Image credit: Adrian Paenza.
The practical world record, because that those of you wondering, goes to this team of students, that — with a 13,000 foot-long role of toilet file — regulate to attain a whopping 13 folds!
Pretty incredible, no it? “Only” 29 an ext folds to make it to the Moon, however practically, that means you’d need a roll of record many billions of times as long, which — as you can expect — is much much longer than the Earth-Moon distance.
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But, still, 42 crease is a pretty little number! are you surprised? Well, that’s the power of one exponential, the it lets you turn little things into large things by just compounding what you have over and over again. And incredibly, it only takes 42 foldings that a document to gain from the planet to the Moon, and only around 94 foldings of a paper to do something the dimension of the whole visible Universe. And also now you recognize how countless times you’d have to fold a item of record to reach the Moon!
An earlier version that this write-up originally appeared on the old Starts with A Bang blog at Scienceblogs.