Okay, as numerous of you had heard, I"ve got a brand-new job as a permanent Professor. And also not only am i pretty excited around it, I assumed I"d share with you among the an ext interesting things I teach on the first day.

You are watching: How many times to fold a piece of paper to reach the moon

I obtained this idea from talk to Michael, the chair of the department (and this is no the very first time he"s taught me other neat). Chances are, if you"re in a classroom, that one point everyone has actually is a item of paper.


If friend folded this piece of paper in half, it would currently be twice as thick as it to be before:



So my inquiry is this: how plenty of times would you have to fold this paper onto chin to reach the Moon?

I"ll offer you a opportunity to guess, so choose the closestly one native the options below.

How countless times would certainly you have to fold a page to develop something thick sufficient to with the Moon? 

Well, let"s see just how we"d figure it out. Ns don"t know just how thick one piece of document is, but I recognize it"s pretty thin. Ns can, however, estimate how big those 500 page reams are. They"re around 2 inch high, so perhaps that"s around 5 cm. That way one web page is about 0.01 centimeter high. And also what that the Moon?



Mean distance from the earth is around 384,000 km, or about 3.84 x 1012 pages away. For this reason you"d mean that you"ll need an awful lot of foldings to obtain there, right? Well, hang on because that a second. Once I begin with one unfolded web page (zero foldings), it"s one page thick. When I wrinkles a page once, it will certainly be 2 pages thick. Yet -- and this is crucial -- as soon as I wrinkles it twice ~ above itself, it"s not three, however 4 pages thick.



If i fold it a third time, I"ll view that it"s 8 pages thick.

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Can you check out a pattern here? document folding is exponential, so that if i fold that a 4th time, it"ll it is in 16 pages special (so that option is clearly wrong), a 5th time will offer me 32 pages thick, and so on. By time I acquire to 9 foldings, mine folded paper is bigger 보다 my initial ream the 500 sheets. By time I acquire to 20 foldings, mine folded record is more than 10 kilometers high, which surpasses Mt. Everest.

41 foldings will obtain me slightly an ext than halfway to the Moon, therefore that means that 42 foldings is every it takes! (Of course, an excellent luck folding a real item of record more than 7 or 8 times...) quite incredible, isn"t it? however that"s the power of one exponential, that it allows you turn little things into large things by just compounding what you have over and also over again. And also incredibly, it just takes 42 foldings that a document to gain from the planet to the Moon, and only about 94 foldings that a record to do something the size of the entire visible Universe!