# Paper Folding to the Moon

Note: This post has been updated and improved for 2014 here, at the new Starts With A Bang blog. What follows below is the original version from 2009.

Okay, as many of you had heard, I've got a new job as a full-time Professor. And not only am I pretty excited about it, I thought I'd share with you one of the more interesting things I taught on the first day. I got this idea from talking to Michael, the chair of the department (and this is not the first time he's taught me something neat). Chances are, if you're in a classroom, that one thing everyone has is a piece of paper.

If you folded this piece of paper in half, it would now be twice as thick as it was before:

So my question is this: how many times would you have to fold this paper onto itself to reach the Moon? I'll give you a chance to guess, so pick the closest one from the options below.

Well, let's see how we'd figure it out. I don't know how thick one piece of paper is, but I know it's pretty thin. I can, however, estimate how big those 500 page reams are. They're about 2 inches high, so maybe that's about 5 cm. That means one page is about 0.01 cm high. And what of the Moon?

Mean distance from the Earth is about 384,000 km, or about 3.84 x 1012 pages away. So you'd expect that you'll need an awful lot of foldings to get there, right? Well, hang on for a second.

When I start with an unfolded page (zero foldings), it's one page thick. When I fold a page once, it will be 2 pages thick. But -- and this is key -- when I fold it twice on itself, it's not three, but 4 pages thick.

If I fold it a third time, I'll see that it's 8 pages thick. Can you see a pattern here? Paper folding is exponential, so that if I fold it a fourth time, it'll be 16 pages thick (so that option is clearly wrong), a fifth time will give me 32 pages thick, and so on. By time I get to 9 foldings, my folded paper is bigger than my original ream of 500 sheets. By time I get to 20 foldings, my folded paper is more than 10 kilometers high, which surpasses Mt. Everest. 41 foldings will get me slightly more than halfway to the Moon, so that means that 42 foldings is all it takes! (Of course, good luck folding a real piece of paper more than 7 or 8 times...)

Pretty incredible, isn't it? But that's the power of an exponential, that it lets you turn small things into huge things by simply compounding what you have over and over again. And incredibly, it only takes 42 foldings of a paper to get from the Earth to the Moon, and only about 94 foldings of a paper to make something the size of the entire visible Universe! And how surprised are you that the answer is so small a number?

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lol 42.

Aw, I saw this on facebook and thought it was gonna be an open question type of post, so I figured it out before coming over here. Too bad you can't actually fold a piece of paper more than 7 times.

We all knew this was the answer to life, the universe, and everything. I actually guessed, figuring Douglas Adams would have been right. In all seriousness though, it really puts a perspective on scale. We're used to seeing such big numbers, but at some point, those numbers are not intuitive anymore. So our national debt is in the trillions, well, that's a lot of money. I mean stacking a million dollars is quite a feat, now dealing with a trillion is easy mathematically, but intuitively, it's about as difficult as dealing with exponential systems, universal scales, even physical distances. We throw around 380,000 km, but that's still quite a number. Try walking that you triathletes.

By Helioprogenus (not verified) on 31 Aug 2009 #permalink

Cute. Did any of your students check for reasonableness?

If the C bonds are about 150e-12, it would take 2.5e18 carbon bonds to go to the moon. Since that number is five orders of magnitude less than Avagadro's number and a piece of paper is 5g or so, not only could you reorder a single piece of paper to the moon -- you should be able to fold yourself beyond Pluto.

I remembered the wrong distance for the Moon's orbit, and I guessed a bad value for the thickness of paper, and I still came up with 40 as my answer. A nice reminder that good order-of-magnitude estimates can be made even without precise data.

But, you can only fold a piece of paper 6 times before it is too strong to fold! I don't think even today's technology would be able to fold it 42 times.

By Katherine (not verified) on 31 Aug 2009 #permalink

From Mythbusters on Discovery.com:

Episode 72: Underwater Car
Meanwhile Grant, Tory and Kari roll out the Seven Paper Fold myth. Is it possible to fold a piece of paper in half more than seven times? Taking this myth to the outer limits, our crew sets up at a location that has plenty of space â NASA. Here, in the biggest build they have ever attempted, their mission is to put together a piece of paper that's the size of a football field.
Premiere: Jan. 24, 2007

By Sweetwater Tom (not verified) on 31 Aug 2009 #permalink

re: the Mythbusters episode a few years ago, they did actually get more than seven folds (if I recall, it was something like 12 folds?) but they had a gigantic piece of paper, and they used a forklift to assist in their work....

But I do like this problem because it has several layers of math, and I can look at it with my middle schoolers.

I'm reminded of a very old "I Love Lucy" episode where she discovered that if she didn't like a particular brand of baked beans, she could return it to the store and get DOUBLE her money back. She kept up with the scheme (of course with plenty of hijinx storing all of the cans and cases at home) until she actually ate some beans and realized that she really loved them after all. OK, so maybe that's probably not as cool as folding paper, but it was a pretty good visual lesson for me 30+ years ago.

I teach 9th grade earth science and will definitely use it to start our unit on the moon! Thanks for the awesome idea.

By OneInterestedTeacher (not verified) on 31 Aug 2009 #permalink

That pattern btw, is powers of 2. Binary - 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32767, 65536, 131072.... 18 bits thus far.

Being around computers for as long as I have I can also count in Base 8 and Base 16.

So if a person can get 6 folds, and a forklift can get double that, what sort of technology would you need to get to 42? ;) Though I suppose giant paper isn't as thin as regular paper so maybe you wouldn't need so many folds?

By Katherine (not verified) on 31 Aug 2009 #permalink

I don't know if today's technology could fold a sheet of paper 42 times or not, but I am pretty sure that on a NASA program you could simply pile all the documentation you have to create into a stack and climb the stack to the moon.

I hope you also point out to the students that the paper stack would become invisible to the human eye around the time it reached the edge of Earth's atmosphere. By the time it reached the moon, the folded sheet would measure only a few hundred atoms on a side... give or take!

By archimedes (not verified) on 31 Aug 2009 #permalink

Each folding cuts the area of the paper in half.

After 42 folds, assuming the paper started at 0.203 x 0.254 meters (8 x 10 inches) with zero folds, the area would be 1.17x10^-14 square meters.

Which would be a square about 10^-7 m, or a hundred nanometres, on a side. And I'm told atoms are roughly 0.1 to 0.7 nm in diameter, hence the paper is a few hundred atoms on a side, give or take.

Does this seem right?

By archimedes (not verified) on 31 Aug 2009 #permalink

I'm told it doesn't matter how big the piece of paper is initially. You can't fold it more than 6 times. Is that because it's paper? Surely that wouldn't apply to every material?

Ok, please think for a second regarding the required paper size. When folding a square piece in the described way, you will have to cover the outer layer with a strip at least as long as the final thickness. I first thought you need to start with a 384,000 km square sheet (that's 290 times the surface of the earth, and twice the surface area of Jupiter). Than I realized, the length of the sheet gets cut in half every time. So, to end up with a 384,000 gm stack, you need to start with 2^41 x 384,000 km length. That's roughly 90,000 ly in length.

The "possible number of foldings" depends on the ratio between the initial length of the unfolded paper and the thickness of the paper; once the stack becomes a cube (when the folded thickness equals the length of a side) the concept of a "fold" breaks down.

The length of a side decreases as 1/sqrt(2) (assuming a square paper for simplicity), and the thickness doubles with each fold (assuming incompressibility). If I did the math right, then, assuming a paper that starts with length L and thickness T,

N = max folds = 2/3/log(2) * log (L/T) = 2.2146 log(L/T)

An 8.5x11 piece of paper would have an L of about 250 mm, and a T of about .1 mm, for a ratio of 2500; that means a maximum of 7 folds (they reach equality at 7.5).

The sheet of paper used in Mythbusters was "the size of a football field". Lets call that 70m for L, and assume thickness is unchanged; the L/T ratio is 700000, and you should be able to get 12 folds (12.94; just a little bigger or thinner and you'd make 13).

To get 42 folds with a .1mm paper is going to require a starting side of 9.23*10^14 m, or 35.6 light-days, or 6170 AU.

jace, now that's some good insight on the problem. And not so good English on my part.

By multipath (not verified) on 01 Sep 2009 #permalink

Mu, where did you get the idea that the surface area of the Earth is 1324Km square? It is 510,072,000Km square. A simple check would have shown this.

By SecondCobra (not verified) on 01 Sep 2009 #permalink

Earth is not square! If you walk a straight line its a circle. There isn't enough cellulose on Earth to make a paper that will reach the moon in any practical manner, but check out the space elevator.

It's kinda like the question:
"How long was Margaret Thatcher Prime Minister?"
a. 11 years
b. 300 years
c. 2,000 years
UHM, it's a trick question. I would guess b. 300 years.
It was a very long time.
JTD

By J Todd DeShong (not verified) on 02 Sep 2009 #permalink

Congratulations on your new job! Do we have to call you Prof. now?

My notebook conveniently has about 16 pages to 1mm, so that's 2^4 or a mere 4 folds to 1mm. 1Km is another 20 folds. 384403 is another 18 or 19. Gee, that's tricky; I'd better backtrack and stop this rounding at each step. 42.48 - damn that half fold! Huh. To think all I had to do was read The Hitchiker's Guide to The Galaxy and I would have discovered the answer.

Aaaahahaha ... I had a look at the results and you can tell how many people just guess.

SecondCobra, 384,000 km square = 147,456,000,000 km^2 area, divide by 510,072,000 km^2 = 289.1. Want to try again?
Jace, thanks for the side length correction, I missed the side length gets only cut in half every second fold.
In any case, your folding will be limited by relativity :). You need 50 + years to get the ends of the first fold to come together to keep the corner movement below light speed.

Posted by: J Todd DeShong

"How long was Margaret Thatcher Prime Minister?"
a. 11 years
b. 300 years
c. 2,000 years
UHM, it's a trick question. I would guess b. 300 years.
It was a very long time.

Correct answer is; not long enough.

By Chris' Wills (not verified) on 04 Sep 2009 #permalink

Stop trolling Chris. Thatcher is and was PM for too long. Thatcher (the woman) was PM until 1990. Thatcher (the concept) hasn't abdicated yet. Notice how neo-liberal New Labour has been, yet?

Mu - I stand corrected :( I read your comment as square Km. Will read more carefully next time.

By SecondCobra (not verified) on 09 Sep 2009 #permalink

Sorry if this has been answered above but 20 times would only be just over 1KM, not 10KM like you have suggested.

"By time I get to 20 foldings, my folded paper is more than 10 kilometers high, which surpasses Mt. Everest."

correct me if I'm wrong, but by my calculations...

2^20*0.01cm = 10485.76cm = 104.86m

Great post!

By JohnBruno (not verified) on 05 Nov 2009 #permalink

if you think of the piece of paper is space time, you would only fold the paper once.

WHO DO ORbit MENT.

By jordynwallace (not verified) on 01 Apr 2010 #permalink

So can anyone figure out how many folds it would take to get to the edge of our observable universe? and how wide the paper would be once it got there?

you guys have to decide if you stay in inches and join Liberia and Burma as the only countries still using this vintage system or you choose to join the world that are using the metric system. Using both in the same article is insane.

You are all gotdamn wunderkinds. First off: Thatcher Ruled, Rules and Always Will Rule. Now, Paper is meant for fingerpainting and paper-airplanes and sometimes anal-hygiene, not incredibly thin paper-chains to the moon. Not to mention that greenpeace would never allow it. Now, the real question is, how many times would you have to fold your iPhone/Android-phone onto itself before you reached the hight/width of Steve jobs pile of cash?

42 is the Ultimate Answer to the Ultimate Question of Life, The Universe, and Everything. :)

Depending on the thickness, 50 folds goes to the sun.

But a 12 yr old girl took a whole roll of toilet paper and brought it to the mall where she set a record of 12 folds that was 40 cm thick. She did it after her teacher told her folding gold foil was a cop out.

Article above is absolutely wrong. 20 foldings of 0.01 cm (0.1mm) will give you 104.8576 metres ( 0.1 km).

0.1mm * 2 ^ 20 = 104.8576 metres i.e 0.1 km approx.
For reaching mount everest with a thickness of 0.1mm, a paper should be folded 27 times

0.1mm * 2 ^ 27 = 13.4 km which surpasses mount everest by approx 5 km.

Loved the post and the discussion surrounding it. I think that John is correct and Everest would be surpassed with 26 folds not 20. I have used this in the past with my Year 9 and they loved it. Goes well with the power of ten video.

I'm glad some people know how to add. Props to John Bruno and Elendilm for adding correctly. I think author was in a hurry and when added to 10485.76, forgot they were adding centimeters and not converted to kilometers yet. :)

By Anthony M (not verified) on 31 Aug 2012 #permalink

u r not showing how to do it

Just amused at the thought of tne 42d fold... You'd have 2 halves each half the distance to the moon.. Need some serious swinging space to manoever that around.. Hope it's not raining (or snowy or windy) anywhere for that distance.. Or any buildings, trees, people... Might be easier to start from the moon (handy if you're stuck there and need to slide back to earth?) .. Then again, the fold in the paper itself need be the length of the folded paper itself so you really would need to start with a pretty long sheet...

By Foldy Foldy (not verified) on 27 Dec 2012 #permalink

that's ridiculously wrong oO you'd need a giant paper, because a notebook page can't possibly have enough material to reach the moon

Although folding may be impossible more than a few times just do cutting in half. You can demonstarte using scissors or just rip for the first few iterations. Although putting them on top of each other and repeating still very tricky but easier than folding multiple times

By Graham Bagshaw (not verified) on 07 Feb 2013 #permalink

Talking about students making common sense checks I did have one student ask me "Has anyone done this yet?"

By Graham Bagshaw (not verified) on 07 Feb 2013 #permalink

Somebody help a poor math schlub out with an algebraic exponential equation, please! f(x) = ab^x

By Lance Nixon (not verified) on 24 May 2013 #permalink

Folding paper
~~~~~~~~~~

When my son was near the end of his primary school years, I thought that it was time that I should impart some of my Weird Freaky Science Wisdom - and have a little bit of fun as well.

I told him that I would give him a million dollars if he could fold a piece of paper in half, and in half again, and so on for a total of 10 times. Of course he tried, and of course he failed.

I knew that this would happen, because it was "Accepted Wisdom" that it was impossible to fold a piece of paper in half 10 times (or seven, or nine, for that matter.). I told him that it couldn't be done, even if he used paper the size of a football field. But I now know that I was wrong.

The first time you fold it in half, it becomes 150 mm long and 0.1 mm thick. The second fold takes it to 75 mm long and 0.2 mm thick. By the 8th fold (if you can get there), you have a blob of paper 1.25 mm long, but 12.8 mm thick. It's now thicker than it is long, and, if you're trying to bend it, seems to have the structural integrity of steel.

A typical claim on the Internet might run, "No matter its size or thickness, no piece of paper can be folded in half more than 7 times", and as you stare sadly at your block of folded paper, you tend to agree.

In fact, if you had a sheet of paper, and folded it in half 50 times, how thick would it be?

The answer is about 100 million kilometres, which is about two thirds of the distance between the Sun and the Earth.

And so Accepted Wisdom on Paper-Folding ruled, until 2001.

That was when a high school student, Britney Gallivan (of Pomona, California) was given a maths problem. She would get an extra maths credit, if she took up the option of solving the problem of folding a sheet in half 12 times. She tried and failed with reasonably-sized sheets of paper.

So she got smart, and used something incredibly thin - gold foil, only 0.28 of millionth of a metre thick. She started with a square sheet, 10 cm by 10 cm. It took lots of determination and practice, as well as rulers, soft paint brushes and tweezers, but she finally succeeded in folding her gold foil in half 12 times. She ended up with a microscopic square sheet of gold foil.

But her maths teacher said that ultra-thin gold foil was too easy - she had to fold paper 12 times.

She studied the problem, and came with two mathematical solutions.

The first solution was for the classical fold-it-this-way, fold-it-that-way method of folding the paper. Here you fold the paper in alternate directions. She derived a formula relating the number of folds possible (n) to the width (w, of the square sheet you start with) and the material's thickness (t):
scientic formula

The second solution was for folding the paper in a single direction. This is the case when you try to fold a long narrow sheet of paper. She derived another formula relating the number of folds possible in one direction (n) to the minimum possible length of material (l) and the material's thickness (t):
scientic formula

When she looked closely, she found that if you are trying to fold the sheet as many times as possible, there are advantages in using a long narrow sheet of paper.

Her formula told her that to successfully fold paper 12 times, she would need about 1.2 km of paper.

After some searching she found a roll of special toilet paper that would suit her needs - and that cost US \$85. In January 2002, she went to the local shopping mall in Pomona. With her parents, she rolled out the jumbo toilet paper, marked the halfway point, and folded it the first time. It took a while, because it was a long way to the end of the paper. Then she folded the paper the second time, and then again and again.

After seven hours, she folded her paper for the 11th time into a skinny slab, about 80 cm wide and 40 cm high, and posed for photos. She then folded it another time (to get that 12th fold essential for her extra maths credit), and wrote up her achievement for the Historical Society of Pomona in her 40 page pamphlet, "How to Fold Paper in Half Twelve Times: An "Impossible Challenge" Solved and Explained". She wrote in her pamphlet, "The world was a great place when I made the twelfth fold."

Britney Gallivan succeeded because she was as contrary and determined as Juan Ramon Jiminez, the Spanish poet and winner of the 1956 Nobel Prize for Literature. He wrote, in a metaphor for the questioning and resilient human spirit, "If they give you ruled paper, write the other way."

~ Dr. Karl © 2013 Karl S. Kruszelnicki Pty Ltd

I read it in Boy when I was a kid and it's stuck with me. ;)

I need to to thank you for this wonderful read!! I absolutely enjoyed every little bit of it. I have got you book-marked to look at new things you post

By how to make an… (not verified) on 24 Nov 2013 #permalink

Thus awesome , can i get a systematic formula for this

By Prince Tetteh (not verified) on 23 Feb 2014 #permalink

You don't tell how many people did it.

If u cut the paper you can fold it better...

By Clara Olsen (not verified) on 18 Mar 2014 #permalink

We know that a paper can not be folded more than 7 times using our hands. But can a device be made to fold it 42 times (or even 20 times)..?

By Rajat Gaur (not verified) on 18 Mar 2014 #permalink

A few people beat me to my comment already but if you ever worked at a book bindery place you will know that can't succesfully fold more than a few dozen sheets of paper at a time. So...if you actually cut the paper in half and then stack the halves instead of folding it perhaps you could be more successful in exceeding 7.

I came up with 2,199,023,255,552 pages after 42 folds. Now I just need to know the conversion of cm to km to figure the height of all that.

By Richard La France (not verified) on 18 Mar 2014 #permalink

these are absolutely some of the best comments i have ever had a chance to read. i LOVE intellectual arguments ( and no honestly i didnt understand HALF of it ;) i'm the more artsy type of nerd) this was just epic.

By leannemccullough (not verified) on 18 Mar 2014 #permalink

Depends on the thickness of the paper.

With a slight variation, this could be tested practically. Instead of folding the paper, cut the paper and stack the cut pieces in layers. You probably want to do that inside of a very narrow tube. My feeling is that you would be dividing molecules *long* before you reached the Moon, likely before you reached 50 meters. I don't have a good idea how high the stack would be before you were dividing atoms, but probably short of the Moon and the thickness of the paper would have stopped mattering long before then. This is an exercise that only makes sense in a situation where the paper remains paper no matter how many times it is cut or folded. In other words, fantasy land.

Anybody know if Roald Dahl's "Boy" was the first instance of this being put down in print?

So how thin would a piece of paper folded 42 times actually be and would it be visible to the naked eye (or even under a standard microscope).... or rather how big would it have to be to be visible to the naked eye?

You are incorrect. You would have to fold the paper 145 times to reach the moon.

Your mistake was estimating the thickness of paper as opposed to finding the actual number. Paper is 0.00254 cm thick. Much thinner than your estimate.

By Brandon Capra (not verified) on 19 Mar 2014 #permalink

this is most definitely not true, sadly.

needless to say is a piece of paper is 0.003". if you fold it 42 times you will still only end up with 0.126". lets get real here you'll still only get less than half an inch. this physics or mathematical formula is ridiculous. the moon is 380,000km from here, that is that, and a piece of paper is 0.003" and that is that.

you would need 127000000 pieces of paper..... rounded up.

Of course today's technology couldn't fold a piece of paper 42 times fools! It would reach out to the moon if they did! That's the whole point of the article.

By Jonathan Herman (not verified) on 19 Mar 2014 #permalink

^^^ Sarcasm

By Jonathan Herman (not verified) on 19 Mar 2014 #permalink

Although an interesting thought, it violates physical boundaries. In your calculations you do not account for the fact that the surface area of the paper is decreasing exponentially by the second power; decreasing to half of the original surface area after the first fold and one sixteenth of the original surface area after the fourth fold (try it out with a piece of paper!). At this rate of exponential decrease the surface area would become incredibly small. So small in fact that if a regular eight and a half by eleven inch piece of paper were to actually be folded 42 times, its surface area would be 4.27304^(-85) meters cubed. At this theoretical surface area the paper would cease to make sense as the Bohr model proposed by Niels Bohr states the radius of the hydrogen atom is 5.3 x 10^(-11) meters. This radius gives the hydrogen atom a planar surface area of 8.8247^(-21). The paper would have to be smaller than a hydrogen atom but tall enough to reach the moon? Impossible. Nonetheless this is actually pretty interesting because in your proposed hypothetical the height was increasing linearly by a factor of two (x^2) and in my deductions the surface area was decreasing by the reciprocal of that (1/x^2). This gives closure to the mathematical equality and although none of these proposed ideas make physical sense it is nice to know that the laws of math are safe once again.
-Engineering major

By Norberto Martinez (not verified) on 19 Mar 2014 #permalink

c, No wonder Canada will never put a man on the moon. Math is not your favorite subject!

By c is an idiot (not verified) on 20 Mar 2014 #permalink

Really interesting topic, and great discussion comments.
Re. post #49 from Jai Ganesh Nadar, really interested to know the scientific formulas which have been referenced, but were not visible in the post....can these be re-posted please?

The first solution was for the classical fold-it-this-way, fold-it-that-way method of folding the paper. Here you fold the paper in alternate directions. She derived a formula relating the number of folds possible (n) to the width (w, of the square sheet you start with) and the material’s thickness (t):
scientic formula

The second solution was for folding the paper in a single direction. This is the case when you try to fold a long narrow sheet of paper. She derived another formula relating the number of folds possible in one direction (n) to the minimum possible length of material (l) and the material’s thickness (t):
scientic formula

By Hangin' in there (not verified) on 20 Mar 2014 #permalink

#77 was unnecessary and pointless

...its surface area would be 4.27304^(-85) meters cubed.

Area measured in meters cubed? I really hope you are not, actually, an engineering student - and I'm sure the good folks at UC Davis would agree if they were to see that.

Yes well its finals week and i wrote that at 3am. It was obviously something that just slipped up and i meant to write "squared". Everyone makes mistakes, including you and your incorrect comma usage. The rate of decrease in surface area still holds true and my qualitative deductions still make sense.

By Norberto Martinez (not verified) on 20 Mar 2014 #permalink

If I ever have a band we'll have an album called "42 Foldings to the Moon"

including you and your incorrect comma usage.

No, sorry, wrong again: ``actually'' is a non-essential clause in that sentence, and should be set off by commas.

@"c" #63: I think you need to (a) read the article again, and (b) learn how multiplication works.

Start with a piece of paper, with thickness 0.003" (as you claim). Fold it once. Now you have a *double thick* piece, 0.006" thick. Fold that object again. Now the thing is 0.012" thick. Two folds get you FOUR times as thick (2^2). Fold again, and it's 0.024" thick (three folds, EIGHT times as thick, 2^3). Keep going. Each fold _doubles_ the total thickness, it does not just add one more layer.

I leave the rest of the arithmetic as a homework problem.

By Michael Kelsey (not verified) on 21 Mar 2014 #permalink

If you were traveling down the street and five of your four wheels fell off your canoe, and a train left Japan going 40 mi. an hour, headed for China, how many pancakes would it take to build a doghouse?? WRONG.....elephants can't fly.

(Bogus algebraic question scoff at by millions of college students.)

Lol everyone who read this must have seen it from Buzzfeed first.... why else would they have all voted 42

By AJ Marchbanks (not verified) on 22 Mar 2014 #permalink

you guys have way too much time on your hands ...

This is for dean. Maybe we should put you between commas as well, since your two comments were, basically, non-essential, added nothing to the great exchange here, and were just the typical ego-trip of a little mind who sees one error in someone else's statement and jumps on it with both feet, not allowing for typos, tiredness, etc.

Norberto Martinez: the laws of math may be safe again, but none of us is safe from pedantic airbags like your pal dean.

Ethan, Thank you for your insight. However, you are a douche and I don't appreciate you wasting my time with this douchebachery. People who like expotential growth are themselves products of half lives.

My brother showed this to me yesterday and I was having trouble conceptually understanding this so I sat with this for a while and was thinking about what i specially don't understand about this. My question is how can a piece of paper (or anything for that matter) be folded and exceed its initial dimensions. A standard piece of paper is 8 and 1/2 by 11 inches and its depth is 0.1mm. If you stand up a piece of paper it is 11 inches tall. If you fold it once i understand the thickness increases by 2x but to get that the height has to be decreased by 2x. If you fold it again the depth becomes 4x what it initially was but the length and the width are decreased by 2x. you can keep doing this exponentially always increasing the depth and decreasing the length and width but how can you get the piece of paper to exceed its original dimensions.

By Ethan Blank (not verified) on 15 May 2014 #permalink

I just folded a piece of printer paper in half eight times. But I have a trick. I folded it five times width-wise, so it keeps the same length, then I folded the paper rope three times.
In somewhat related news; I can count from zero to 1023 on both my hands. (Thirty-one on just one hand.)

By cyalknight (not verified) on 15 May 2014 #permalink

The real question is whether we could make a piece of paper that is big enough to fold 42 times.

Hmm, yes, if you could fold it 42 times it would reach the moon (38k miles past, in fact...). However, the initial size of the piece of paper would have to be astronomical. For example, if I wanted to end up with a 1" square at the end of folding 42 times, I would have to start with paper that was at least 17.6 billion inches (or about 278k miles) wide.

this "trick" shows how math can hav no connection to reality. it's too bad that people rely on math as if it always does.

9 foldings is about 5 cm. 10 foldings i about 10 cm. But as mentioned, how can 20 foldings be 10 Kilometers long? 10 additional foldings (2^10 = 1024) will only make it about 10000 cm long or 100 meters?

but sir we can not fold a paper more than seven times if u will fold the paper from the middle than it is not possible

By Karan Rana (not verified) on 09 Jun 2014 #permalink

Don't fold the paper... cut it and stack it. Same result, easier to get to the moon. Brainiacs :)

I don't get it. This does not make any sense to me.

whoa

By JingIeBeIls (not verified) on 12 Jul 2014 #permalink

It would burn up in the atmosphere

By Hahafunnyguy (not verified) on 09 Aug 2014 #permalink

The moon is 238,855 miles from Earth and a piece of paper of (.1 cm) thick folded 42 times exponentially would be 43,980,465,111 cm thick, which equals to 273,282 miles, which would not only reach the moon but it would actually overshoot it by about 35,000 miles which would be about five times the distance from the surface of the earth to the outer most layer of our atmosphere (Exosphere 6,200 miles) of about 10,000 miles longer than the circumference of the earth around the equator (24,901 miles)

Exponential huh? Try 2 to the 42nd power.

It's impossible to fold it so,but i like the way he has thought,which shows to others how to look @ a problem simply...

Can somebody help me out and show me the steps in the equation. I did the equation but was off by one decimal place when getting to 20 folds.

If anybody needs the mathematical working of this above claim, here it is:

FoldscmmKm
20.020.00020.0000002
40.040.00040.0000004
80.080.00080.0000008
160.160.00160.0000016
320.320.00320.0000032
640.640.00640.0000064
1281.280.01280.0000128
2562.560.02560.0000256
5125.120.05120.0000512
102410.240.10240.0001024
204820.480.20480.0002048
409640.960.40960.0004096
819281.920.81920.0008192
16384163.841.63840.0016384
32768327.683.27680.0032768
65536655.366.55360.0065536
1310721310.7213.10720.0131072
2621442621.4426.21440.0262144
524288.005242.8852.42880.0524288
1048576.0010485.76104.85760.1048576
2097152.0020971.52209.720.21
4194304.0041943.04419.430.42
8388608.0083886.08838.860.84
16777216.00167772.161677.721.68
33554432.00335544.323355.443.36
67108864.00671088.646710.896.71
134217728.001342177.2813421.7713.42
268435456.002684354.5626843.5526.84
536870912.005368709.1253687.0953.69
1073741824.0010737418.24107374.18107.37
2147483648.0021474836.48214748.36214.75
4294967296.0042949672.96429496.73429.50
8589934592.0085899345.92858993.46858.99
17179869184.00171798691.841717986.921717.99
34359738368.00343597383.683435973.843435.97
68719476736.00687194767.366871947.676871.95
137438953472.001374389534.7213743895.3513743.90
274877906944.002748779069.4427487790.6927487.79
549755813888.005497558138.8854975581.3954975.58
1099511627776.0010995116277.76109951162.78109951.16
2199023255552.0021990232555.52219902325.56219902.33
4398046511104.0043980465111.04439804651.11439804.65
8796093022208.0087960930222.08879609302.22879609.30
17592186044416.00175921860444.161759218604.441759218.60
35184372088832.00351843720888.323518437208.883518437.21
70368744177664.00703687441776.647036874417.777036874.42
140737488355328.001407374883553.2814073748835.5314073748.84
281474976710656.002814749767106.5628147497671.0728147497.67
562949953421312.005629499534213.1256294995342.1356294995.34
1125899906842620.0011258999068426.20112589990684.26112589990.68
2251799813685250.0022517998136852.50225179981368.53225179981.37
4503599627370500.0045035996273705.00450359962737.05450359962.74
9007199254740990.0090071992547409.90900719925474.10900719925.47
18014398509482000.00180143985094820.001801439850948.201801439850.95
36028797018964000.00360287970189640.003602879701896.403602879701.90
72057594037927900.00720575940379279.007205759403792.797205759403.79
144115188075856000.001441151880758560.0014411518807585.6014411518807.59
288230376151712000.002882303761517120.0028823037615171.2028823037615.17
576460752303423000.005764607523034230.0057646075230342.4057646075230.34
1152921504606850000.0011529215046068500.00115292150460685.00115292150460.69
2305843009213690000.0023058430092136900.00230584300921369.00230584300921.37
4611686018427390000.0046116860184273900.00461168601842739.00461168601842.74
9223372036854780000.0092233720368547800.00922337203685478.00922337203685.48
18446744073709600000.00184467440737096000.001844674407370960.001844674407370.96
36893488147419100000.00368934881474191000.003689348814741910.003689348814741.91
73786976294838200000.00737869762948382000.007378697629483820.007378697629483.82
147573952589676000000.001475739525896760000.0014757395258967600.0014757395258967.60
295147905179353000000.002951479051793530000.0029514790517935300.0029514790517935.30
590295810358706000000.005902958103587060000.0059029581035870600.0059029581035870.60
1180591620717410000000.0011805916207174100000.00118059162071741000.00118059162071741.00

All things considered, it is physically impossible to double a sheet of paper on itself (fold in half), more than 8 times.

Wouldn't ripping it and stacking the pieces on top of each other have the same effect?

I also believe the calculation is incorrect as for the 20 folds

0.01mm = 1* 10^-7 km

2^20 * 1*10^-7 = 0.1048576km

which is roughly 104m while 27 folds would surpass the Everest.
I'm not a mathematician though, I may be wrong! :)

By Giuseppe Romagnuolo (not verified) on 18 Apr 2015 #permalink

No one is taking into account infinite gravity... or even "close to infinite gravity" what if said paper is only a single molecule thick and being folded on the surface of a neutron star? It could then be folded in half WELL over 200 times allowing the gravity of the star to "fold" it and flatten it quite nicely to a density equal to the neutron star . I dare say that in a black hole one could fold said paper an infinite amount of times... OR what about the far future?.. When the expansion of space-time of the universe surpasses the speed of light? One couldn't fold paper fast enough to ever catch up to the ever expanding void. AND if this reality is in fact a simulation then the paper in question is "simulated paper" and no paper is in fact is ever being folded..

By Shawn Wilson (not verified) on 03 Sep 2015 #permalink

Yes, Shawn, nobody is taking into account things that don't matter or even exist.

Tell you what, work out how you fold paper against the force of infinite gravity and tell us how many foldings you can manage.

Then tell us how far away the moon is when it is affected by infinite gravity.

This problem is a take on the following story
King of Persia asked a mathematician to solve a problem which he did. So the king said what reward would you wish for the assistance that you gave me in solving that problem The mathematician said very little your majesty see this chess board give me two grains of wheat for the first square, then 4 for the next square then 16 for the next and continue until you get to the last square. King thought that can't be difficult so he granted the mathematician's wish. They calculated that they had to give the man the total produce of the country for the next 15 years to satisfy the demand. This has historical evidence but not clear if the demand was fulfilled.

By Bob Abrahams (not verified) on 19 Sep 2015 #permalink

So if it takes 1 piece of paper 42 folds to get to or past the moon

Does that mean it would only take 2 pieces of paper 21 folds

Or that it would take 3 pieces of paper 10.5 or 11 folds

Or that it would take 4 pieces of paper 6 folds and your to the moon

Or does it mean you can get numbers to say anything you want them to

By David Perry (not verified) on 19 Sep 2015 #permalink

"Or does it mean you can get numbers to say anything you want them to"

No, it means you can say nonsense and it will say anything you want it to.

David Perry.. your maths leave a lot to be desired.

2 pieces of paper would require 41 folds not 21, 4 pieces would require 40 folds not 6.. What part of an exponential series do you not get?

Yes you can make numbers say whatever you want them to, in your case however, What you get them to say is complete and utter rubbish.

By Keith Estrel (not verified) on 20 Sep 2015 #permalink

Try this with money, not folding it, but doubling it, over and over again.

Does any of this take into account that the folded edge of a piece of paper is thicker than the two layers?

and for two pieces of paper, it would take 21 folds EACH, or 42 folds. :)

No, it doesn't.

You cant fold it. The width of paper then becomes the height of the stack. Which means one giant piece of paper. You can cut though. Hypotheticaly.

By Svart Gult (not verified) on 08 Oct 2015 #permalink

Could someone help me? How do you work this out???

This is 100% FALSE based on the assumptions going into it.

This shows a picture of a pink 8.5x11 piece of paper and says
" how many times would you have to fold this paper onto itself to reach the Moon?"

THIS paper. If you add a stipulation that a hypothetical paper can be as big as necessary to make 42 folds, then yeah, you've got something there, but the reality is no single piece of paper ever made would be big enough to do this.

By Fisharmor (not verified) on 21 Mar 2016 #permalink

I don't get it. It doesn't alighn with my calcs, no matter how many times.
started with 0.01cm. first fold makes it 0.02 [multiple by 2].
so, every time i multiple by 2, right?
0.01, 0.02, 0.04, 0.08, 0.16, 0.32, 0.64, 1.28 [cm!], 2.56, 5.12, 10.24 [10 folds!], 20.48, 40.96, 81.92, 163.84, 327.68, 655.36, 1310.72 [17 folds, 13 meters], 2621.44, 5242.88, 10485.76 [20 folds].
so i got to 104 METERS.
did i do something wrong? i honestly don't get it.

Mathematically, it's correct, but the steel of paper would have to be larger than 240000 miles wide.

By ray uhler (not verified) on 06 Apr 2016 #permalink