Maximum Folds: Exploring the Physical Limitations of Folding Paper

[BobG]

Instead of the logic riddles, how about something a little more physical.

What's the maximum number of times thay you can fold an 11 x 8 1/2 inch sheet of paper in half. In other words, you fold the paper in half once and now have a double thickness sheet of half the area. Fold it again and you have a quadruple thickness sheet one quarter the area.

I'll post the world record for folding paper in half in a day or two.

 

[ascky]

I can only get eight... (isn't the world record 12)

 

[Gokul43201]

Am I allowed to use the 500 atm hydraulic press in the next building ?

 

[ascky]

And I thought I was being clever with a clamp!

 

[vikasj007]

i guess, that if you are not using a hydraulic press, and are doing it just by hand, then 8 is the maximum no. of times you can fold any paper.(of any thickness)

i had read it somewhere, and as far as i tried it came out to be true.(i tried with about 7-8 papers of different thickness.)

 

[hemmul]

Note, that the area of a paper decreases exponentially as S/2^n where S is the initial area, n-the number of folds. It is nearly impossible to fold a _thick_ sheet of paper if it's linear size is comparable with a finger's diameter... A4 paper is folded up to 8 times.
To make it 9 we have to use A3.
10 requires A2.
11 - A1...
well, i think if i ever have a bigger paper i will definitely find a more interesting job that just folding it

 

[NoTime]

Use thin tissue paper
Got 11 with 4/11 single ply TP

 

[ek]

I saw this on Beakman's World (early 90's science show) like twelve years ago. He said the max was eight.

 

[BobG]

Britney Gallivan folded paper in half 12 times while a junior in high school.

The first image I get out of that is sitting in a bar drinking a Foster's and having this burley girl walk in and crushing my beer can so hard the beer splashes off the ceiling.

Actually, she's got a little more analytical approach. She even developed two equations to determine the minimum length necessary to make another fold. She even published a 40 page booklet "How to Fold Paper in Half Twelve Times - An “Impossible Challenge" solved and explained". Sounds like a best-seller to me. (I might buy one. I haven't decided yet.)

http://www.osb.net/Pomona/12times.htm

(Having not read the book, I was only able to fold the paper in half 8 times.)

 

[Britney]

Folding paper in half 12 times

Just a note that the the paper folding limit link has changed to: http://www.osb.net/pomona/12times.htm
The p in pomona has to be small.

Thanks for the nice comments Bob,
Britney

 

[vikasj007]

so you are the britney who folded the paper 12 times?

hey, can you give some hints about how you did that, i can never get beyond 8.

 

[Britney]

Yes I am the one.

The two formulas at the listed website are correct and have been tested with over 50 different thickness and lengths of materials. Fold carefully. It does not require force. Paper is quite solid, try squeezing a phone book in half or stretching a piece of paper. For one directional folding use what I call the rotational sliding shown in the picture and it will work out. Having a material reserve of 20% makes it easier to compensate for imperfections on a given number of folds.

The equations tell what you need to have to fold a given number of times. The story of the problem and the derivation of the equation are explained in the book, but the answer by itself is easy to use and is all a person needs to use to fold a given number of times.

I forget the details now but some one said they had folded a ten by twelve foot plastic sheet some nine times. I calculated they could have done the same number of folding with a one and a half foot square piece of the same plastic. I then carefully folded the same thickness plastic and sure enough the small amount was all it took. They were just not careful. As the work is exponential so make sure to allow a day to fold a piece of paper in half twelve times. That is not counting the preparatory work. The initial work I did was quite time consuming.

By the way, I think the paper folding work is going to be mentioned on the CBS show Numb3rs very soon.

 

[bjr_jyd15]

Anyone catch Numbers last last night? Britney is famous! Charlie, the genius mathematician, was explaining how the pyramid scheme exponentially grows and used the paper-folding analogy to show how it works. He said, In fact, a high school student named Britney Gallivan devised a way to fold paper in half 12 times, and she even did it and she has the record. (I paraphrased)

I thought that was pretty cool- good job Britney :)

 

[edward6512]

A group of students in Massachusetts folded a piece of paper 13 times last weekend. See this link:

http://www.necn.com/04/07/11/Students-claim-world-record-folding-toil/landing_scitech.html?blockID=499544&feedID=4213

This isn't rocket science: the key is having really, really long paper and a lot of patience. This one started 2.5 miles long.

 

[edward6512]

I believe that britney's paper started pretty long as well -- something like 4,000 feet in length.