Paper Folding Riddle

I did this one at college! The answer is yes, but we used a very large piece of very thin tissue paper, and it wasn't very flat, even using a steam iron to after every fold! We started with a piece 3m long and 1m wide, and folded the first 7 folds all along the width, ending up with something just over 10mm wide. We then managed to get 2 more folds longitudinally, if that makes sense! We went for 10 but had a catastrophic failure. The paper split.

eight folds which results in 256 layers is just about possible but it is about the limit, the usual challenge is to do it ten times which is just about impossible

what about rubber sheet?, or gold leaf?

Ahh! I think I've spotted the flaw here! NOT PAPER!

That's not the flaw... this is a mathematical limit based on an assumption of uniform thickness. See if you can prove it...

yes, That is why I suggested a stretchable or ductile material to supply the extra material needed to furbish the radius as the number of folds gets high.

By revision and extension:

Take a standard chess/checker board and place a 1-cent piece on the first square, 2 on the second square, etc. till you have coins (or tokens) on each square of the board.

How may coins/tokens are there on the board?

4, all the rest were stolen by opportunistic thieves (now rich as Croesus)

18,446,744,073,709,600,000 Cents. But you won't be able to spend them as no-one accepts small change these days!

Like the "Penny-a-day, then doubled every day for thirty days" problem posed to me when I was in elementary school. I grew up praying I could get someone to pay me a salary based on that amount.

Can you change my (insert your currency symbol here)20,000,000,000,000,000,000 Bill

See Bernie Ecclestone, he can!

Do you have an awsome slide-rule, or a calculator with limited resolution?

I just tried it on a standard 8.5x11 sheet and I got about 40 folds. No problem, I just folded it like an accordian. I probably could get more if I tried.

I then tied it in a knot and wore it as a bow tie.

You didn't halve the area each time as specified.

The current record belongs to a girl in California who did it for EXTRA CREDIT as a Junior high school student. She holds the record with 12 folds.

*gah to smart for me*

Her name was Britney Gallivan.

There are NO details about how she did it at that URL, only the story of what she did and how to order a book on her feat, which presumably will then tell you HOW she did it!

For my part, I believe the key is using a material or a coating on the paper that has very low friction, allowing slippage. Then, as you make each fold, do not pull the running end even with the stationary (bottom end), but leave an allowance for creep. As you fold over, the last top half becomes the inside turns at the fold, which has a shorter circumference and so allow the longer bottom layers to "roll" around more.

If done slowly, and massaging the layers before, during, and after each fold, so that "slip happens" and tension is reduced, you can get pretty far. I am guessing this is the technique used. Of course, if an elastic material was used this would not be a problem.

I really don't know about the math behind the formulas, but I guess if I took the time I could work it out.

""The folding stuff

The British Origami Journal from February reports that paper has now been folded

12 times. Britney Gallivan folded a kilometer length of loo tissue 0.008 cm thick.""

that is folded to 1024 sheet thick x .008CM =~8 CM thick pile when folded.

I wonder if gradual stretch in the loo tissue was analgous to stretch in a rubber sheet.

In the past the limiting stage I personally saw was tearing of the paper on the outside of the fold

Two to the power of twelve is 4096 hence the pile would be 32 cm thick, rather unlikely!

yes, I forgot how to count my fingers duh.

well, some one on british origami probably bought the solution and she took a long length of toilet paper. Since toilet paper is a loosely laid mat it is possible that as it was folded a distributed rearrangement of the fibers allowed the paper to yield lengthwise while fully supported so that it did not tear. In addition, it may have torn and the tears are not evident. with 1000 meters by the last fold it would be 3/4 of a meter long.

Possibly you need a brand of toilet paper with no serrations as it might be likely yo tear at the serrations?

So 1000/4096=3/4??

yes, I forgot how to count my fingers duh.

well, some one on british origami probably bought the solution and she took a long length of toilet paper. Since toilet paper is a loosely laid mat it is possible that as it was folded a distributed rearrangement of the fibers allowed the paper to yield lengthwise while fully supported so that it did not tear. In addition, it may have torn and the tears are not evident. with 1000 meters by the last of 12 folds it would be ~ 3/4 of a foot long. Probably too thick to fold any more by now.

Possibly you need a brand of toilet paper with no serrations as it might be likely yo tear at the serrations?

OK then, Go to a paper mill and buy a roll of cigarette paper. they are about two meters wide and about the same diameter. We do the surface preparation work at a local firm that makes the machinery. I make about 32 layers to the millimeter, my micrometer gauges are downstairs, and I am too lazy to get it. Pi r ^2 x height = volume, let's ignore the spindle. this is just a crude guesstimate. Two Pi cubic meters. let's call that 6 cubic meters of paper. How long? well the circular area is about three million square millimeters, each square millimeter has we said 32 layers of paper i.e. 96 million millimeters of paper in a full roll. let's start folding length-ways. five folds gets us back to 3 kilometers, twelve folds will make our block of paper 23.4375 meters long. So now we buy 4096 of these rolls of paper, so as to stick them end to end, because we got blind drunk at the Office New Years Party, and Faxed the order through........Hold on....Happy New year CR4 Readers. Have a great 2007

What is Alastair smoking?

Perfectly Legal and above board, sir.

Check out "Our Esteemed Clients"

http://www.jjfox.co.uk/static/19%20St%20James/clients.htm

I was named after Prince Alastair of Connaught. my other name in the 'book' is Alastair Fife.

Yes, Reminds me of the "North Atlantic Squadron"

Here we come with Fife and Drum.......

If you google "North Atlantic Squadron" most of what you get will be xxx rated, and I can recall many of the verses from my time in the RCAF.

I nearly laughed till I cried aurizon, I am a semi-retired R.M.P.T.A. Chaplain,

Then I read:-

"The service police are a bunch of sluts,
They should be hung up by their nuts,
A bunch of hicks from out of the sticks
In the North Atlantic Squadron."

I shall forward it to the Boss, e@hay.org, (Colonel)

Definitely saved to entertainment favourites

"cats on the rooftops, cats on the tiles"

Google that

For the Attention Of:-

http://www.rafmusic.co.uk/holding_page.html

Go on Merlin, we dare you. Shhh.