Paper Folding Skeptic

[T'ai Chi]

It is impossible to fold a piece of paper in half more than 7 or 8 times.

Yeah, I've heard that one before too. Ever since about the 5th grade or so!

Some interesting links:

http://www.maa.org/mathland/mathtrek_01_26_04.html

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

http://mathworld.wolfram.com/Folding.html

As the first link points out, there are sites that still stick to the 7 or 8 times myth.

[CFLarsen]

I always understood it as you had to fold first "north-south", then "west-east", then "north-south", and so on.

Folding a thin sheet of gold 12 times? Red herring. Showing mathematical equations? Theory is one thing, real-world another. A photo? I have no idea if there are 11 folds.

Sure, I can be convinced. But show me, step by step.

[MRC_Hans]

Yes, the folding is to be in alternate directions, but the basic problem is the same.

It is neither a myth nor a natural law, it is a practical observation. As the number of folds increase, the stac kbecomes impossibly thick and the folds use up the available area (which becomes smaller for each fold). The 7-8 folds apply to normally available pieces of paper. No doubt, if you had a sheet of superthin paper the size of Texas (and somewhere to spread it out), you might get to 12 folds. Perhaps if we ever send tourists into space, some people can make the stunt in free-fall ;).

Hans :p

[richardm]

Originally posted by MRC_Hans
No doubt, if you had a sheet of superthin paper the size of Texas (and somewhere to spread it out), you might get to 12 folds. Perhaps if we ever send tourists into space, some people can make the stunt in free-fall ;).

Hans :p

Wouldn't the problem of the thickness of the stack be independent of the size of the paper? If it was bigger you'd just have more leverage to tear it!

[Darat]

(Because I am very bored and at home.)

Just tried this with two types of paper, had some success getting an "8 fold" with using tissue paper and making it wet.

But the 8th fold, is I think a bit dodgy, so I'd say from my quick experiment that 8 folds is probably just about possible but not easy.

http://www.darat.demon.co.uk/8folds.jpg

[BillyJoe]

My experiment was much simpler than Darats.....

The paper in my Computer printer folds only 6 times

Who would have guessed?

[MRC_Hans]

Originally posted by richardm


Wouldn't the problem of the thickness of the stack be independent of the size of the paper? If it was bigger you'd just have more leverage to tear it! Mmmm, maybe. I would tend to think that the thickness of the fold in relation to the area of it would be the limiting factor. But of course, tear is a problem.

Hans

[CFLarsen]

Originally posted by Darat
(Because I am very bored and at home.)

Why didn't you try this at work? :)

Originally posted by Darat
Just tried this with two types of paper, had some success getting an "8 fold" with using tissue paper and making it wet.

No can do. You cannot change the conditions. No wet paper.

Originally posted by Darat
But the 8th fold, is I think a bit dodgy, so I'd say from my quick experiment that 8 folds is probably just about possible but not easy.

The fold has to be all the way, not half way down. 7 times, so far. Even with thin, wet paper, and a pretty large piece, too.

Anybody else with waaay too much time on their hands? :)

[Diogenes]

Originally posted by T'ai Chi
It is impossible to fold a piece of paper in half more than 7 or 8 times.

Yeah, I've heard that one before too. Ever since about the 5th grade or so!

Some interesting links:

http://www.maa.org/mathland/mathtrek_01_26_04.html

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

http://mathworld.wolfram.com/Folding.html

As the first link points out, there are sites that still stick to the 7 or 8 times myth.
Myth?


Off to the dictionary with you... Again...

[LW]

Originally posted by CFLarsen

Anybody else with waaay too much time on their hands? :)

Or an access to a 6-ton press...

[CFLarsen]

Originally posted by LW
Or an access to a 6-ton press...

No, gotta be done by hand.

[Hexxenhammer]

I believe it because Mr. Wizard told me so. He never steered me wrong as a child....except for that accident with the hydrogen...but the hair grew back.

[bug_girl]

this week in science news:

http://www.sciencenews.org/20040124/mathtrek.asp
"Gallivan described how she obtained her equations and her efforts to solve the folding problem in a booklet published by the Historical Society of Pomona Valley, to which Gallivan belongs (see http://www.osb.net/Pomona/12times.htm).

In January 2002, Gallivan herself demonstrated how to fold a large sheet of paper in half 12 times.

It pays to question received wisdom, at least as far as paperfolding is concerned."

[richardm]

Originally posted by bug_girl
this week in science news:

http://www.sciencenews.org/20040124/mathtrek.asp
"Gallivan described how she obtained her equations and her efforts to solve the folding problem in a booklet published by the Historical Society of Pomona Valley, to which Gallivan belongs (see http://www.osb.net/Pomona/12times.htm).

In January 2002, Gallivan herself demonstrated how to fold a large sheet of paper in half 12 times.

It pays to question received wisdom, at least as far as paperfolding is concerned."

http://www.osb.net/Pomona/Equation%205.gif
, where W = Width of paper and n = number of folds required.

Well, I take it back, Hans. It appears that size does matter after all :D

[bug_girl]

Originally posted by richardm
Well, I take it back, Hans. It appears that size does matter after all :D

well, if you guys had just started by asking me, i could have saved you a lot of trouble!:D

[Diogenes]

Originally posted by bug_girl
this week in science news:

http://www.sciencenews.org/20040124/mathtrek.asp
"Gallivan described how she obtained her equations and her efforts to solve the folding problem in a booklet published by the Historical Society of Pomona Valley, to which Gallivan belongs (see http://www.osb.net/Pomona/12times.htm).

In January 2002, Gallivan herself demonstrated how to fold a large sheet of paper in half 12 times.

It pays to question received wisdom, at least as far as paperfolding is concerned."

The artice did not clarify if the 12 times was accomplished by folding in half at right angles with each successive fold.. ( which has been a parameter of the ' 8 Fold ' problem ).. The formula given, specifies folding in the same direction, and previous discussions have indicated it is possible to make it to 8 and beyond with this method..

P.S.

http://www.osb.net/Pomona/03Brit2.jpg


If you want to call that " A piece of Paper " then this

http://www.glasnet.ru/~asebrant/edut/boulder.jpg
Is a grain of ( very course ) sand...

[davefoc]

OK,
If we narrow the claim down to a single 8.5 x 11 inch piece of paper of standard paper (about 4mil thick), dry, folded in an alternating fashion I get six folds and a tenuous seventh.

Other experiments:
Newspaper: 8 folds, no real chance of a ninth

Glad wrap sheet approximately one by two feet.: nine folds, no chance of a tenth

Standard 8.5 x 11 sheet wet: seven folds, no chance of 8

I thought of ironing the creases but that doesn't look like it would help. It looks like last fold is limited by capablility of material to stretch, the thickness of the material and the ability of the folder to apply sufficient bending force on the folded paper. I also thought of soaking the paper in oil but that seemed messy and I have already spent more time on this than any sain person would that wasn't avoiding work on what he should be doing.

[Yahweh]

Thickness of paper makes quite a difference...

Tissue Paper will easily fold 10 or 12 times...

Of course "pixie dust" makes practically any paper fold 10 or 12 times, I've just misplaced my magic pixie dust... now where did it run off to...

[Interesting Ian]

If you could fold a piece of paper (average thickness) 50 times, its height would stretch into the asteroid belt.

[Yahweh]

10 Folds:

http://home.ripway.com/2004-1/51619/PaperFolding.jpg

Do I get a prize?

[BillyJoe]

Originally posted by davefoc
.... but I have already spent more time on this than any sain person would.... :D

[BillyJoe]

Originally posted by Interesting Ian
If you could fold a piece of paper (average thickness) 50 times, its height would stretch into the asteroid belt. Aha, NOW I understand the problem. :)

BillyJoe.
(I haven't doen the maths though - I do hope it is correct)

[Cecil]

Originally posted by Interesting Ian
If you could fold a piece of paper (average thickness) 50 times, its height would stretch into the asteroid belt. You only need 29 folds to get to the ISS, but 67 folds will get you to Alpha Centauri.

What do I do with my proposal for a folded-paper propulsion system? :D

[davefoc]

Cecil's post made me curious about alpha centauri. Some interesting facts from this site:

http://homepage.sunrise.ch/homepage/schatzer/Alpha-Centauri.html

Alpha Centauri is part of a three star system
Alpha Centauri meets many of the important criteria required for a solar system that would support life although it's not known if it actually has any planets.
Alpha Centauri is not quite the closest star to us. Alpha proxima (part of alpha Centauri's group) is slightly closer (4.22 versul 4.35 light years)

As to Cecil's calculations he seems to be using some thick paper.

29 folds of .004 thick paper only makes a stack 33.7 miles high (according to my calculations) which is well below the 239 miles that NASA lists for the International space station. My .004 thick paper requires 32 folds to make it to the space station (pile thickness 271 miles).

My paper required 69 folds to make it to 6.3 light years thick. The stack pulled up a little short of alpha centarui (4.35 light years) with 68 folds.

I got 71,079,539.57 miles for 50 folds. Didn't quite make it to the sun from earth.

[geni]

Your facts missed out something important about Alpha Centauri :

Greatest computer game ever.

[Interesting Ian]

Originally posted by davefoc
Cecil's post made me curious about alpha centauri. Some interesting facts from this site:

http://homepage.sunrise.ch/homepage/schatzer/Alpha-Centauri.html

Alpha Centauri is part of a three star system
Alpha Centauri meets many of the important criteria required for a solar system that would support life although it's not known if it actually has any planets.
Alpha Centauri is not quite the closest star to us. Alpha proxima (part of alpha Centauri's group) is slightly closer (4.22 versul 4.35 light years)

As to Cecil's calculations he seems to be using some thick paper.

29 folds of .004 thick paper only makes a stack 33.7 miles high (according to my calculations) which is well below the 239 miles that NASA lists for the International space station. My .004 thick paper requires 32 folds to make it to the space station (pile thickness 271 miles).

My paper required 69 folds to make it to 6.3 light years thick. The stack pulled up a little short of alpha centarui (4.35 light years) with 68 folds.

I got 71,079,539.57 miles for 50 folds. Didn't quite make it to the sun from earth.

I said into the asteroid belt for 50 folds, not the sun.

[Cecil]

Originally posted by davefoc
As to Cecil's calculations he seems to be using some thick paper.

29 folds of .004 thick paper only makes a stack 33.7 miles high (according to my calculations) which is well below the 239 miles that NASA lists for the International space station. My .004 thick paper requires 32 folds to make it to the space station (pile thickness 271 miles).

My paper required 69 folds to make it to 6.3 light years thick. The stack pulled up a little short of alpha centarui (4.35 light years) with 68 folds. Yeah, I didn't know the standard thickness of paper offhand, so I guessed 0.5mm. That gives a height of 268km for 29 folds, and 67 folds gets you 7.6ly.

The problem is, after the 66th fold the dimensions of the paper (assuming 8.5" x 11" x 0.5mm originally) are 0.033nm x 0.025nm x 3.8ly. How do you fold THAT? :D

Originally posted by geni
Your facts missed out something important about Alpha Centauri :

Greatest computer game ever. Edited to add that I couldn't agree more. ;)