View Full Version : How do I repeat a calculation 1000 times

Vince

11-08-2002, 06:34 PM

Many years ago a school teacher posed the question, as a curiosity only. "If you take a sheet of film 1 thousandth of an inch thick and fold it in half 1 thousand times, how thick will the folded sheet be?"

It is of course physically impossible, but the answer will change your perspective a little.

My teacher thought the answer was on the order of 100 miles, but he was wrong by a factor of a trillion or so. I solved the question years ago, the hard way, and forgot the answer! It was millions of lightyears I think.

Can someone tell me how to use my computer to calculate it?

Thanks in advance. Vince

Elwin Way

11-08-2002, 06:42 PM

Wouldn't the answer be (1x2^1000)/1000 ?

Terry Porritt

11-08-2002, 06:46 PM

That's right Elwin, a computer is not needed. Dont forget to put in the units, inches :)

robsonde

11-08-2002, 06:46 PM

(2^1000)/1000 sounds right to me.....

it works out at about 1x10^298

godfather

11-08-2002, 06:50 PM

As a matter of interest, how many times can you fold a sheet of paper in half (meaning fold once = double thickness, fold twice = 4 x thickness...)

The answer is about 7 only .... try it!

Terry Porritt

11-08-2002, 07:04 PM

Also whats interesting Godfather, is that the maximum number of folds is not very much dependent on paper size either.

-=JM=-

11-08-2002, 07:20 PM

It's also just as hard with tissues as well.

Graham Petrie

11-08-2002, 08:53 PM

hmmm - 2.7x10^293km!

The no. of times you can fold a peice of paper is dependent on two factors - the thickness of the paper and, its ability to stretch. The outer side of the folded paper must be able to stretch (and the inner side compress) to allow the paper to fold in half, and thickness helps only slightly.

Paper - very hard to get more than 7. Other materials can be folded slightly more, but not by much.

G P

pporritt

12-08-2002, 01:31 AM

If you could remove the word "fold" from the question, and instead cut the paper in half, you would be able to go further. But even then, starting with a piece of paper .001" thick, and 100 sq. inches, after 10 folds the pile would be more than half-an-inch thick, but only 0.2 sq.in. in area. I think that shows why "folding" would very quickly become out of the question.

After 17 iterations, the pile would be 65" high, but hard to work with because of its small area (.0015 sq.in or .04"x.04" square)

After 30 iterations, the pile would be more than 8 miles high, but so small in area that it would be invisible to the naked eye.

The results after 1000 iterations are meaningless - light would take billions of years to travel from one end to the other.

Graham L

12-08-2002, 04:30 PM

This is just an extreme version of the very old one: the reward of 1 grain of corn on the first square of the chessboard, two grains, four grains ...

Exponentials ...

Baldy

12-08-2002, 04:38 PM

Ain't Physics weird, and PressF1 is definately getting very strange........

Thought Poppa would have a comment on this thread. You're slipping PJ

Graham L

12-08-2002, 05:20 PM

And I would have taken the beautiful princess and half the kingdom, anyway. Easier to carry. ;-)

Poppa John

13-08-2002, 12:09 AM

Baldy. I am still around. In a lot of pain just now & not good company. The grains of corn one I do remember tho. Take a chess board, put 1grain of corn on the first square, two on the next etc doubling each time for the 64 squares. Do you remember getting "Lines" at school for punishment? One school I went to had this instead of "Lines". We had to work it out by hand/head, no calculators then. If you got it wrong it had to be done again. Good for mental arithmatic tho. Didn't do much for my IQ apparently Painful Poppa John (Take Painful any way you like) :D Still happytho. :D

pporritt

13-08-2002, 12:34 AM

I have always been fascinated with the chessboard problem. But, I think you will find that it was rice, not corn...

Peter

Elwin Way

13-08-2002, 12:46 AM

Wanna know something funny? If I can't get to sleep, I don't count sheep. I work out Pi to as many decimal places as possible.

So far my record is 14 :^O

-=JM=-

13-08-2002, 12:51 AM

I prefer e. It's just a lot nicer number i think.

Disclaimer: I do not endorse the drug ecstasy. I'm referring to the number e.

Dragonslayer

13-08-2002, 01:56 AM

Sounds like the chances of winning lotto (40x39x38x37x36x35)? but people still buy the tickets, and then you add the powerball chance (Total x 40) and you can really see why "your in the money"

Graham L

13-08-2002, 12:08 PM

Not quite that bad Dragonslayer. Divide by 720, because that's the number of ways the 6 numbers can come out. (Combination rather than permutation).

But, to win the jackpot you first have to win the major prize, then get lucky.

Graham Petrie

13-08-2002, 06:53 PM

Yes Graham, but don't forget that is only if you only consider 1st division. The chances of winning a prize (no matter the size) *poetic* :-) is actually alot better.

G P

What if he was gay? What if he was offered the prettiest camel and half the kingdom?

I thought I was sad. I don't even know how to work out Pi, or are you just doing 22/7?

I double:

1

2

4

8

16

32

etc.

Get into a mess around the millions or tens of millions. My son gets to about 65536. Sad.

robo.

Elwin Way

13-08-2002, 08:22 PM

Yep, 22/7. without paper, calculator or blackboard. :D

Graham L

14-08-2002, 04:11 PM

I like the Dogbert cartoons. He had a stall selling half price lottery tickets "with nearly as good a chance of winning as full price ones". A customer looks at one and complains" "That's last week's." Dogbert: "And your point is?"

Vince

21-08-2002, 03:29 AM

> I have always been fascinated with the chessboard

> problem. But, I think you will find that it was

> rice, not corn...

>

> Peter

You'r right Peter, it was rice, and the process involved putting on each square, the number of the square TIMES the number of grains on the previous square; if memory serves. Vince,...another Canadian.

Graham L

21-08-2002, 03:57 PM

Doubling does it. 2^63 is a BIG number.

Poppa John

21-08-2002, 04:35 PM

If 7 folds of the paper is correct & I believe it to be so. Then how come a Japanese Samurai sword, steel, gets folded many more times than 7 ??

Poppa John :)

Graham L

21-08-2002, 04:42 PM

Totally different process. The steel is folded, hammered out flat, heated again and folded, hammered out ... The paper is getting thicker at each step. The steel becomes twice the thickness then is reduced to single thickness again repeatedly. It becomes homogenised.

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