The area formula also works with numbers that aren’t whole. A standard piece of paper has a height of 8.5 inches and width of 11 inches. What is the area?
Answers
You all are missing a very important part of this proposition. IF.
This statement it meant to emphasize a kind of paradox.
Each time you fold, the assumption is that the thickness would double. Let's say the initial thickness of a piece of paper is .004 inches (500 sheets in a ream, about 2 inches thick, thats .004 each). If you doubled a .004 sheet 10 times, it would be about 4 inches thick. Double 10 more times, 350 ft. Double 10 more times (you are now at 30), 68 miles! Double 10 more times (now at 40 total), 69,000 miles. Twice more gets you to about 280,000 miles.
The moon is about 240,000 miles.
The problem is, what happens when you fold a paper? The surface area cuts in half. So, lets look at what surface area would HAVE to do at each point we looked at above. The surface area of a paper is 8.5*11…thats 93.5 square inches. After 10 folds, each time halving the area, you would have an area of about .1 square inch, less than the area of a small postage stamp. After 20 foldings, the area would be .00009 square inches (each side would be about the width of two slices of paper)! After 30 foldings, the area would be .00000009 square inches, about 1/3 of a human hair on each side! After 42 foldings, the area would be .00000000002 square inches, close to bacteria size.
So, picture it: IF you COULD fold it 42 times, you would have a thickness reaching the moon, but a surface area that is essentially invisible. You would have created a filament. Thats the paradox. Its impossible, except in your mind.
But it illustrates what it is meant to illustrate: the power of geometric series, doubling or halving. It gets out of hand very quickly!
By the way, my numbers are close, I think, if not perfect. I am not a biologist or a stamp collector. If someone wants to take exception to the size of stamps or bacteria, let me know :)