Friday, May 8, 2009

The Improbable Power of Exponentiation

If you are a math teacher, you're probably familiar with this activity.
Get a big sheet of paper and a good paper cutter. Cut the sheet in half, and stack the pieces together. Turn the pile 90 degrees, cut it in half again, and stack the cut pieces again. Keep doing this until you've cut and stacked the sheet 100 times.

If your cutter is really good, so that it cuts a thick stack of paper as quickly and easily as a single sheet, and it takes ten seconds to make a cut, stack the pieces, and position them for the next cut, then you'll be finished in 16 minutes, 40 seconds.

If the paper is 0.1 millimeter thick (about 0.004 inch), like ordinary medium-weight letter paper, then a stack of 500 pieces would be 50 millimeters (about 2 inches) thick.

The question is: How thick will the pile be after you cut and stack the paper 100 times?
Jay sent in a nice website to guide students through the activity. Make sure to look at the answer. Jeff Root does an excellent job at getting one to understand in a physical way 2^100.

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