The funnest math problem you’ve ever done

I used this as an illustration in a lecture I gave on the nature of technological progress. Since technology progresses at an exponential rate, rather than a liner rate, I wanted a way to convey how astronomical the yields of exponential growth are. This is the best illustration I could come up with.
Here’s the question: If I have a piece of printer paper large enough to fold in half as many times as I’d like, and sayI fold that piece of paper in half one hundred times, so that its thickness doubles each time, how thick would the paper be after I finished?
The answer? It’s not 100 pages thick. That’s growth at a linear rate – adding one each time. Instead, remember that it doubles each time. So the first fold gives you two sheets thick, the second fold, four, the third fold, eight, the fourth, sixteen, and so on. After the hundredth fold? Well, the stack of paper would be thicker than the galaxy…much thicker. Here’s the math:
Printer paper = .008 inches thick
0.008 inches doubled one hundred times = 0.008 x 2^100
2^100 = 1,267,650,600,000,000,000,000,000,000,000 (one nontillion)
0.008 x 2^100 =  10,141,204,800,000,000,000,000,000,000 inches (10 octillion, or ten million trillion, inches)
1 mile = 63,360 inches
10,141,204,800,000,000,000,000,000,000 inches divided by 63,360 =
160,056,894,000,000,000,000,000 miles (one-hundred-sixty thousand trillion miles)
1 light-year = 5,878,488,100,000 miles
160,056,894,000,000,000,000,000 divided by 5,878,488,100,000 = 27,227,561,100 light-years
Milky Way = 1,000 light-years thick
So, thats over 27 billion light-years, or, from one edge of the galaxy to the other 27,227,561 times.
Hope you enjoyed.
  1. #1 by Michael Glawson on 3.4.10 - 12.27 pm

    Thanks to Corey for correcting my math at one point.

  2. #2 by Corey Scogin on 3.4.10 - 11.01 pm

    I really like this example. I, however, hope that if you gave lecture notes, you didn’t spell linear “liner”. You can always count on me to be the db that corrects the minor details. -Corey

    • #3 by Michael Glawson on 3.9.10 - 4.08 pm

      Oops. No I didn’t pass it out in that form. That’s actually how south carolinians say “linear”.

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