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in reply to (jeffa) Re: Recursion
in thread Recursion

Are you thinking of the sum of the first N natural numbers?

I've heard the legend/story that he (Guass) came up with this when he was somewhere between 10 and 15 years old (for the record, I might have come up with this when I was 10, but cartoons were more interesting than math then).

Anyway, it's S=N*(N+1)/2



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Sum of numbers between 1 and N
by tedv (Pilgrim) on Nov 15, 2000 at 21:42 UTC
    It's quite possible that Gauss figured that out when he was young. I actually figured it out when I was 8. Being a young, anti-social kid, I tried adding numbers between 1 and as high as I could go, trying to find a pattern. The funny part was that I didn't know what variables were, although I did know fractions. My formula was something like, "Take a number, add one, divide by two, and then multiply it by half of the original number." It seemed very strange to me that that formula seemed to hold for any number I gave it. One day I even added all the numbers up to 20 in my hand to see if I got 210.

    Anyway, one day I told my math teacher that I figured out this neat formula and then she introduced me to concepts like "variables" and "functions". :)

    -Ted
[reply]
      Gauss did indeed figure this out at the age of 8 .. a teacher had given her unruly class the "busywork" problem of summing the first 100 integers. Gauss is also notorious for catching errors in his father's bookkeeping at an even earlier age. This from A Biography of Gauss
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