daniil's Journal: How history of Mathematics was made

Here's an interesting article from American Scientist Online about the famous story of Carl Friedrich Gauss and the schoolmaster who gave his class the tedious assignment of summing the first 100 integers. The author thinks that "only one kind of student would ever be likely to add the numbers from 1 through 100 by performing 99 successive additions -- namely, a student using a computer or a programmable calculator", yet still finds that other, quite apparent shortcuts "can't match the elegance and ingenuity of Gauss's method."

I thought the solution was obvious ...

[tomhudson]

... so I checked the article, and it uses the same obvious solution. Anyone who bothered to add up all the numbers would quickly run out of fingers ...

Re:I thought the solution was obvious ...

[daniil]

Anyone who bothered to add up all the numbers would quickly run out of fingers ...

Yes, that's exactly the point the author of the article is trying to make. We don't know how the other kids (or the teacher) solved the problem (probably by using a less elegant heuristic). We don't even know if this ever happened at all. The only thing here we know for sure is that Gauss was a bloody brilliant guy.

c'mon.

[weierstrass]

it's not really that hard to find the answer by simple addition. and yes, i think this is how the teacher intended they should find it.

Re:I thought the solution was obvious ...

[Shadow Wrought]

Once again I am reminded of why I am not a math major. I woulda sat there and added them up. *sigh*

Re:I thought the solution was obvious ...

[tomhudson]

See, there's the difference. I learned early that if you can count on your fingers, you can also use them as placeholders while you find easier ways to work through a problem, etc.

For example, anything x 11

1. Add a zero
2. Add back the original amount

Anything x 5

1. Double it
2. Divide by 2

Converting celcius to fahrenheit:

1. Shift right 1 decimal place (29 becomes 290)
2. take off the original amount (290-29 is the same as 291-30, = 261)
3. double it, and shift left 1 decimal place (261x2=522, or 52.2)
4. add 32 (52.