That's the coolest obvious thing I've seen all week. It may help me remember the exact formula for sums on the fly when I haven't thought about them recently. Nifty.

Love it! We do a unit on sums of consecutive numbers in my summer pre-algebra program. This would be one more great way to show them "why" the formula works once they're derived it.

It might be easier to understand *faster* if you annotated it a bit...

For example, have little size markers on the top and on the right that show how long the things are, and also have a REALLY thick line dividing the two sides, or perhaps a break between them... or perhaps an intermediate step
showing that the line of objects can be built up into the stack of objects.

I spent five minutes going "But that doesn't work!" and seriously confusing my roommates and then realized I'd completely missed the "2*" on the left. heh. Penny = oblivious.

Pretty cool though.

If you haven't read it, I recommend Journey through Genius. At least, I really loved it when I was in high school. I'm not sure how good it would be to read as a B.S..

I came up with a geometrical derivation of this result when I was 14 (area of big triangle + n small triangles = n^2/2 + n*(1/2)). My math teacher later told me he too had come up with it when we was a teenager (counting dots, rather than squares).

Some friends of mine in grad school figured out how to do a similar 3-dimensional proof of 1 + 4 + 9 + ... + n^2 = n * (n+1) * (2*n+1) / 6. It turns out that six pyramid thingies can make a rectangular prism.