Comment by nhebb

When I was a kid we were somewhere that was boring as hell, so I laid on a bench and stared up at the tiled ceiling. I noticed that for a square (n x n) block of tiles that n^2 = sum(1..n) + sum(1..n-1). From playing with the numbers in my head, I was able to derive the formula the sum(1..n) = n(n+1)/2. Later when I learned Gauss' formula in school for the sum if integers, I was like "Hey, I invented that!". Those kinds of thought experiments just don't happen if you're staring at an Xbox all day.