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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 o
by nhebb 14y ago
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.
- wowfat 14y agowow, that would not happen to me if i was bored!
- deleted 14y ago[deleted]
- taejo 14y agoNice. I figured out sum(1..n) = n(n+1)/2 in a slightly way (well, sum(0..n-1) = n(n-1)/2). My grandfather played chess in a club, and he had these sheets of game results where everybody played everybody else once. I wondered how many blocks there were in the table. Well, it looks like a right triangle of height n and base n (which has area nn/2) but with n little triangles notched out (total area n/2). So the area of the blocks is (nn-n)/2, and each has area 1, so there are n(n-1)/2 of them.