/sci/ - Science & Math

Not math, but an arithmetical recreation and therefore slightly related. It occurred to me that [math]31^2 - 19^2 = 600[/math],* a nice difference. I then recalled that the nth square is the sum of the first n odd numbers, and as I expected, the (later) partial sum was 12 terms, or six pairs of 100. The recreation is generalized in the picture, and amounts to

(49 + 51) = 100,
(47 + 53) + (49 + 51) = 200, etc.

Of course, the importance of 25, 50 and pairs here reminded me of the old saw where Gauss quickly summed 1-100.

*Initially, this came to mind via some cultural references. 361 is the number of spaces on a Go board, while 961 is the largest square of a prime (or: prime power with non-unit exponent) which is yet under 1000, objects which come up in the flick Cube.