4 ms·
For anyone else whose jaw dropped at "the sum of a sequence of odd numbers is always the next perfect square", Wikipedia has a helpful visualization: http://en
by powrtoch 16y ago
For anyone else whose jaw dropped at "the sum of a sequence of odd numbers is always the next perfect square", Wikipedia has a helpful visualization:
http://en.wikipedia.org/wiki/Square_number#Properties http://en.wikipedia.org/wiki/Square_number#Properties
- tonystubblebine 16y agoThe visualization makes it seem obvious. Thanks.
- jacobolus 16y ago> anyone else whose jaw dropped Wait, really? You never worked out in school (or on your own before it ever came up in school) that 1 + 2 + 3 + ... + n = n * (n + 1) / 2 and likewise that 2 + 4 + 6 + ... + 2n = n * (n + 1) and 1 + 3 + 5 + ... + (2n - 1) = n * n ? (of course, it also comes up geometrically if you start looking at the number of little squares in a big square, and count the next row)
- barrkel 16y agoIt always struck me as obvious; with a square of n*n, just add n + n (for the two sides) + 1 (for the corner) and you get the next square. 2n+1 progresses 1, 3, 5 etc., plain as day. What got me thinking about it (at perhaps 11 or 13 or so) was trying to turn it into a way of calculating the square root.
- InclinedPlane 16y agohttp://en.wikipedia.org/wiki/Method_of_finite_differences http://en.wikipedia.org/wiki/Method_of_finite_differences