Vedic math fun

Read a neat article on Wired about Vedic math. From the shallow treatment given, the techniques seem useful mainly as shortcuts to allow computation of large results quickly - I was awed by one rule that allows for quick computation of squares of numbers ending in '5' (25, 85, 115, etc). This reminded me immediately of the only fun proofs I've ever done, from abstract algebra, when we got to play around for awhile with properties of small numbers. So, of course, I set out to see if I could prove the theorem allowing this neat shortcut. Turns out it wasn't hard at all...of course the hard work was for the Vedic math folk to even come up with this technique in the first place.

We're looking to compute the following:
'n5'^2 =
((2n + 1) * 5)^2, for n=0,1,2,...
= 25 * (4n^2 + 4n + 1)
= 100n^2 + 100n + 25
= 100(n)(n+1) + 25

This is the result that Vedic math so simplifies: To square the number 'n5', multiply n*(n+1) and add the characters '25' to the right of it. So 35^2 = 3*4 + '25' = '12' + '25' = 1225. Neat!

This in no way means I have any more than a passing interest in math - I'm quite glad to be done with it.