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# Re: OT CHAT Re: Non-Human Phonology

From: Mark J. Reed Monday, December 4, 2006, 21:41
```On 12/4/06, Roger Mills <rfmilly@...> wrote:
> I assume this is also a well-known fact:
> The difference between any two consecutive perfect squares is equal to (1*)
> the sum of their sq.roots (I.e. 36-25 = 11 = 6+5
>
> The difference between the square of x^2 and (x+2)^2 is 2* (the sum of
> x+x+2) ( 64-36 = 28 = 2*(8+6)
Along the same lines - actually, this is the same statement as the
second one above, mathematically, but perhaps that's not obvious - the
differences between consecutive perfect squares form the series of odd
numbers.

This is, zero squared plus 1 is one squared plus 3 is two squared plus
5 is three squared plus 7 is four squared, etc.  So you can calculate
the square of any integer n by adding up the first n odd numbers. For
instance, 27 squared is 1 + 3 + 5 + 7 + 9 + ... + 49 + 51 + 53 = 729.

Whether this is any easier than just doing the multiplication is
dubious, of course. :)

--
Mark J. Reed <markjreed@...>
```