Start with 1:

O
The next square is 4, so add 3:
AA
AO
Next is 9, so add 5:
AAA
AOO
AOO
Notice that each time, you are adding 2 * Length of side, plus 1.
This was discussed here a while back, relating to Ada Lovelace=20
programming the Babbage machine.

Kerry


Electron wrote:
> Hello,
>
> analogously to [division] computing the quotient by counting how many tim=
es you
> can subtract the divisor, you can compute the square root of a number cou=
nting
> how many times you can subtract sequential odd numbers (1,3,5,7,9,=85).
>
> [ try it -- it works!]. e.g. 25 -1-3-5-7-9 =3D 0
>
> OK, but can someone explain me *why* it works? :-)
>
> Thanks,
> Mario
>
>  =20

--=20
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