all squares of integer size have perfect sq areas. A=s^2
starting from 1x1 square,
+
you can add 1 block horiz and 1 block vert to form this shape:
++
+
then you can add 1 corner block to complete a larger square sized 2x2
++
++
For square of size N, you can add 2N blocks(one horiz, one vertical)
and 1 corner block to complete a larger square of size (N+1)
+++ ... +
+++ ... +
.
.
+++ ... +
thus starting from N=1, Square of 1x1, area=1, you can add odd number
2N+1 of blocks to form another square, where its area is a perfect
square. 2N+1 is conseq sequence of numbers 3,5,7 as N increases by 1
every repetiton.
As stated by others N^2+2N+1 = (N+1)^2, but it's easier to visualize the squares.

Posted by karrio
on 20040608 12:06:39 