Power Of Squares

I spent one day thinking in squares
With roots that times across in pairs
I saw as new pattern declares
Then it was shown within these squares

Adjacent squares seem to have news
I find their difference goes by twos
As the X runs around my views
I’ll times and add to show its news

Take the X in second power
Plus two X plus one to flower
Adding up to show the tower
Of (next X) in second power

X^2 = Y
2X + 1 = Z
(X + 1) ^2 = Y+Z
X^2 + 2X + 1 = (X + 1) ^2

by Paul Moosberg

Comments (2)

Oh dear, I fear you may have discovere algebra. Don't tell anyone. Otherwise, they may develop the science of rocketery - the secret of parabolas. Eek!
it's really funny because the difference (shown as Z) between X^2 and (X+1) ^2 compared to the difference (Z) of (X+1) ^2 and (X+2) ^2 is always uping by two. 4^2 = 16 2*4+1 = 9 (4+1) ^2 = 25 (4^2) + (2 * 4 + 1) = (4 + 1) ^2 - 5^2 = 25 2*5+1 = 11 (5+1) ^2 = 36 (5^2) + (2 * 5 + 1) = (5 + 1) ^2 and the equation just keeps working and working. i am pretty sure i can't be the first person to notice this pattern? it doesn't work when you cube the X but it works everytime when you square it (^2) .i would like to find a pattern between any of the powers not just squares, but it works!