Pattern of odd numbers between consecutive perfect squares

[BTruesdell07]

THERE IS A PATTERN IN SQUARED NUMBERS
0x0 =0
+1
1x1 =1
+3
2x2 =4
+5
3x3 =9
+7
4x4 =16
+9
5x5 =25

I discovered this pattern while working on a math problem my math eacher gave me.
I thought it is interesting

 

[whozum]

I believe it was archimedes who first discovered that pattern. The difference of consecutive squares spell out the odd numbers.

 

[honestrosewater]

(x + 1)² - x² = x² + 2x + 1 - x² = 2x + 1.

 

[BTruesdell07]

I never said that I was the first to discover it I just said I discovered it doing math home work.

 

[whozum]

So, congratulations? We were just giving you some history and elaboration.