Squares and Odd Numbers

When you sum odd numbers you get square numbers!

  • 1 is a square number (= 1 × 1)
  • 1 + 3 = 4, and 4 is a square number (= 2 × 2)
  • 1 + 3 + 5 = 9, and 9 is a square number (= 3 × 3)
  • etc!

Like this:

Odd
Number
Running
Total
 
1 1 = 1 × 1
3 4 = 2 × 2
5 9 = 3 ×3
7 16 = 4 × 4
9 25 = 5 × 5
11 36 = 6 × 6
etc...

Is this some kind of magic?

odd square numbers

Not really, just look at this picture:

  • 1 is a square (a 1×1 square)
  • Add 3 and you get a 2×2 square
  • Add 5 and you get a 3×3 square
  • etc

It is good to know this, as it may help you solve things later.