Squares and Odd Numbers
Add up odd numbers from 1 onwards and 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?
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 one day.
There are more such tricks, see Partial Sums.