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.
28139, 26140, 26141, 3011, 602, 26142, 8346, 26143, 8352, 26144