# 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.