maths magic numbers

 

Squares

The result of squaring a number can also be arrived at by progressively adding consecutive odd numbers as shown below.

1² = 1
= 1
2² = 4
= 1+3
3² = 9
= 1+3+5
4² = 16
= 1+3+5+7
5² = 25
= 1+3+5+7+9
6² = 36
= 1+3+5+7+9+11
7² = 49
= 1+3+5+7+9+11+13
8² = 64
= 1+3+5+7+9+11+13+15
9² = 81
= 1+3+5+7+9+11+13+15+17
10² = 100
= 1+3+5+7+9+11+13+15+17+19

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