maths magic numbers

 

Squares

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

= 1
= 1
= 4
= 1+3
= 9
= 1+3+5
= 16
= 1+3+5+7
= 25
= 1+3+5+7+9
= 36
= 1+3+5+7+9+11
= 49
= 1+3+5+7+9+11+13
= 64
= 1+3+5+7+9+11+13+15
= 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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