Amazing Number Patterns 3 – Square Numbers

This is the third post of the Amazing Number Patterns Series. In this post, we exhibit another pattern that can be derived from square numbers — this time, with a diagram.

As the diagram shows, we have

$2^2$  = 1 + 2 + 1

$3^2$ = 1 + 2 + 3 + 2 + 1

$4^2$ = 1 + 2 + 3 + 4 + 3 + 2 + 1.

Hmmm, mathematics is indeed the science of patterns.

Now, will this pattern continue for larger squares? Hint: You have to learn mathematical induction to answer this question.

You may also want to check out  Number Patterns 1 and  Number Patterns 2.