Posted by **Roxane smith** on Sunday, September 11, 2011 at 7:25pm.

Mark read that the ancient Greeks use to arrange pebbles to represent numbers. He used square on a grid instead of pebbles to model both triangular and square numbers

How can you divide a square number into q two triangular numbers?

(6 triangular number) and (9 sqaure)

- Math -
**MathMate**, Sunday, September 11, 2011 at 9:11pm
Say represent 5² as a square:

OOOOO

OOOOO

OOOOO

OOOOO

OOOOO

and split it up into two triangles next to the diagonal:

O

OO

OOO

OOOO

OOOOO

and (it should be the mirror image)

OOOO

OOO

OO

O

So in general, for an n×n square, we can split it into the larger triangle of base n using n(n+1)/2 pebbles, and the smaller of side (n-1) using n(n-1)/2 pebbles.

The total:

n(n+1)/2+n(n-1)/2

=(n²+n +n²-n)/2

=n²

- Math -
**Roxane smith**, Sunday, September 11, 2011 at 10:54pm
Thanks :)

- Math -
**MathMate**, Sunday, September 11, 2011 at 11:28pm
You're welcome!

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