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!

## Answer this Question

## Related Questions

- Math PLEASE HELP ASAP - -PLEASE INCLUDE SOLUTIONS AND EXPLAIN HOW YOU DID IT ...
- math - The triangular numbers are the numbers 1, 3, 6, 10, 15, . . .; the square...
- science - usually, which is younger, the pebbles in sand, or the sand ...
- math - Tricia wants to create a path out of pebbles. She has 8 bags of pebbles ...
- physics - Romeo is chucking pebbles gently up to juliet’s window, and he wants ...
- Math - A magic square is a square of numbers with each row, column, and diagonal...
- MATH - The triangular numbers are the numbers 1, 3, 6, 10, 15, . . .; the square...
- Physics - Romeo is chucking pebbles gently up to Juliet's window and he wants ...
- Math - A magic square is a square of numbers with each row, column, and diagonal...
- Math - Which numbers are perfect squares? A) 64 b)900 c)120 d)1000 e)100 F) 10 ...

More Related Questions