Posted by Roxane smith on .
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,
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 (n1) using n(n1)/2 pebbles.
The total:
n(n+1)/2+n(n1)/2
=(n²+n +n²n)/2
=n² 
Math 
Roxane smith,
Thanks :)

Math 
MathMate,
You're welcome!