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 (n1) using n(n1)/2 pebbles.
The total:
n(n+1)/2+n(n1)/2
=(n²+n +n²n)/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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