Math

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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 -

    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 -

    Thanks :)

  • Math -

    You're welcome!

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