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Math Help - Nth term for diagonals/sides

  1. #1
    Senior Member Mukilab's Avatar
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    Nth term for diagonals/sides

    Find the nth term formula for the number of sides in a shape against how many diagonals this shape has.

    I have the answer but is there I need workings because I do not know how to approach this.
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by Mukilab View Post
    Find the nth term formula for the number of sides in a shape against how many diagonals this shape has.

    I have the answer but is there I need workings because I do not know how to approach this.
    Suppose a polygon has n vertices (and sides).


    The number of diagonals from a single vertex is 3 less the the number of vertices or sides, or (n-3).

    So n-3 diagonals can be drawn from each vertex.

    But each diagonal has two ends, so we would be counting each one twice.

    Dividing by two gives the actual number of diagonals.
    Number of diagonals = \frac{n(n-3)}{2}
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  3. #3
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    On n vertices there are \binom{n}{2}-n diagonals.
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