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Math Help - Polygon diagonals

  1. #1
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    Polygon diagonals

    Please don't shoot if this is in the wrong section. I'm pretty sure its not, but I've said that before. I think it should go in this section because its actually an algebraic sum.. right?

    Anyway. I've got this problem:
    A polygon with n sides has a total of \frac{1}{p} n(n-q) diagonals, where p and q are integers.

    Find the values of p and q.

    I don't know what to do! There are no integers in the sum to start with...
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  2. #2
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    Quote Originally Posted by yorkey View Post
    this problem:
    A polygon with n sides has a total of \frac{1}{p} n(n-q) diagonals, where p and q are integers.
    Find the values of p and q.
    A polygon with n sides has \binom{n}{2}-n diagonals.
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  3. #3
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    Are you saying they gave the wrong formula?
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    Quote Originally Posted by yorkey View Post
    Are you saying they gave the wrong formula?
    No indeed!
    I am saying you can use what I wrote to solve the problem.
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  5. #5
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    Quote Originally Posted by yorkey View Post
    Please don't shoot if this is in the wrong section. I'm pretty sure its not, but I've said that before. I think it should go in this section because its actually an algebraic sum.. right?

    Anyway. I've got this problem:
    A polygon with n sides has a total of \frac{1}{p} n(n-q) diagonals, where p and q are integers.

    Find the values of p and q.

    I don't know what to do! There are no integers in the sum to start with...
    1. Examine a number of polygons:

    3gon ---> 0 diagonals
    4gon ---> 2 diagonals
    5gon ---> 5 diagonals

    2. Use the given equation, sub in the values you've found in #1 and solve for p, q:

    \left|\begin{array}{r}\frac1p \cdot 4(4-q)=2 \\\frac1p \cdot 5(5-q)=5 \end{array}\right.
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