Need some help with a proof (using the pigeon hole principle)

AI Thread Summary
The discussion centers on proving that in a convex polygon with 2*n vertices, at least one diagonal is not parallel to any of the polygon's sides, using the pigeonhole principle. The user has successfully solved five out of six related problems but struggles with this specific proof. They seek guidance on how to approach the problem and mention the need to use the pigeonhole principle exclusively. The user also notes the formula for calculating the number of diagonals in such a polygon, which is 2n*(2n-3)/2, indicating a potential avenue for their proof. Overall, the conversation highlights the challenge of applying the pigeonhole principle in geometric contexts.
allistair
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I got 6 problems that I needed to proove using the pigeon hole principle and I was able to solve 5 of them but this last one is giving me some problems.

In each convex polygon with 2*n vertices there is at least one diagonal that isn't parallel with either one of the sides of the polygon.

I would appreciate some help to point me in the right direction or maybe an example of a similar proof that uses the pigeon hole principle, thanks in advance
 
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isn't this a Descrete Maths problem?
 
i'm obligated to use the pigeon hole principle, i can't use anything else (i'm not sure what you mean by 'discrete math', or did you mean that i posted this in the wrong forum?)
 
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How many diagonals are there? How many can be parallel to a side?
 
I'm trying to find a function that gives the number of diagonals in funtion of the number of vertices but i don't see a connection both of them

i looked it up and apparently there is a formula for it, for a polygon with 2n vertices the number of diagonals is 2n*(2n-3)/2, i hope i'll be able to use this
 
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