How to find if diagonal lines intersect If I know that there are n vertices in some regular n-gon, how can I find out if diagonals made from pairs of vertices intersect. I've tried thinking of it in terms of a square, hexagon, dodecagon, etc. Thanks!
Edit.
If I have three diagonals can I show that they intersect at the same point? So, lets say I have a hexagon, with three diagonals. Can I show that they intersect at the same point?
 A: Let's color the two diagonals red and blue. Number you vertices consecutively, so that vertex 1 is one of the endpoints of the red diagonal.
Now consider the possible cases for the order in which you encounter the other colored vertices:


*

*Red, blue blue. In this case the two diagonals don't intersect, because the red line doesn't "clip" either endpoint of the blue line.

*Blue, red, blue. In this case the two diagonals do intersect: it is impossible to go from the first blue vertex to the second without crossing the red line.

*blue, blue, red. This is a "mirrored" version of the first case, and again the diagonals don't intersect.
So if you number the red and blue vertices $r_1, r_2, b_1, b_2$, with $r_1 = 1$ and $b_1 < b_2$, then the diagonals intersect if
$$b_1 < r_2 < b_2.$$
The above assumes that the two diagonals don't share a vertex. It's not 100% clear whether or not two diagonals that share a vertex should be considered intersecting; if you decide they should, it's easiest to check for when the two diagonals do not intersect:
$$r_2 < b_1\quad \textrm{or}\quad b_2 < r_2.$$
