Consider a convex n-gon P (all interior angles strictly less than 180°).
A diagonal in P is a straight line segment connecting two of P's vertices which aren't neighbours.
What is the largest number of diagonals you can draw in P so that each of the drawn diagonals intersects at most two others (in the interior of P)?
Give a proof for your answer.
Diagonals in Polygons
- daniel.is.fischer
- Posts: 2400
- Joined: Sun Sep 02, 2007 10:15 pm
- Location: Bremen, Germany
Diagonals in Polygons
Il faut respecter la montagne -- c'est pourquoi les gypaètes sont là.
Re: Diagonals in Polygons
n ans
3 0
4 2
5 5
I can always draw n diagonals in any n gon with n > 4, but is that optimal ? edit: I hope so, because I think I can prove it
3 0
4 2
5 5
I can always draw n diagonals in any n gon with n > 4, but is that optimal ? edit: I hope so, because I think I can prove it
- daniel.is.fischer
- Posts: 2400
- Joined: Sun Sep 02, 2007 10:15 pm
- Location: Bremen, Germany
Re: Diagonals in Polygons
No, it's not optimal. For example, in an octogon, you can draw 11 diagonals such that each intersects at most two others.
Like that:
Like that:
Il faut respecter la montagne -- c'est pourquoi les gypaètes sont là.