Polygon Diagonal
A polygonal diagonal is a line segment connecting two nonadjacent polygon vertices of a polygon.
The number of ways a fixed convex 
-gon can be divided
into triangles by nonintersecting diagonals is 
(with 
diagonals),
where 
is a Catalan
number. This is Euler's polygon
division problem. Counting the number of regions determined by drawing the diagonals
of a regular 
-gon is a more difficult problem, as is
determining the number of 
-tuples of concurrent
diagonals (Kok 1972).
The number of regions which the diagonals of a convex polygon divide its center if no three are concurrent in its interior is
 |  |  |
(1)
|
 |  |  |
(2)
|
The first few values are 0, 0, 1, 4, 11, 25, 50, 91, 154, 246, ... (OEIS A006522).
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polygon diagonal
