|
|
A230281
|
|
The least possible number of intersection points of the diagonals in the interior of a convex n-gon with all diagonals drawn.
|
|
3
|
|
|
|
OFFSET
|
3,3
|
|
COMMENTS
|
Perhaps a(9) = 94.
After removing two points from the regular 12-gon, that is, removing the corresponding points at 12 o'clock and 2 o'clock, there will be only 157 intersection points of the diagonals, it is less than 161, which is the number of intersections of diagonals in the interior of regular 10-gon. So, a(10) <= 157 < 161 = A006561(10). - Guang Zhou, Jul 27 2018
The greatest possible number of intersection points occurs when each set of four vertices gives diagonals with a unique intersection point. Thus, a(n) <= binomial(n,4) = A000332(n). - Michael B. Porter, Jul 30 2018
|
|
LINKS
|
|
|
EXAMPLE
|
a(6) = 13 because the number of intersection points of the diagonals in the interior of convex hexagon is equal to 13 if 3 diagonals meet in one point, and this number cannot be less than 13 for any hexagon.
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,more,nice
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|