Purevsuren Damba and Uuganbaatar Ninjbat,
Side Disks of a Spherical Great Polygon,
Forum Geometricorum,
18 (2018) 195—201.
Abstract.
Take a circle and mark n ∊ N points on it designated
as vertices. For any arc segment between two consecutive vertices which does
not pass through any other vertex, there is a disk centered at its midpoint and
has its end points on the boundary. We analyze intersection behavior of these
disks and show that the number of disjoint pairs among them is between (n-2)(n-3)/2
and n(n-3)/2 and their intersection graph is a subgraph of a
triangulation of a convex n-gon.