On the perimeter of fat objects.
Prosenjit K. Bose, Otfried Cheong, Vida Dujmovi · 2010
We show that the size of the perimeter of (; )-covered objects is a linear function of the diameter. Specically, for an (; )-covered object O, per(O) c diam(O) sin2 , for a positive constant c. One easy consequence of the result is that every point on the boundary of such an object sees a constant fraction of the boundary. Locally {fat objects are a generalization of (; ){covered objects. We show that no such relationship between perimeter and diameter can hold for locally -fat objects.