⊆ o, each of the angles of ∆ is at least β, and the length of each of its edges is at least δ·diameter(o). An object o in the plane is (β,δ)-covered if for each point P ∈ o there exists a (β, δ)-triangle ∆ of o that contains P. For convex objects, the two definitions are equivalent, in the sense that if o is α-fat, for some constant α, then it is also (β,δ)-covered, for appropriate constants β and δ, and vice versa. However, for non-convex objects the definition of being fat is more general than the definition of being (β, δ)-covered. Applications Fat objects are used in various problems, for example: Motion planning - planning a path for a robot moving amidst obstacles becomes easier when the obstacles are fat objects. Fair cake-cutting - dividing a cake becomes more difficult when the pieces have to be fat objects. This requirement is common, for example, when the "cake" to be divided is a land-estate. More applications can be found in the references below. References Geometry Computational geometry