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The fair pie-cutting problem is a variation of the fair cake-cutting problem, in which the resource to be divided is circular.
As an example, consider a birthday cake shaped as a disk. The cake should be divided among several children such that no child envies another child , with the additional constraint that the cuts must be radial, so that each child receives a circular sector.
A possible application of the pie model might be for dividing an island’s shoreline into connected lots.
Another possible application is in division of periodic time, such as dividing a daily cycle into "on-call" periods.
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