MathDB

20

Part of 1969 IMO Shortlist

Problems(1)

Relation between boundary, interior points and area

Source:

9/29/2010
(FRA3)(FRA 3) A polygon (not necessarily convex) with vertices in the lattice points of a rectangular grid is given. The area of the polygon is S.S. If II is the number of lattice points that are strictly in the interior of the polygon and B the number of lattice points on the border of the polygon, find the number T=2S−B−2I+2.T = 2S- B -2I + 2.
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