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numbers of areas of convex polygons

Source: Polish MO Recond Round 1990 p6

September 9, 2024
geometrycombinatoricscombinatorial geometryareasconvex polygon

Problem Statement

For any convex polygon W W with area 1, let us denote by f(W) f(W) the area of the convex polygon whose vertices are the centers of all sides of the polygon W W . For each natural number n≥3 n \geq 3 , determine the lower limit and the upper limit of the set of numbers f(W) f(W) when W W runs through the set of all n n convex angles with area 1.
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