Abstract
We consider an affinely invariant functional on the classP m of the plane convex polygons, withm sides,m>4. We give, for allm, a geometrical property of the maximizing polygons. Form=5, 6 the maximum is attained if and only if the polygons are affinely regular. The maximum inP 2n is a bound of another functional which arises in reconstructing plane convex bodies from the length of its chords alongn directions.
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Longinetti, M. Una proprietà di massimo dei poligoni affinemente regolari. Rend. Circ. Mat. Palermo 34, 448–459 (1985). https://doi.org/10.1007/BF02844537
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DOI: https://doi.org/10.1007/BF02844537