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A stability theorem for the area sum of a convex polygon and its polar reciprocal. (English) Zbl 0913.52002
The author proves a stability theorem regarding the following result: for \(P\) a planar, convex polygon inscribed in the unit circle \(K\) and \(P^*\) its polar reciprocal with respect to \(K\), the area sum of both polygons is larger than or equal to \(G\), with equality only if \(P\) is a square.
MSC:
52A40 Inequalities and extremum problems involving convexity in convex geometry
52A10 Convex sets in \(2\) dimensions (including convex curves)
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