Abstract
Given any plane strictly convex region K and any positive integer n≥3, there exists an inscribed 2n-gon Q 2n and a circumscribed n-gon P n such that
The inequality is the best possible, as can be easily seen by letting K be an ellipse. As a corollary, it follows that for any convex region K and any n≥3, there exists a circumscribed n-gon P n such that
This improves the existing bounds for 5≤n≤11.
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Ismailescu, D. Circumscribed Polygons of Small Area. Discrete Comput Geom 41, 583–589 (2009). https://doi.org/10.1007/s00454-008-9072-z
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DOI: https://doi.org/10.1007/s00454-008-9072-z