Abstract
We continue the investigation of the problem of construction of a minimum-area ellipse for a given convex polygon (this problem is solved for a rectangle and a trapezoid). For an arbitrary polygon, we prove that, in the case where the boundary of the minimum-area ellipse has exactly four or five common points with the polygon, this ellipse is the minimum-area ellipse for the quadrangles and pentagons formed by these common points.
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B. V. Rublev and Yu. I. Petunin, “Minimum-area ellipse containing a finite set of points. I,” Ukr. Mat. Zh., 50, No. 7, 980–988 (1998).
W. Blaschke, Kreis und Kugel, Walter de Gruyter, Berlin (1956).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol.50, No.8, pp. 1098–1105, August, 1998.
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Rublev, B.V., Petunin, Y.I. Minimum-Area ellipse containing a finite set of points. II. Ukr Math J 50, 1253–1261 (1998). https://doi.org/10.1007/BF02513081
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DOI: https://doi.org/10.1007/BF02513081