Abstract
From the geometric point of view, we consider the problem of construction of a minimum-area ellipse containing a given convex polygon. For an arbitrary triangle, we obtain an equation for the boundary of the minimum-area ellipse in explicit form. For a quadrangle, the problem of construction of a minimumarea ellipse is connected with the solution of a cubic equation. For an arbitrary polygon, we prove that if the boundary of the minimum-area ellipse has exactly three common points with the polygon, then this ellipse is the minimum-area ellipse for the triangle obtained.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 7, pp. 980–988, July, 1998.
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Rublev, B.V., Petunin, Y.I. Minimum-Area ellipse containing a finite set of points. I. Ukr Math J 50, 1115–1124 (1998). https://doi.org/10.1007/BF02528822
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DOI: https://doi.org/10.1007/BF02528822