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Classroom note: Compact, convex, and symmetric sets are discs

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Define the centre of a parallelogram to be the intersection of its diagonals. It was shown in an earlier paper that the intersection of arbitrarily many parallelograms with the same centre is the unit disc about that centre in a metric defined using ideas from Linear Algebra. In this note, it is shown that this characterizes compact, convex sets, which are symmetric about a point.
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Document Type: Research Article

Affiliations: Department of Mathematics Millsaps College Jackson MS 39210 USA, Email: [email protected]

Publication date: 01 March 2004

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