Euclidean symmetries

Estermann measure

In plane geometry the Estermann measure is a number defined for any bounded convex set describing how close to being centrally symmetric it is. It is the ratio of areas between the given set and its smallest centrally symmetric convex superset. It is one for a set that is centrally symmetric, and less than one for sets whose closure is not centrally symmetric. It is invariant under affine transformations of the plane. (Wikipedia).

Estermann measure
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From playlist Fine Measurements

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From playlist MIT 18.102 Introduction to Functional Analysis, Spring 2021

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István Fáry | Curve of constant width | Convex hull | Affine transformation | Isaak Yaglom | Reuleaux triangle | Kovner–Besicovitch measure | Convex set