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Blaschke–Lebesgue theorem

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This is an old revision of this page, as edited by ArnoldReinhold (talk | contribs) at 02:58, 15 May 2020 (Adding local short description: "Plane geometry theorem on least area of all curves of given constant width", overriding Wikidata description "Plane geometry theorem" (Shortdesc helper)). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

In plane geometry the Blaschke–Lebesgue theorem, named after Wilhelm Blaschke and Henri Lebesgue, states that the Reuleaux triangle has the least area of all curves of given constant width. By the isoperimetric inequality, the curve of constant width with the largest area is a circle.

In 1952 Ohmann proved the analogue of the Blaschke–Lebesgue theorem for Minkowski planes which uses a concept analogous to that of the Reuleaux triangle and constructed using the triangle equilateral relative to the given gauge body.[1]

References

  1. ^ Gruber, Peter M. (1983), Convexity and its Applications, Birkhäuser, p. 67, ISBN 9783764313845


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