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Steiner's formula and a variational proof of the isoperimetric inequality

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arxiv 1909.06347 v3 pith:4P33T2WN submitted 2019-09-13 math.DG math.CA

Joseph Ansel Hoisington This is my paper · ORCID
classification math.DGmath.CA
keywords inequalityisoperimetricproofsteinerformulaplaneareabypasses
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We give a new proof of the isoperimetric inequality in the plane, based on Steiner's formula for the area of a convex neighborhood. This proof establishes the isoperimetric inequality directly, without requiring that we separately establish the existence of an optimal domain. In doing so, this proof bypasses the main difficulty in all of the proofs Steiner outlined for the plane isoperimetric inequality.

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  1. Buffon Needle Problem Over Convex Sets

    math.CA 2024-11 conditional novelty 5.0 of 10

    For sufficiently small needle lengths, the unit disk has higher Buffon needle containment probability than any other convex set of perimeter 2π.

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