Maximum Area Enclosed By A String

Problem Statement: Given a string of length S, find the shape and the maximum area that can be enclosed by this string.

Solution:

We all know the answer is a circle. Here is a derivation from the dynamic optimization view point.

Snapshot of Mathcad Screen (max-area.gif)

Mathcad File (max-area.mcd)

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Computer Methods in Chemical Engineering -- Maximum Area Enclosed By A String
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Nam Sun Wang

Department of Chemical & Biomolecular Engineering

University of Maryland

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