Paper Title:

On the Oldest Problem in the Calculus of Variations: A New Message from Queen Dido

Author(s):

Olivier de La Grandville

Faculty of Economics,
Goethe University Frankfurt,
Theodore Adorno Platz 4, 60323 Frankfurt,
Germany.
E-mail: odelagrandville@gmail.com

Abstract:

We consider the problem of finding the optimal curve of given length linking two points in a plane such as it encloses a maximal area. We show that if the curve is not described by a single-valued function, its determination does not necessarily imply to work with a parametric representation of the curve. We show that a simpler approach is at hand -- and, who knows? -- this might well be the method Queen Dido used.

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