Dido's Problem

Find the figure bounded by a line which has the maximum area for a given perimeter. The solution is a semicircle. The problem is based on a passage from Virgil's Aeneid:

"The Kingdom you see is Carthage, the Tyrians, the town of Agenor;

But the country around is Libya, no folk to meet in war.

Dido, who left the city of Tyre to escape her brother,

Rules here--a long and labyrinthine tale of wrong

Is hers, but I will touch on its salient points in order....Dido, in great disquiet, organised her friends for escape.

They met together, all those who harshly hated the tyrant

Or keenly feared him: they seized some ships which chanced to be ready...

They came to this spot, where to-day you can behold the mighty

Battlements and the rising citadel of New Carthage,

And purchased a site, which was named 'Bull's Hide' after the bargain

By which they should get as much land as they could enclose with a bull's hide."

REFERENCES:

Thomas, I. Greek Mathematical Works, Vol. 2: From Aristarchus to Pappus. London: Heinemann, 1980.

Tikhomirov, V. M. Stories About Maxima and Minima. Providence, RI: Amer. Math. Soc., pp. 9-18, 1991.

Virgil. Translated by C. D. Lewis. Book I, lines 307-372 in The Aeneid. New York: Doubleday, pp. 22-23, 1953.

Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, pp. 122-124, 1991.