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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 wrongIs 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 tyrantOr keenly feared him: they seized some ships which chanced to be ready...They came to this spot, where to-day you can behold the mightyBattlements and the rising citadel of New Carthage,And purchased a site, which was named 'Bull's Hide' after the bargainBy which they should get as much land as they could enclose with a bull's hide."..

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