The Sagacity of Circles: A History of the Isoperimetric Problem - The Isoperimetric Problem in Literature

Although the isoperimetric problem is primarily mathematical in nature, it is unique in that poets and historians of both the ancient and medieval world incorporated it into their works. Most famously, Virgil made use of the concept in his Roman epic The Aeneid, written in the first century B.C.E. In Book I of The Aeneid, Queen Dido flees her murderous brother Pygmalion to the shores of North Africa where she founds the city of Carthage. Virgil notes:

“They sailed to the place where today you’ll see

Stone walls going higher and the citadel

Of Carthage, the new town. They bought the land,

Called Drumskin [Byrsa] from the bargain made, a tract

They could enclose with one bull’s hide” (Book I, 16).

[Click here for a view of ancient Carthage.]

According to legend, Dido made the hide given to her by the natives of Carthage into a long rope and, using the coast as part of her boundary, enclosed her lands in a semi-circle, thus using the fact that it was this shape which contains the greatest area [Nahin, 45]. It is from Virgil’s tale that mathematicians give the name “Dido’s Problem” to the isoperimetric problem. An earlier account of Carthaginian folklore compiled in the 3rd century C.E. by the Roman historian Marcus Junianus Justinus gives a more descriptive account of the legendary founding of Carthage by Dido, called Elissa by the Greeks:

“Then [Elissa] bought some land, just as much as could be covered by a cow’s hide, where she could give some recreation to her men… She next gave orders for the hide to be cut into very fine strips, and in this way she took possession of a greater area than she had apparently bargained for” (Book XVIII, 157).

[For classroom activities involving Dido and bees (see pages 1 and 6), click here. The lessons are from the CD entitled Historical Modules for the Teaching and Learning of Mathematics, published by the MAA.]

Much later, the isoperimetric problem appeared in Geoffrey of Monmouth’s Historia Regum Britanniæ (History of the Kings of England), an early account of the Arthurian legends written in the 12th century C.E. In this tale, a German duke by the name of Hengist appeals to King Vortigern for land in return for military service:

“’Grant,’ saith [Vortigern], ‘unto thy servant but so much only as may be compassed round about by a single thong within the land thou hast given me, that so I may build me a high place therein whereunto if need be I may betake me’... Straightaway … Hengist took a bull’s hide, and wrought the same into a single thong throughout. He then compassed round with his thong a stony place that he had right cunningly chosen, and within the space thus meted out did begin to build a castle that was afterwards called in British, Kaercorrei, but in Saxon, Thongceaster, the which in Latin’s speech is called Castrum corrigae” [Monmouth, 105-6].

The isoperimetric problem, therefore, held a particular appeal to not only the figures of the mythological past, but to the poets and historians who wrote of their deeds.