Dido's Problem/Historical Note

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Historical Note on Dido's Problem

There are several more or less romantic legends of the origin of Dido's Problem.

One of the more prosaic is that the founders were granted as much land as a man could plough a furrow round it in a day, given that a ploughman works at a constant rate.

A more fanciful one concerns Queen Dido, who was given a bull's hide, and told she could take as much land for her new city as she could enclose. According to the legend, she cut it (or arranged to have it cut -- she was a queen, after all) into one long strip of leather.

In the words of Virgil:

So they reached the place where you will now behold mighty walls and the rising towers of the new town of Carthage;
and they bought a plot of ground named Byrsa ...
for they were to have as much as they could enclose within a bull's hide.
-- Virgil, Aeneid, Book $\text I$, ll. 360 -- 70

In both cases, the resulting length was used to measure out a semicircle whose diameter formed the coastline.

The legend of the bull's hide is repeated throughout history in the contexts of the founding of several cities.