Geometry and land

Question

The word "geometry" in Greek means "measurement of Earth/land". This may imply that geometry was originally invented in order to solve problems related to land. Are there historical accounts of concrete problems related to land, either from ancient Greece or elsewhere, whose solution required the development of geometric concepts or theorems?

Answer 1

The standard reference for geometry as land measuring is Herodotus in The Histories, written c. 440 BC. He describes how the Egyptians had to measure the land after each flooding of the Nile:

This king also (they said) divided the country among all the Egyptians by giving each an equal parcel of land, and made this his source of revenue, assessing the payment of a yearly tax. And any man who was robbed by the river of part of his land could come to Sesostris and declare what had happened; then the king would send men to look into it and calculate the part by which the land was diminished, so that thereafter it should pay in proportion to the tax originally imposed. From this, in my opinion, the Greeks learned the art of measuring land.

For another reference, the Roman poet Virgil wrote c. 20 BC about how Carthage was founded by Queen Dido and her followers, perhaps around 800 BC or so:

They came to this place, and bought land, where you now see the vast walls, and resurgent stronghold, of new Carthage, as much as they could enclose with the strips of hide from a single bull, and from that they called it Byrsa.

From this is derived the isoperimetrical Dido's Problem, which is to enclose as much land as possible by a curve of fixed length, where the land is bounded by the sea (or a straight line) on one side.