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A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.

G. H. Hardy

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# Eratosthenes and the Mystery of the Stades

## Distance from Alexandria to Syene

3.  That the distance between Alexandria and Syene is 5000 stades.

There is little doubt that Eratosthenes got this figure directly from his earlier map of the known world [4, p.62].  How he initially obtained this value is a controversial question which may never be answered, but it is doubtful that Eratosthenes actually measured the distance himself [5, p.154 ].  The writings of Strabo the Geographer (ca. 20 BCE) suggest that the lands along the Nile were measured every year.

In Egypt, the Nile passes in a straight line from the little cataract above Syene and Elephantine, at the boundary of Egypt and Ethiopia, to the sea.  The country was divided into nomes [provinces], which were subdivided into sections […] There was need of this accurate and minute division because of the continuous confusion of the boundaries caused by the Nile at the time of its increases [flooding], since the Nile takes away and adds soil, and changes conformations of land, and in general hides from view the signs by which one’s own land is distinguished from that of another.  Of necessity, therefore, the lands must be re-measured again and again.  And here it was, they say, that the science of land-measuring originated [5, p.152 ].

The Nile flooded regularly every year, changing the landscape around it, so every year there were disputes between landowners over property lines.  Thus, the lands around the Nile had to be re-surveyed each year after the flood.  Long distances were measured by professional distance walkers, called bematists, who walked at a very regular pace and counted each step.  Shorter distances were measured with lengths of knotted rope by men called harpedonaptai, which means “rope stretchers” [4, pp.56-58].  Knowing that Alexandria and Syene are both located on the Nile, Eratosthenes could have calculated the distance by compiling the yearly measurements of the land between the two cities [5, p.153].  The fact that 5000 stades is a round number might suggest that it was the traditionally accepted figure for the distance between the cities, established well before the time of Eratosthenes [6, p.411 ].  Whatever his reasoning, as the foremost authority on geography in the ancient world, Eratosthenes is justified in assuming that the distance between Alexandria and Syene is 5000 stades.