240 BCE


The book of science

Tom Sharp

Eratosthenes geodesy cartography


  • Eratosthenes realized that the earth was a sphere.
  • He knew that at noon on the summer solstice in Aswan
  • a man looking down blocked the sun’s reflection
  • on the water at the bottom of a deep well,
  • whereas at the same time in Alexandria
  • the shadow of a gnomon made an angle of one-fiftieth of a circle,
  • which meant that the distance from Alexandria
  • to Aswan was one-fiftieth of earth’s circumference.
  • Given the distance between Aswan and Alexandria,
  • Eratosthenes calculated the circumference of the earth.


  • Eratosthenes invented geography.
  • On his map of the known world
  • he named and located four-hundred cities,
  • he divided the world into five climate zones,
  • and he placed parallels and meridians
  • so that distances could be estimated easily.


  • Judging the accuracy of Eratosthenes’ calculation
  • is confused by uncertainty over his unit of distance.
  • A stadion is six hundred feet, but a foot
  • could be different lengths in different countries.
  • The first international standard meter,
  • one ten-millionth part of the quarter of a meridian,
  • which is the distance from the north pole to the equator,
  • quickly proved to be impractical.
  • Extending the calculation of pi to more and more digits
  • will always fall far short of infinity,
  • and the number of irrational numbers
  • is an even bigger infinity.

Geodesy is the study of the size and shape of the earth. In addition to estimating the circumference of the earth, there are reports that Eratosthenes estimated the length of the year, distances to the moon and sun, and the diameter of the sun.

See also in The book of science:

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