|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 the 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.