Measuring the earth's circumference
The two cities Eratosthenes used to measure the
circumference of the
earth were
Alexandria and
Syene, not
Cyrene. Syene is modern-day
Aswan,
Egypt. Cyrene was Eratosthenes' birthplace; it corresponds to modern-day
Shahhat,
Libya.
The method used by Eratosthenes works like this:
- Assumption: the sun is infinitely far from the earth. This is borne out by the fact that the first quarter and last quarter phases of the moon each occur 90 degrees away from the sun.
- Eratosthenes observes that on the summer solstice the sun is directly overhead at Aswan. On that same day the sun makes an angle of just over 7 degrees with the zenith at Alexandria. This gives him the angular separation of the two cities on the curve of the earth's surface. Call it a.
- Eratosthenes hires someone to measure the distance between Alexandria and Syene. Call it d
- The ratio of a to a full circle (360 degrees) must equal the ratio of d to the circumference of the earth (C). Since a and d have been measured, it is easy to calculate C = 360/a * d
- Eratosthenes did his calculations using stadia as his unit of distance. The exact length of a stadium is uncertain, so it's not clear how good this measurement is; however, even the worst estimates suggest it was good to about 4% of the currently accepted value.
Eratosthenes' other achievements
In
astronomy Eratosthenes also measured distances to the sun and moon, using observations of lunar eclipses, and he calculated a value of about 24 degrees for the tilt of the earth's
rotational axis.
In geography Eratosthenes sketched the route of the Nile river as far as Khartoum. He also suggested that the river had its source in lakes to the south and that heavy rains in those regions were the reason for the river's yearly floods.
Eratosthenes also wrote history and commentary about several branches of mathematics, and he contributed to that field a method of finding prime numbers and a method for constructing mean proportionals between two line segments, a construction necessary in duplicating the cube.
Finally, as if all that weren't enough, he wrote a number of works of poetry, literature, and philosophy.
References
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Eratosthenes.html