Eratosthenes of Cyrene is recognized as an all-round scholar with a wide variety of interests and accomplishments. Aside
from being chief librarian at the Library of Alexandria, a position he assumed in 236 BC, he is best known for his
incredibly accurate measurements involving the circumference of Earth, the distance to both the Sun and the Moon as
well as the tilt of Earth's axis in relation to its orbital plane around the Sun.
In computing the circumference of Earth, Eratosthenes made the correct assumption that this distance is so great
that the Sun's rays are essentially parallel when they reach the planet. He noted that the Sun's shadow fell upon a
well precisely at noon on the summer solstice (June 21st) when he was in the city of Syene. In contrast, the Sun cast
a shadow whose angle was 7° 12' at the same time and date but in Alexandria, a city whose distance was 5000 stadia
from Syene. Since this angle (7° 12') corresponds precisely to 1/50th of 360°, it follows that 360° would correspond
to 250,000 stadia (50x5000) or 41,000 km (1 stadia = 164 meters) and represents an estimate which is less than 1,000
km from the currenty accepted value! This error has been attributed to the fact that the distance between Syene
and Alexandria was not 5000 but 4860 stadia and that his estimate of the angle of the shadow at Alexandria, 7° 12',
was a mere 16' in error with respect to the actual value.
Using data from lunar eclipses, Eratosthenes also computed the distance to the Moon and Sun, 780,000 and 4,080,000
stadia respectively, using a methodology described in writings which did not survive the great fire at the Library of
Alexandria. As noted by Cleomedes:
"... Ερατοσθένης τόν ηλίον απέχειν από της γης σταδίων μυριάδας, τετρακοσίας καί οκτακισμύριας, τήν δέ σελήνην απέχειν
της γης μυριάδας εβδομήκοντα οκτώ σταδιών ..."
Equally impressive was his successful attempt to measure the tilt of Earth's axis in relation to its orbital plane
using tools which he constructed himself for the measurement, for example, of the celestial coordinates of various
stars which he systematically observed. His estimate of the Earth's tilt, 23° 51' 20", was well less than one-half of
one degree in error from the established value of 23° 28'.
Other accomplishments attributed to Eratosthenes include the development of a calendar year which included leap years,
an attempt to derive a time scale by which events of the past could be accurately referenced (such as the battle of
Troy having occurred in 1184 BC), a star catalog of nearly 700 stars, a collection of constellation names and their
associated myths of the time, many efforts in geometry and arithmetic including the "Eratosthenes sieve" (prime number
and numerical theory) and various other contributions to disciplines such as geography and music.
Eratosthenes of Cyrene has been honored with the naming of a crater in the northwest quadrant of the Moon after him
(see Rukl: 21). Lying on the southeast perimeter of Mare Imbrium, crater Eratosthenes (14.5° N, 11.3° W), measuring
58-km in diameter, is characterized with steep slopes, measures 3.57 km high and is best observed immediately after
first quarter or just before third quarter. A wide-field view of Mare Imbrium including an image of crater
Eratosthenes is available elsewhere on this site (see here)
with high-power images available shortly.
For a thorough discussion on the life and ingenious work of Eratosthenes of Cyrene, the reader is referred to: