A simple way of calculating the Earth’s → circumference
using two sticks and
two theorems of the → Euclidean geometry.
Eratosthenes calculated the length of a → meridian
arc by measuring the shadow cast by a vertical → gnomon
at noon on the → summer solstice. In Cyene
(→ tropic of Cancer), no shadow is
cast whereas in Alexandria, further north, the shadow is cast at an angle of
1/50 of 360° (measured using a → scaphe), or 7.2°,
from the vertical. The circumference is therefore equal to 50 times
the distance between the two cities. The distance from Syene to Alexandria
was 5,000 stadia, which when multiplied by 50 gives the measure for the Earth’s
circumference, 250,000 stadia. Estimating the accuracy of this result is not easy
because the unit of stadium is not uniquely defined in the ancient world.
The most likely reconstruction puts Eratosthenes’ stadium in the range 155-185m,
implying an error of about 3% below or 15% above the true value.
The modern value for the equatorial circumference of the Earth is 40,075 km.
As scholars have pointed out, Eratosthenes’ experiment
was marred by several errors: Syene is not on the Tropic of cancer,
it is not on the same meridian as Alexandria, and the distance between
the two cities is less than he estimated. But the errors tended to cancel
each other out, so his estimate was relatively accurate.
See also: → Mamun’s method,
→ Biruni’s method.
See also: Eratosthenes (c. 276-194 B.C.), Gk. mathematician, astronomer, and geographer.
He studied in Athens and later became a librarian in Alexandria. His treatise
On the Measuring of the Earth is lost. The account of his experiment
has been preserved in Cleomedes (probably first century A.D.). See also
→ sieve of Eratosthenes; → experiment.
