Eratosthenes of Cyrene (Greek ;
c. 276 BC – c. 195 BC) was a
Greek
mathematician, elegiac
poet,
athlete,
geographer, and
astronomer. He made several discoveries and
inventions including a system of
latitude
and
longitude. He was the first Greek to
calculate the
circumference of the earth
(with remarkable accuracy), and the tilt of the earth's axis (also
with remarkable accuracy); he may also have accurately calculated
the
distance from the earth to the
sun and invented the
leap day. He also
created a
map of the
world based on the available geographical knowledge of the era.
Eratosthenes was also the founder of scientific chronology; he
endeavored to fix the dates of the chief literary and political
events from the conquest of Troy.
According to the entry in the
Suda ( 2898), his
contemporaries nicknamed him (
beta, the second letter of
the
Greek alphabet) because he
supposedly proved himself to be the second best in the world in
almost any field.
Life
Eratosthenes was born in Cyrene (in modern-day Libya).
He was the
third chief librarian of the Great Library of Alexandria, the center of science and learning in the ancient
world, and died in the capital of Ptolemaic Egypt. He was never
married.
Eratosthenes studied in Alexandria and
claimed to have also studied for some years in Athens.
In 236 BC
he was appointed by Ptolemy III
Euergetes I as librarian of the Alexandrian
library, succeeding the second librarian, Apollonius of Rhodes, in that
post. He made several important contributions to
mathematics and
science,
and was a good friend to
Archimedes.
Around 255 BC he invented the
armillary
sphere.
In On the Circular Motions of the
Celestial Bodies, Cleomedes credited
him with having calculated the earth's circumference around 240 BC, using knowledge
of the angle of elevation of
the sun at noon on the summer solstice in
Alexandria and in the Elephantine Island near Syene (now
Aswan, Egypt).
Aristotle had argued that humanity was
divided into Greeks and everyone else, whom he called
barbarians, and that the Greeks should keep
themselves racially pure. He thought it was fitting for
the Greeks to enslave other
peoples. But Eratosthenes criticised Aristotle for his blind
chauvinism; he believed there was good and bad in every
nation.
Eratosthenes' measurement of the earth's circumference
Measurements taken at Alexandria (A)
and Syene (S)
Eratosthenes measured the
circumference of the earth without leaving
Egypt.
Eratosthenes knew that on the summer solstice at local noon in the Ancient
Egyptian city of Swenet (known in
Greek as Syene, and in the modern day as Aswan) on the Tropic of
Cancer, the sun would appear at the zenith, directly
overhead. He also knew, from measurement, that in his
hometown of Alexandria, the angle of elevation of the sun would be
1/50 of a full circle (7°12') south of the zenith at the same time.
Assuming that Alexandria was due north of Syene he concluded that
the distance from Alexandria to Syene must be 1/50 of the total
circumference of the earth. His estimated distance between the
cities was 5000
stadia (about 500
geographical miles or 800 km). He rounded the result to a final
value of 700 stadia per degree, which implies a circumference of
252,000 stadia. The exact size of the stadion he used is frequently
argued. The common Attic stadium was about 185 m, which would imply
a circumference of 46,620 km, i.e. 16.3% too large. However,
if we assume that Eratosthenes used the "Egyptian stadium" of about
157.5 m, his measurement turns out to be 39,690 km, an error
of less than 1%.
Although Eratosthenes' method was well founded, the accuracy of his
calculation was inherently limited. The accuracy of Eratosthenes'
measurement would have been reduced by the fact that Syene is
slightly north of the Tropic of Cancer, is not directly south of
Alexandria, and the sun appears as a disk located at a finite
distance from the earth instead of as a point source of light at an
infinite distance. There are other sources of experimental error:
the greatest limitation to Eratosthenes' method was that, in
antiquity, overland distance measurements were not reliable ,
especially for travel along the non-linear Nile which was traveled
primarily by boat. Assuming enough difficulties in measurements,
the accuracy of Eratosthenes' size of the earth is
surprising.
Eratosthenes' experiment was highly regarded at the time, and his
estimate of the earth’s size was accepted for hundreds of years
afterwards. His method was used by
Posidonius about 150 years later.
Other astronomical distances
Eusebius of Caesarea in his
Preparatio
Evangelica includes a brief chapter of three sentences on
celestial distances (
Book XV, Chapter 53). He states simply that
Eratosthenes found the distance to the sun to be " " (literally "of
stadia myriads 400 and 80,000") and the
distance to the moon to be 780,000
stadia.
The expression for the distance to the sun has been translated
either as 4,080,000 stadia (1903 translation by
E. H. Gifford), or as 804,000,000 stadia (edition of
Edouard des Places, dated
1974-1991). The meaning depends on whether Eusebius meant 400
myriad plus 80,000 or "400 and 80,000" myriad.
This testimony of Eusebius is dismissed by the scholarly
Dictionary of Scientific
Biography. It is true that the distance Eusebius quotes for the
moon is much too low (about 144,000 km) and Eratosthenes
should have been able to do much better than this since he knew the
size of the earth and
Aristarchus
of Samos had already found the ratio of the moon's distance to
the size of the earth. But if what Eusebius wrote was pure fiction,
then it is difficult to explain the fact that, using the Greek, or
Olympic, stadium of 185 meters, the figure of 804 million stadia
that he quotes for the distance to the sun comes to 149 million
kilometres. The difference between this and the modern accepted
value is less than 1%. Scribal errors in copying the numbers,
either of Eusebius' text or of the text that Eusebius read, are
probably responsible.
The smaller of the foregoing two readings of Eusebius (4,080,000
stadia) turns out to be exactly 100 times the terrestrial radius
(40,800 stadia) implicit in Eratosthenes' Nile map and given in the
1982 paper by Rawlins (p. 212) that analysed this map (see
Further Reading). Greek
scholars such as
Archimedes and
Posidonius normally expressed the sun's distance
in powers of ten times the earth's radius. The Nile map – Eusebius
consistency is developed in a 2008 Rawlins paper. The data would
make Eratosthenes' universe the smallest known from the Hellenistic
era's height, and made the sun smaller than the earth. His
indefensible lunar distance would require the moon to go
retrograde among the stars every
day for observers in tropical or Mediterranean latitudes, and would
predict that half moons occur roughly 10° from
quadrature.
The Eusebius-confirmed 1982 paper's empirical Eratosthenes
circumference (256,000 stadia instead of 250,000 or 252,000 as
previously thought) is 19% too high. But the 2008 paper notes that
the theory that atmospheric refraction exaggerated his measurement
(a theory originally proposed in the 1982 paper, applied to either
mountaintop dip or lighthouse visibility) is thus bolstered as the
explanation of Eratosthenes' error. This is because accurately
measuring the visibility distance of the Alexandria lighthouse
(then world's tallest, built at Eratosthenes' location and during
his time) and computing the earth's size from that should have
given a result 20% high from refraction, very close to his actual
19% error. The 2008 paper wonders if the 40,800 stadia estimate
originated with
Sostratus of
Cnidus (who designed the lighthouse), and offers a
reconstructive speculation that the lighthouse was about 93 meters
high, which is much below previous suppositions.
Prime numbers
Eratosthenes also proposed a simple
algorithm for finding
prime numbers. This algorithm is known in
mathematics as the
Sieve of
Eratosthenes.
Works
Named after Eratosthenes
See also
Notes
- The Suda states that he
was born in the 126th Olympiad, (276–272 BC). Strabo (Geography, i.2.2), though, states
that he was a "pupil" (γνωριμος) of Zeno of Citium (who died 262 BC), which
would imply an earlier year-of-birth (c. 285 BC) since he is
unlikely to have studied under him at the young age of 14. However,
γνωριμος can also mean "acquaintance," and the year of Zeno's death
is by no means definite. Cf. Eratosthenes entry in the
Dictionary of Scientific
Biography (1971)
- The Suda states he died at
the age of 80, Censorinus (De die natali, 15) at the
age of 81, and Pseudo-Lucian (Makrobioi, 27) at the
age of 82.
- See also Asimov, Isaac. Asimov's Biographical Encyclopedia
of Science and Technology, new revised edition. 1975. Entry
#42, "Eratosthenes", Page 29. Pan Books Ltd, London. ISBN 0 330
24323 3. It was also asserted by Carl Sagan, 31 minutes into his
Cosmos episode The Shores of the Cosmic Ocean [1]
- Oxford Reference (subscription required)
- * p439 Vol. 1 William Woodthorpe Tarn Alexander the
Great. Vol. I, Narrative; Vol. II, Sources and
Studies0. Cambridge: Cambridge University Press, 1948. (New
ed., 2002 (paperback, ISBN 0-521-53137-3)).
- There is a huge Eratosthenes-got-it-right literature based upon
attacking the applicability of the standard 185m stadium to his
experiment. Among advocates: F. Hultsch, Griechische und
Römische Metrologie, Berlin, 1882; E. Lehmann-Haupt, Stadion
entry in Paulys Real-Encyclopädie, Stuttgart, 1929; I.
Fischer, Q. Jl. R. astr. Soc. 16.2:152–167, 1975;
Gulbekian (1987); Dutka (1993). The means employed include worrying
various ratios of the stadium to the unstably defined "schoenus",
or using a truncated passage from Pliny. (Gulbekian just computes
the stadium from Eratosthenes' experiment instead of the reverse.)
A disproportionality of literature exists because professional
scholars of ancient science have generally regarded such
speculation as special pleading and so have not bothered to write
extensively on the issue. Skeptical works include E. Bunbury's
classic History of Ancient Geography, 1883; D. Dicks,
Geographical Fragments of Hipparchus, University of
London, 1960; O. Neugebauer, History of Ancient Mathematical
Astronomy, Springer, 1975; J. Berggren and A. Jones,
Ptolemy's Geography, Princeton, 2000. Some difficulties
with the several arguments for Eratosthenes' exact correctness are
discussed by Rawlins in 1982b page 218 and in his Contributions and Distillate.
See also, at [2], "The Shores of the Cosmic Ocean", chapter
1 of Cosmos: A Personal Voyage, a TV series by
Carl Sagan,
Ann Druyan and
Steven
Sotter (1978–1979), where a description of Eratosthenes'
experiment is presented.
- Other than the distance to the moon, no celestial distance is
unambiguously established as known in antiquity even to within a
factor of two. As late as a century ago, the earth's distance from
the sun (the A. U.) was known less accurately than
16%.
- Mentioned by Hero of Alexandria in his
Dioptra. See p. 272, vol. 2, Selections Illustrating
the History of Greek Mathematics, tr. Ivor Thomas, London:
William Heinemann Ltd.; Cambridge, MA: Harvard University Press,
1957.
Further reading
- Kathryn Lasky. The Librarian Who Measured the Earth.
New York: Little, Brown and Company, 1994. ISBN 0-316-51526-4. An
illustrated biography for children focusing on the measurement of
the earth. Kevin Hawkes, illustrator.
External links