Eratosthenes (276 BC-194 BC)
Eratosthenes was a Greek mathematician, geographer and astronomer. He was born in Cyrene (now Libya) and died in Ptolemaic Alexandria. He is noted for devising a system of latitude and longitude and computing the size of the Earth.
Eratosthenes studied at Alexandria and for some years in Athens. In 236 BC he was appointed by Ptolemy III Euergetes I as librarian of the Alexandrian library. He made several important contributions to mathematics and science, and was a good friend to Archimedes. Around 255 BC he invented the armillary sphere, which was widely used until the invention of the orrery in the 18th century.
Circa 200 BC Eratosthenes is thought to have coined or to have adopted the word geography, the descriptive study of the Earth.
Eratosthenes' other contributions include:
- The Sieve of Eratosthenes as a way of finding prime numbers.
- The measurement of the Sun-Earth distance, now called the astronomical unit (804,000,000 stadia, 1 stadion=148.5 m ).
- The measurement of the distance to the Moon (780,000 stadia).
- The measurement of the inclination of the ecliptic with an angle error of 7'.
- He compiled a star catalogue containing 675 stars, which was not preserved.
- A map of the Nile's route as far as Khartoum.
- A map of the entire known world, from the British Isles to Ceylon, and from the Caspian Sea to Ethiopia.
Eratosthenes will always be remembered for the calculation of the Earth's circumference circa 240 BC, using trigonometry and knowledge of the angle of elevation of the Sun at noon in Alexandria and Syene (now Aswan, Egypt). The calculation is based on the assumption that the Earth is spherical and that the Sun is so far away that its rays can be taken as parallel.
Details of his method he published in a work On the measurement of the Earth which unfortunately was lost. We know indirectly about his method from other authors.
Eratosthenes knew that on the summer solstice at local noon on the Tropic of Cancer, the Sun would appear at the zenith, directly overhead - though Syene was in fact slightly north of the tropic. He also knew, from measurement, that in his hometown of Alexandria, the angle of elevation of the Sun would be 7° south of the zenith at the same time. Assuming that Alexandria was due north of Syene - Alexandria is in fact on a more westerly longitude - he concluded that the distance from Alexandria to Syene must be 7/360 of the total circumference of the Earth. The distance between the cities was known from caravan travellings to be about 5,000 stadia (1 stadion=148.5 m). He established 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 no longer known (the common Attic stadion was about 185 m), but it is generally believed that Eratosthenes' value corresponds to between 39,690 km and 46,620 km. The circumference of the Earth around the poles is now measured at around 40,008 km. Eratosthenes result is not bad at all.
Very interesting is that the measurement of the distance between Alexandria and Syene is based on the estimated average speed of a caravan of camels that traveled this distance(!). Camels traveled the distance many times to obtain an average estimate of the distance. Whether this is true is not clear.
Links
Noon Day Project - Stevens Institute of Technology
Measure the Sun's Angles - Stevens Institute of Technology
The EarthDial Project: Eratosthenes experiment - The Planetary Society, Bill Nye
Eratosthenes Experiment: A Worldwide Science and Math Experiment - youth.net
How to Measure the Size of the Earth - Astronomy On-Line
Eratosthenes Finds Diameter of Earth! - Dennis P. Donovan, Rice University
Eratosthenes of Cyrene - Michael Lahanas
Measuring the Size of the Earth - D. Trapp, ie-Physics
Measurement of Earth's Circumference - J. W. Dooley, MU-Physics
Eratosthene's Diameter of Earth - John H. Lienhard
The Librarian who Measured the Earth - Noon Day Project, Stevens Institute of Technology
Eratosthenes of Cyrene - MacTutor
Ancient Measurements of the Circumference of the Earth - Livio C. Stecchini
Books
The Librarian Who Measured the Earth, Kathryn Lasky, Kevin Hawkes
