Essay, Research Paper: Eratosthenes

Mathematics

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Eratosthenes was born in Cyrene which is now in Libya in North Africa. His
teachers included the scholar Lysanias of Cyrene and the philosopher Ariston of
Chios who had studied under Zeno, the founder of the Stoic school of philosophy.
Eratosthenes also studied under the poet and scholar Callimachus who had also
been born in Cyrene. Eratosthenes then spent some years studying in Athens. The
library at Alexandria was planned by Ptolemy I Soter and the project came to
fruition under his son Ptolemy II Philadelphus. The library was based on copies
of the works in the library of Aristotle. Ptolemy II Philadelphus appointed one
of Eratosthenes' teachers Callimachus as the second librarian. When Ptolemy III
Euergetes succeeded his father in 245 BC and he persuaded Eratosthenes to go to
Alexandria as the tutor of his son Philopator. On the death of Callimachus in
about 240 BC, Eratosthenes became the third librarian at Alexandria, in the
library in a temple of the Muses called the Mouseion. The library is said to
have contained hundreds of thousands of papyrus and vellum scrolls. One of the
important works of Eratosthenes was Platonicus which dealt with the mathematics
which underlie Plato's philosophy. Theon of Smyrna tells us that Eratosthenes'
work studied the basic definitions of geometry and arithmetic, as well as
covering such topics as music. Eratosthenes also worked on prime numbers. He is
remembered for his prime number sieve, the 'Sieve of Eratosthenes' which, in
modified form, is still an important tool in number theory research.
Eratosthenes made a surprisingly accurate measurement of the circumference of
the Earth. Details were given in his treatise On the measurement of the Earth
which is now lost. However, some details of these calculations appear in works
by other authors such as Cleomedes, Theon of Smyrna and Strabo. Eratosthenes
compared the noon shadow at midsummer between Syene (now Aswan on the Nile in
Egypt) and Alexandria. He assumed that the sun was so far away that its rays
were essentially parallel, and then with a knowledge of the distance between
Syene and Alexandria, he gave the length of the circumference of the Earth as
250,000 stadia. Eratosthenes also measured the distance to the sun as
804,000,000 stadia and the distance to the Moon as 780,000 stadia. He computed
these distances using data obtained during lunar eclipses. Ptolemy tells us that
Eratosthenes measured the tilt of the Earth's axis with great accuracy obtaining
the value of 11/83 of 180, namely 23 51 15. Eratosthenes made many other
major contributions to the progress of science. He worked out a calendar that
included leap years, and he laid the foundations of a systematic chronography of
the world when he tried to give the dates of literary and political events from
the time of the siege of Troy. He is also said to have compiled a star catalogue
containing 675 stars. Eratosthenes made major contributions to geography. He
sketched, quite accurately, the route of the Nile to Khartoum, showing the two
Ethiopian tributaries. He also suggested that lakes were the source of the
river. Many scholars before Eratosthenes had made a study of the Nile and they
had attempted to explain the rather strange behavior of the river, but most like
Thales were quite wrong in their explanations. Eratosthenes was the first to
give what is essentially the correct answer when he suggested that heavy rains
sometimes fell in regions near the source of the river and that these would
explain the flooding lower down the river. Another contribution that
Eratosthenes made to geography was his description of the region "Eudaimon
Arabia", now the Yemen, as inhabited by four different races. The situation
was somewhat more complicated than that proposed by Eratosthenes, but today the
names for the races proposed by Eratosthenes, namely Minaeans, Sabaeans,
Qatabanians, and Hadramites, are still used. Eratosthenes writings include the
poem Hermes, inspired by astronomy, as well as literary works on the theatre and
on ethics which was a favorite topic of the Greeks. Eratosthenes is said to have
became blind in old age and it has been claimed that he committed suicide by
starvation.
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