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Eratosthenes: Ptolemaic Alexandria
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Eratosthenes's most famous calculation is the length of the circumference of Earth. On the day of summer solstice (the day of the year with the longest period of daylight), Eratosthenes observed that the sun's rays shone directly down into a well in Syene at noon. The city of Alexandria lies very close to due North of Syene, meaning the two cities experience noon at approximately the same time (this is a necessary condition for the experiment). Eratosthenes measured the angle that the sun's rays made with a vertical stick located in Alexandria at noon on summer solstice and found the angle to be one-fiftieth of a circle, or 7.2°. Using the fact that the sun's rays are virtually parallel, Eratosthenes realized that an angle of 7.2° whose vertex was located at the center of the earth created an arc from Syene to Alexandria. Eratosthenes further estimated that the length of this arc, or distance between the two cities, was approximately 5,000 stades (a stade is an ancient unit of length approximately equal to a tenth of a mile).
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One of Eratosthenes' teachers was Ariston of Chios, who studied under Zeno, who himself was a founder of the Stoic school of Philosophy. His other teaher, Callimachus became the librarian of the Alexandrian library - one of the greatest libraries that ever were, which holdings included hundreds of thousands of papyri and vellum scrolls. Eratosthenes went to Alexandria with Callimachus and when Callimachus died in about 240BC, Eratosthenes became a new librarian. He was a third librarian of this famous library.
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Eratosthenes lived from 271-194 B.C. He was born in Cyrene which was a Greek colony west of Egypt and under Ptolemaic domination. He spent most of his working days in Alexandria. In his early life, he studied at Plato's school in Athens. He held one of the most prestigous postitions in the Hellenistic world, chief librarian at the Museum. He has written works on geography, philosophy, history, astronomy, mathematics, and literary criticism.
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Eratosthenes assumed that the city of syene was on the Tropic of Cancer because at midday on the summer solstice a well, especially dug for this reason, was illuminated to its bottom by the sun's rays. It was ... assumed that the city of Alexandria and Syene were on the same meridian. On the next solstice, Eratosthenes measured the shadow cast at Alexandria at midday by a vertical pointer (thin stylus) of known height. The vertical angle of this shadow was found to be 82 degrees 48 minutes. North Pole Tropic of Cancer Alexandria rays of sun Equator Syene Since the angle of the sun's rays on the summer solstice is 90 degrees, then both vertical lines extended to the center of the earth would form an angle of 7 degrees 12 minutes ( all three angles totaling 180 degrees). Therefore, the arc distance between Syene and Alexandria relative to the earth's circumference would be 7 degrees 12 minutes/360 degrees, or 1/50 of the circumference.
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Eratosthenes was born in 276 B.C. in the city of Cyrene which is in the modern-day country of Libya. He studied for a few years in Athens. Later, he studied and spent most of his adult life in Alexandria. He died in Alexandria in 194 B.C. at the age of 82 years. Some people believe that Eratosthenes starved himself to death on purpose after going blind. He never married.
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Eratosthenes was born in Cyrene (in modern-day Libya). He worked at Alexandria and died in the capital of Ptolemaic Egypt. He was never married. He was reputed to have a haughty character.
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