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The Story of Eratosthenes The Circumference of the Earth

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Eratosthenes was born in Cyrene (in modern day Libya), but worked and died in Alexandria, capital of Ptolemaic Egypt. He never married. He was reputedly known for his haughty character.

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Eratosthenes studied at Alexandria and for some years in Athens. In 236 BC he was appointed as librarian of the Alexandrian library.

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He made several important contributions to mathematics and science, and was a good friend to Archimedes.

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In 195 BC he became blind and a year later he supposedly starved himself to death.

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He is credited with having calculated the Earth's circumference around 240 BC, using trigonometry and knowledge of the angle of elevation of the Sun at noon in Alexandria and Syene.

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Syene Eratosthenes knew that on the summer solstice at solar noon in the town of Syene on the Tropic of Cancer, the sun would appear at the zenith, directly overhead.

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Syene As the legend goes, Eratosthenes was visiting Syene on the Summer Solstice and went to get a drink from the town well.

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Syene While looking down into the well, Eratosthenes observed that the sun was perfectly reflected in the water at the bottom of well.

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Syene A perfect reflection of the sun in the water at the bottom could only happen if the Sun was directly over the well, 90° to the surface.

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Syene 90°

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Alexandria He also knew, from measurement, that in his hometown of Alexandria, the angle of elevation of the Sun would be 7.2° south of the zenith at the same time.

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Alexandria

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Alexandria 7.2°

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Eratosthenes recognized that the difference in the Sun’s angle was due to the curvature of the Earth.

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Syene Alexandria Sunlight Eratosthenes believed that suns rays were parallel. The sun ray hitting Alexandria was parallel to the one hitting Syene.

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Syene Alexandria Sunlight Eratosthenes believed that suns rays were parallel. The sun ray hitting Alexandria was parallel to the one hitting Syene.

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Syene Alexandria Sunlight Eratosthenes believed that suns rays were parallel. The sun ray hitting Alexandria was parallel to the one hitting Syene.

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Syene Alexandria Sunlight Drawing a line straight down from both locations creates a wedge with an internal angle of 7.2°.

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Syene Alexandria Sunlight Drawing a line straight down from both locations creates a wedge with an internal angle of 7.2°. 7.2°

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7.2°

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Eratosthenes also knew that a complete circle had 360°. 360°

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7.2° These two angles can be compared: piece to whole. This makes the ratio 7.2°:360°. 360°

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860 km Eratosthenes also knew the distance between Alexandria and Syene to be approximately 860 km.

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860 km With this information, a proportion can be created to calculate the Earth’s circumference. 360° 7.2° ?

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860 km So… what did Eratosthenes determine the circumference of the Earth to be? The current accepted value for the Polar Circumference is 40,008 km. What was Eratosthenes percent deviation? 360° 7.2° ?

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