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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**

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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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. Syene

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

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

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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. Syene

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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. 90° Syene

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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. Alexandria

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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. Alexandria

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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. 7.2° Alexandria

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

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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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**Eratosthenes believed that suns rays were parallel**

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

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**Eratosthenes believed that suns rays were parallel**

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

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**Eratosthenes believed that suns rays were parallel**

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

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

Alexandria Sunlight Syene

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

Alexandria Sunlight Syene 7.2°

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

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

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**These two angles can be compared: piece to whole**

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

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

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**With this information, a proportion can be created to calculate the Earth’s circumference.**

860 km 7.2° ? 360°

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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? 860 km 7.2° ? 360°

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