# Eratosthenes of Cyrene Answer Questions

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Eratosthenes of Cyrene was best known for measuring the circumference of the Earth. He did so by taking the angle between Alexandria and Syene in Egypt to be 7.12 degrees and the distance between to two to be 4,998 stadia. What is the ratio of distance to angle ( in stadia/degree) ?

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Eratosthenes of Cyrene was best known for measuring the circumference of the Earth. He did so by taking the angle between Alexandria and Syene in Egypt to be 7.04 degrees and the distance between to two to be 5,004 stadia. What is the circumference of the Earth (in stadia) using these data?

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Eratosthenes of Cyrene was best known for measuring the circumference of the Earth. He did so by taking the angle between Alexandria and Syene in Egypt to be 7.0 degrees and the distance between to two to be 5000 stadia. Eratosthenes later rounded the circumference of the Earth to 252,000 stadia, most likely just because that number is easily divisible by 60. This comverts to 40,074 km. The currently accepted polar circumference of the Earth is 40,008 km. What is the relative error in this measurement? Express this as a percentage to two significant digits.