Eratosthenes' 7.2-degree shadow at Alexandria gave a circumference near 25,000 miles

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Key facts

• Eratosthenes: curator of the library at Alexandria, travelled about 500 miles to Syene (modern Aswan) near 23.5 degrees north, where he had observed a deep shaft with water at the bottom.
• At Syene on the summer solstice the sun was directly overhead at noon and cast no shadow, so sunlight reached straight down the shaft and reflected off the water.
• At Alexandria on the same date a vertical pole or obelisk cast a shadow corresponding to a solar angle of 7.2 degrees; he used the Babylonian 360-degree division, and 360 divided by 7.2 gave 50.
• He multiplied the 50 degrees by the roughly 500-mile distance to obtain about 25,000 miles, close to the actual circumference of the Earth.
• Dividing the circumference by pi gives a diameter of roughly 7,920 miles; a second observation of the moon taken 12 hours later, combined with trigonometry known to Greek mathematicians, yields distances to the moon and sun.

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