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To estimate the Earth’s circumference, Eratosthenes calculated the length of a meridian arc by measuring the shadow cast by a vertical axis at noon on the summer solstice. In Syene (northern tropic), no shadow is cast whereas 800 kilometres further north, in Alexandria, the shadow is cast at an angle of 7.2° from the vertical, that is to say 1/50 of 360°. The circumference is therefore equal to 50 times the distance between the two cities.

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