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Calculating the circumference of the Earth

When Eratosthenes was informed that on the summer solstice at midday in Syene (known in the mondern
day as Aswan) which lies almost on the same meridian as Alexandria, that a well (or a vertical pillar) had no shadow, he observed that at the same moment in Alexandria the angle of his shadow was 7.2°. Considering the phenomenon as the result of the sphericity of the Earth, he concluded the following proportions of arcs and angles: 7.2°/360°= Distance Syene – Alexandria / Circumference of the Earth. Given the distance Syene  Alexandria that was 5.000 stadia, he calculated the circumference equal to 250.000 stadia, i.e. 39.690 km (almost equal to the accepted today value of 40.615 km).

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