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The Sand Reckoner of Archimedes

tr. by Thomas Heath


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This short treatise of Archimedes on the amount of sand grains which could be contained in the ancient model of the universe is remarkable. It uses some extremely large numbers, given that this was antiquity and Europeans did not yet have the benefit of decimal notation. It also anticipates the method of Calculus: measuring by subdivision into very small quanta, in this case grains of sand. Also of interest are Archimedes' (incorrect but informed) estimates of the relative size of the sun, moon and earth. The argument can be followed by anyone who has mastered basic algebra.

The Sand-Reckoner