The Sand-Reckoner
Notebook
The Sand-Reckoner, addressed to King Gelon of Syracuse, is Archimedes's demonstration that finite numbers — very large ones — can be named and manipulated. Starting from the claim that the number of grains of sand needed to fill the universe is finite, Archimedes invents a place-value system of powers of myriads (10,000) sufficient to express 10^{8×10^{16}}, and computes an upper bound on the size of the cosmos using the heliocentric hypothesis of Aristarchus — the earliest surviving reference to that theory. The essay thus combines the first exposition of large-number notation with the first engineering estimate of cosmological scale. This edition is T. L. Heath's 1897 English rendering from an OCR transcription; minor artifacts remain in mathematical notation.
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