Book:Archimedes/The Sand-Reckoner

Archimedes: The Sand-Reckoner

Published $\text {c. 250 BCE}$.

Subject Matter

• Number Theory

Archimedes describes a system of notation for designating very large numbers, up to $N^{N^N}$, where $N = 10^8$.

Contents

• Upper Bound for Number of Grains of Sand to fill Universe

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Historical Note

The Sand-Reckoner by Archimedes was addressed to King Gelon of Syracuse (who appears to have lived some $250$ years earlier).

It is in this book that we learn that Aristarchus of Samos had first proposed a heliocentric universe, nearly $2000$ years before Nicolaus Copernicus.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $-1$ and $i$
• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $10^{51}$
• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.5$: Archimedes (ca. $\text {287}$ – $\text {212}$ B.C.)
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $-1$ and $i$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $10^{51}$