# Eratosthenes' Measurement of Earth

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## Theorem

The circumference of Earth was measured by Eratosthenes of Cyrene to be of the order of $45 \, 000 \, \mathrm{km}$.

## Proof

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## Source of Name

This entry was named for Eratosthenes of Cyrene.

## Historical Note

It is not certain what the length of the unit used by Eratosthenes of Cyrene when he made his measurement of the circumference of the Earth.

The Olympic stade of $176.4 \, \mathrm m$ would give a circumference of $44 \, 100 \, \mathrm {km}$, an error of $10 \%$.

The Italian stade of $184.8 \, \mathrm m$ would give a circumference of $46 \, 100 \, \mathrm {km}$, an error of $15 \%$.

## Sources

- 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {B}.16$: The Sequence of Primes: Footnote $1$ - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $2$: The Logic of Shape: Problems for the Greeks