Eratosthenes' Measurement of Earth

Theorem

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

Proof

This needs considerable tedious hard slog to complete it. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Finish}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

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