Propositiones ad Acuendos Juvenes/Problems/25 - De Campo Rotundo/Historical Note

Historical Note on Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $25$: De Campo Rotundo

The area $\AA$ of a circle in terms of its circumference is:

$\AA = \dfrac {C^2} {4 \pi}$

However, what Alcuin has done is used a value for $\pi$ of $4$.

The actual value (assuming $144$ square perches to the acre) is approximately $88.4$ acres.

Another translator uses a tortuous method to obtain $\AA = 96$ acres, but this uses a value for $\pi$ of $3$.

Sources

• 1992: John Hadley/2 and David Singmaster: Problems to Sharpen the Young (Math. Gazette Vol. 76, no. 475: pp. 102 – 126)  www.jstor.org/stable/3620384