Pie with square

[Paul Dale]

The diagram is labelled badly

Anyway, e is easy:

\( e^2 = \frac {\pi r^2} 9 \)
\( \therefore e = \frac { r \sqrt \pi } 3 \)

The conversion to a percentage is left up to the reader.


I started working on d using \( 2 \int_0 ^{\frac d 2} \sqrt {r^2 - x^2} dx \) but got lost in the LaTex expression morass far too quickly.

An afterthought: it might be better working on the red bits for d: \( \pi (r - \frac d 2)^2 - (e-d)^2 = \frac {4\pi r^2} 9 \) which is a messy quadratic in d.

- Pauli