Correction to: A Closed-Form Solution to the Geometric Goat Problem

Correction to: The Mathematical Intelligencer https://doi.org/10.1007/s00283-020-09966-0

A Closed-Form Solution to the Geometric Goat Problem″ was published in the fall 2020 issue of the Mathematical Intelligencer. An attentive reader has pointed out an error in the statement of Theorem 2: the domain of integration in each of the four integrals should be $|z-3\pi /{4}|=\pi /4$, not $|z-3\pi /{8}|=\pi /4$. Here is the correct statement of the theorem:

FormalPara Theorem 2.

Let $z_0$ denote the unique zero of the entire function $f(z)=\sin z-z\cos z-\pi /2$ inside the interval $]\pi /2,\pi [$.

• 1. We have

  $$\begin{aligned} z_0=\frac{\displaystyle \oint _{|z-3\pi /4|=\pi /4} {z\,dz}/({\sin z-z\cos z-\pi /2})}{ \displaystyle \oint _{|z-3\pi /4|=\pi /4}{dz}/({\sin z-z\cos z-\pi /2})}. \end{aligned}$$

• 2. In the situation of the goat problem, the radius R of $k_2$ is given by

  $$\begin{aligned} R=2r\cos \left( \frac{1}{2} \frac{\displaystyle \oint _{|z-3\pi /4|=\pi /4}{z\,dz}/{(\sin z-z \cos z-\pi /2)}}{\displaystyle \oint _{|z-3\pi /4|=\pi /4} {dz}/{(\sin z- z\cos z-\pi /2)}}\right) . \end{aligned}$$