Following the notation in Example 3.53, consider the standard simplex $\Delta^{n}$ and the concave function $\vartheta=\frac{1}{2}\varepsilon_{n}$ on $\Delta^{n}$. From examples 3.53 and 5.18(1), we deduce that the corresponding metric is the Fubini-Study metric of ${\mathcal{O}}(1)^{{\text{\rm an}}}$.