  We discuss the classical results of Stanis{\l}aw Go\l\k{a}b, on the values of
pi in arbitrary normed planes, including the classification of extremal values.
We reprove the result of J. Duncan, D. Luecking, and C. McGregor, which states
that any norm with quarter-turn symmetry has pi-value $\geq \pi$. We also show
that a norm is Euclidean iff it has quarter-turn symmetry in some basis and has
pi-value $\pi$.
