The authors have proved in a previous article that the Steiner ratio (the minimum ratio of the length of a Steiner minimal tree to the length of a minimal spanning tree) for a gradient‐constrained network on three points is
\documentclass{article} \usepackage{amsmath,amsfonts,amssymb}\pagestyle{empty}\begin{document}$ 1/2+(\sqrt{4+3m^2}-1)/(4\sqrt{1+m^2}) 1\le m\le \sqrt{3} (3m+\sqrt{9m^{2}+12})/(4\sqrt{3m^{2}+3}) m\ge \sqrt{3} $\end{document}. © 2010 Wiley Periodicals, Inc. NETWORKS, Vol. 57(4), 354–361