A Counterexample to a Theorem of Fu on Steiner's Problem

Abstract

In a paper by Fu it was stated that a necessary and sufficient condition to obtain a solution was found for Steiner's problem with rectilinear distance. It was further claimed that a process of iteration which was presented leads to a solution. It is the purpose of this correspondence to give a counterexample to Fu's main theorem and show that his iteration scheme does not always yield a solution. Hence Steiner's problem remains unsolved in the general case.