Steiner trees and spanning trees in six-pin soap films

Abstract

The problem of finding minimum (local as well as absolute) path lengths joining given points (or terminals) on a plane is known as the Steiner problem. The Steiner problem arises in finding the minimum total road length joining several towns and cities. We study the Steiner tree problem using six-pin soap films. Experimentally, we observe spanning trees as well as Steiner trees partly by varying the pin diameter. We propose a possibly exact expression for the length of a spanning tree or a Steiner tree, which fails mysteriously in certain cases.