to continue the physical analogy of soap film given above, these goldschmidt solutions can be visualized as instances in which the soap film breaks as the circular wires are stretched apart. however, in a physical soap film, the connecting line segment would not be present. additionally, if a soap film is stretched in this way, there is a range of distances within which the catenoid solution is still feasible but has greater area than the goldschmidt solution, so the soap film may stretch into a configuration in which the area is a local minimum but not a global minimum. for distances greater than this range, the catenary that defines the catenoid crosses the "x"-axis and leads to a self-intersecting surface, so only the goldschmidt solution is feasible.