Slide two rings apart and watch the soap film choose a shape, meet the unstable catenoid, and pop. Every dial below tracks the same slider. For the story behind the numbers, visit the Catenoid page, or read the plain-language version. This instrument runs on a hoop 2 inches across, so every model number is already inches.
The hand. Whoever pulls the rings does work against the film's tug; the film banks that work as surface.
Landscape. Every possible waist has a price; the dip is where the film parks, the ridge is where the unstable catenoid stands, and the toll is the climb between them. The unstable catenoid is the inner branch: the second solution the equations allow, standing on the ridge at the saddle point every escape must cross. It is present at every height below the existence threshold, and never holdable.
Perturbation. The kick a poke must deliver to pop the film early, and how far the hand still has to pull to end it without one.
Geometry & volume. The film's measurements, and how full its surrounding cylinder is; exactly one half at criticality, which is this site's theorem.
Status. Stable means the film is the cheapest thing in the room; metastable means the disks are now cheaper and only the toll keeps the film alive; popped means the parking spot no longer exists.
Reading this page against the Reader's Guide. The outer branch, the stable catenoid, is the Guide's wide film, parked in the dip. The inner branch, the unstable catenoid, is the Guide's slim film, its ghost twin, standing on the ridge. The fold point at h/R = 2λ is the Guide's criticality. The Goldschmidt threshold is the Guide's bills tie. The Goldschmidt configuration, two flat disks, is the Guide's popped state and the table at 100. The bill is surface area indexed to the disks at 100; the toll is the energy barrier between the two.
Energy labels assume an industrial-strength bubble solution and are quoted at the 4 inch hoop comparison scale: there, 100 cost units stand for about 0.8 millijoules, so one unit is roughly 8 microjoules; the 2 inch native hoop carries a quarter of that, about 0.2 millijoules per 100 units. The instrument's hoop is 2 inches across, so every model number is already in inches; where it helps, the readout also shows the 4 inch hoop reading, twice each number, in parentheses. Back to the Catenoid →