In-situ observation of a soap film catenoid - a simple educational physics experiment

TL;DR

This paper presents an educational physics experiment using soap films to observe catenoids, minimal surfaces that illustrate the concept of stationary functionals and local extrema in a tangible way.

Contribution

It introduces an in-situ method for observing soap film catenoids, linking theoretical minimal surfaces with hands-on experimentation for educational purposes.

Findings

Soap films form stable catenoids between rings.

The shape variation can be explained by dynamic mechanics.

The experiment demonstrates stationary points of functionals in physics.

Abstract

The solution to the Euler-Lagrange equation is an extremal functional.To understand that the functional is stationary at local extrema (maxima or minima), we propose a physics experiment that involves using soap film to form a catenoid. A catenoid is a surface that is formed between two coaxial circular rings and is classified mathematically as a minimal surface.Using soap film, we create catenoids between two rings and characterize the catenoid in-situ while varying distance between rings. The shape of the soap film is very interesting and can be explained using dynamic mechanics. By observing catenoid, physics students can observe local extrema phenomena. We stress that in-situ observation of soap film catenoids is an appropriate physics experiment that combines theory and experimentation.