Soap Bubbles and Films Can Solve Complex Mathematics

A team of professors from the University of Málaga say that they have developed a new method of approaching complex mathematical equations and calculations, that revolve around using soap bubbles and films as a source of inspiration.

In addition to fascinating children, these structures are shaping up to become potent mathematical tools, the two investigators say. They make for the basis of innovative mathematics procedures, that are uniquely equipped to solve classic problems.

The researchers published their new approach to conducting calculations in the latest issue of the esteemed American Journal of Physics. The paper was authored by UM professor Carlos Criado and Nieves Álamo, AlphaGalileo reports.

“With the aid of soap films we have solved variational mathematical problems, which appear in the formulation of many physical problems,” Criado explains.

He adds that one of the reasons why these films are such great sources of inspiration is that they tend to always take on the shape that minimizes their elastic energy, and their area implicitly.

As such, soap bubbles turn out to be ideal tools for the calculation of variations “where we look for a function that minimizes a certain quantity (depending on the function),” the UM professor explains.

“Of course there are other ways to solve variational problems, but it turns out to be surprising, fun and educative to obtain soap films in the shape of brachistochrones, catenaries and semicircles,” the investigator goes on to say.

One of the applications is that of determining a concept known as the curve of fastest descent, or brachistochrone. This is the shape that a wire stretched between two points at different elevations takes in order to allow a ball traveling down on it to move as rapidly as possible.

Mathematicians have figured out this issues, and several others, in the past decades or so, but much more still remain to be solved. Those in which minimization of function is required could benefit from the new approach, the UM team believes.

Over the past few years, a number of problems and conjectures have been solved, due either to pure genius or innovations in the science overall. Still, for every mystery that is solved, other mathematical and physical problems queue up, awaiting a solution.