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SOAP FILMS HELP TO SOLVE MATHEMATICAL PROBLEMS

Soap bubbles and films have always fascinated children and adults, but they can also serve to solve complex mathematical calculations. This is shown by a study carried out by two professors at the University of Málaga, who have succeeded in solving classic problems using just such an innovative procedure.

"With the aid of soap films we have solved variational mathematical problems, which appear in the formulation of many physical problems," explains Carlos Criado, professor at the University of Málaga. Together with his colleague Nieves Álamo, he has just published his work in the American Journal of Physics.

Soap films always adopt the shape which minimizes their elastic energy, and therefore their area, so that they turn out to be ideal in the calculus of variations, "where we look for a function that minimizes a certain quantity (depending on the function)," adds the researcher.

"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," Criado emphasizes.

The professor offers the example of the famous problem of the brachistochrone curve. What shape must a wire be in order that a ball travels down it from one end to the other (at a different height) as rapidly as possible? The answer is the brachistochrone (from the Greek brachistos, the shortest, and cronos, time), the curve of fastest descent.

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