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New methods for old problems

The mathematician Johann Bernoulli found the answer centuries ago when he realised that it was a cycloid (the curve described by a point on a circle rolling along a line). That was the origin of the calculus of variations, which was also used in other classic problems, like that of the catenary (the shape of a chain suspended by its endpoints) and the isoperimetric curve (a curve that maximizes the area it encloses).

The study shows that these calculations may be related to Plateau’s problem, that is, to find the shape adopted by a soap film under certain boundary restrictions. Besides, the researchers show how to design the experiments constraining the soap films between two surfaces in such a way as to obtain the appropriate curves.

Other Spanish researchers, like Isabel Fernandez, of the University of Seville, and Pablo Mira, of the Polytechnic University of Cartagena, have succeeded in finding for the first time the solution to specific mathematical problems (the Bernstein problem in the Heisenberg space) with the help of soap films.

TEXT 8

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