In Folha, Viana speaks of 'the most mathematical of designers'.

Crédito: Toshihiro Gamo | Flickr

Reproduction of Marcelo Viana's column in Folha de S. Paulo.

Japanese designer Issey Miyake, the most mathematical of the great fashion designers, sought inspiration in geometry to find innovative and aesthetic solutions to one of civilization's oldest problems: how best to cover the human body, and its curves, with a flat fabric?

The fact that this problem is inherently mathematical may seem surprising, but it did not go unnoticed by great mathematicians throughout history. As early as 1770, Leonhard Euler wondered, "What surfaces can be covered with paper that can be folded but cannot be stretched or torn?"

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In a work published in the annals of the St. Petersburg Academy of Sciences, he called such surfaces "foldable," pointing out that the cylinder and the cone are foldable, but the sphere is not. This is the fundamental problem of cartography: it is not possible to represent the spherical surface of the Earth in the form of a flat map without "stretching" or "tearing" the image.

It is therefore no coincidence that many of Miyake's most spectacular designs have been made with pleated fabrics.

The theory initiated by Euler was continued a century later by Pafnuty Chebyshev, one of the greatest Russian mathematicians of all time, in his 1878 work entitled "On the Cutting of Clothes". An important development is that, instead of paper, he considered clothes made of fabric, which has quite different properties and allowed him to find new solutions to the problem.