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Surface Story

Inspired by spiral soap films, mathematicians zero in on a novel, economical, and infinite helix

Dip a flat wire ring into a basin of soapy water. The ring comes out spanned by a taut, iridescent soap film in the form of a thin disk. Its area is smaller than it would be if the surface had peaks and valleys, or even small wrinkles. A clinging soap film invariably settles into the shape that mathematicians call a minimal surface. They can also imagine minimal surfaces that don't exist in nature.

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