Be Möbius

The simple act of slitting, twisting and re-attaching a band of paper will produce the Möbius strip, one of the greatest wonders and conundrums of the mathematical world. This phenomenon, a known source of fascination for mathematicians, is finding its way into popular culture.

The one-dimensional Möbius (unlike the one-dimensional TV script) is neither simple nor boringly linear. And when applied to logic, it becomes a technique for making two things at once, like a secret which, when told, is no longer a secret. Rather than there being two sides to every story (as rationalists would have you think) a Möbius shape is infinitely variable, the gradient between two different versions of events.

More recently, the geometry of mathematics has spilled into the geometry of design. Architects have replaced the box geometry of buildings with a Möbius logic, like UN Studio's Möbius house which intertwines on a double-locked torus.

Perhaps the most interesting iterations of the Möbius shape are in fashion, a discipline which has long explored mathematical shapes like circles and squares - not only in the patterning of fabric but to create forms which complement the form of the body.

Instead of twisting a strip of paper, designer Yeohlee Teng creates a Möbius from fabric. Her Möbius Cape - a figure-eight shawl that doubles back on itself over the wearer's spine - turns this mathematical conundrum into a fashion solution.

The infinitely variable Möbius has also inspired J. Meejin Yoon, whose My Studio usually works on buildings, to create a Möbius dress. Like its namesake strip, the dress is a long rectangular loop, flipped and connected at the opposite end. Zipped up, the loops create an A-line dress; unzipped, they spire like orange peel.

The twist in the Möbius makes it a unique surface which is one-sided and two-sided at once, a single continuum.

Expanded into 3-D, it generates an object - the Klein Bottle - which has neither an inside nor an outside.