Hyperbolic paper sculptures

Abstract

Topology was one of my favourite subjects at university, but it took a while for me to really explore the possibilities of presenting my drawings on mathematical sculptures. I started using my drawings as the content for artist’s books early on. Then, in 2000, I began playing withMöbius strips, one-sided surfaces. I developed theHappersett Accordion, a folded version of the Möbius strip. By alternating the colours of the drawings on each folded section, I was able to create a Möbius strip with two distinct faces. Ivars Peterson wrote about it in 2001: ‘ . . . a novel twist on the Möbius strip; a playful eye-catching creation . . . ’ (2001). In 2005, I sawDaina Taimina present her hyperbolic forms at the CUNYGraduate Center in New York. Taimina had found paper models too fragile for use as classroommodels, so she used crocheted yarn as the medium. I got to work crocheting my own hyperbolic form, forme, it was a slowprocess. I wanted to find a quickway tomake hyperbolic inspired forms that could be used in an art class. I returned to paper, using card stock tomake sculptures with drawings that were not necessarily going to be handled as much as classroom models. My next paper form was the Circle Hyperbolic. Taking two identical circles each with a radial slit, I combined them by overlapping them by 45 degrees and gluing them together. This starts a spiral. By unspiralling the form so that other edges of the slits can be overlapped and attached, a saddle shape is formed. The resulting sculpture answers the question of what happens if a circle hadmore than 360 degrees or, in this case, 630 degrees? By using the same method to combine three circles into a form with 945 degrees a ruffle started to appear. ‘Chaos Hyperbolic’ (Figure 1) consists of three circles and features my chaos fractal drawings. In 2014, MOMA presented a Lygia Clark retrospective. I was fascinated by the kinetic nature of the hinged metal sculptures. I wrote about them in my blog (Happersett, 2014): ‘ Clark created these sculptures so the viewer could manipulate the shapes creating different forms . . . ’. I even showed how to reproduce one of the simpler forms using tape and cardboard. This led me to explore more complicated shapes with hinges. Over the past few years, I have been making my lace drawings within the confines of quadrilaterals. I decided to try my hand at hyperbolic forms using squares to showcase these drawings. I started with a set of identical squares, each with a single slit running