A simply connected Riemannian manifold… Parkin Drawing Prize 2019

 

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A simply connected Riemannian manifold with negative Gaussian curvature.

(2019). 8010.75 metres of Acrylic Knitting Yarn #622 (9/10ths the height of Mt. Everest) in 10,014,000 ± 0.7% single crochet stitches, 340 x 530 x 430mm 4 kg.
formula

Since discovering hyperbolic space in the 1820s mathematicians sought a way to construct durable physical models of hyperbolic geometry, a feat many believed was impossible. In 1997 Latvian mathematician Daina Taimina realised a solution using techniques handed down to her, she simply crocheted one.

The uncomplicated pattern of an increasing number of stitches in each row creates a complex curl of parallel lines, a maximum surface area in a limited volume and creates an intersection, a meeting point between High Mathematics and Hand Crafts. Using blogs as a site for content and communication, crafters share patterns for hyperbolic geometry to make mathematically interesting adornments, and conversely mathematicians learn craft techniques as functional modeling methods.

There is a limit to the medium, as with many models of exponential growth it cannot sustain itself indefinitely, stitches expand and fibres fray, pulled taut beneath growing pressure, unravelling from within as it begins to disintegrate under its own mass.

It will take approx. 4000 metres of wool to complete the next row.

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Parkin Drawing Prize Exhibition 2019
6 August – 8 September
NZ Academy of Fine Arts, Wellington

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