The Hyperbolic Crochet Coral Reef

The Crochet Coral Reef Project is a worldwide, collective, collaborative installation and community-based experience created by twin sisters Margaret and Christine Wertheim of the Institute For Figuring in Los Angeles.In the interest of contributing to this ever-expanding collection of woolly wonders, In Stiches Collective is facilitating the creation of a Sydney Coral Reef. We invite you to participate in this "celebration of the intersection of higher geometry and craft, a testimony to the disappearing wonders of the marine world."

The Crochet Reef Project was inspired by geometric models of hyperbolic space, originally developed by mathematician Dr Daina Taimina in 1997, using the art of crochet. Until that time most mathematicians had believed it was impossible to construct physical models of hyperbolic forms, yet nature had been doing just that for hundreds of millions of years. It turns out that many marine organisms embody hyperbolic geometry, among them kelps, corals, sponges and nudibranchs. In 2005 Margaret and Christine conceived the idea of crocheting a coral reef by developing Dr Taimina's techniques to make a whole taxonomy of organic, reef-like forms. The Reefs created by using these handicraft techniques not only look like actual coral reefs, they draws on the same geometry endemic in the oceanic realm. The project draws attention to the beauty and fragility of living reefs (the ecosystems system most vulnerable to the effects of climate change), and also links communities through science, mathematics, art & craft.

A full explanation of the project may be seen on the Institute For Figuring's website at www.theiff.org, along with many images of the Core Collection of IFF Reefs and its Satellite Reefs around the world - in Sydney, Chicago, New York, London and elsewhere.

Photo Courtesy of the Institute For Figuring

The following introduction to Hyperbolic Space is condensed from the IFF site.

What is a hyperbolic plane?

A hyperbolic plane is sometimes described as a surface in which the space expands. So as you move away from any point on a hyperbolic surface you get exponentially more space. One way of understanding it is that it's the geometric opposite of the sphere. On a sphere, the surface curves in on itself and is closed. A hyperbolic plane is a surface in which the space curves away from itself at every point. Like a Euclidean plane it is open and infinite, but it has a more complex and counter-intuitive geometry.Why is the hyperbolic plane important historically?Until the 19th century, mathematicians knew about only two kinds of geometry: the Euclidean plane and sphere. The discovery of the hyperbolic plane came from the attempt to prove Euclid's fifth postulate, which is also known as the parallel postulate. For two thousand years, mathematicians accepted this postulate as true, but it had always caused problems. In the 1820s and 1830s Hungarian mathematician Janos Bolyai and Russian mathematician Nicholay Lobatchevsky discovered a geometry in which all of Euclid's postulates held true except for the fifth one. It was a radical shock to their community to find that there existed in principle a completely other spatial structure whose existence was discerned only by overturning a 2000-year-old prejudice about "parallel" lines. The discovery of hyperbolic space marked a turning point in mathematics and initiated the formal field of non-Euclidean geometry. This was of great mathematical and philosophical interest. From the time of the Greeks, it was believed that geometric theorems were such pure and perfect Truth that they did not need to be scrutinized by observations of the real world. In the early twentieth century, Albert Einstein developed The General Theory of Relativity which made extensive use of hyperbolic geometry. Thus, abstract, mathematical philosophy was now firmly in therealm of Science.

A-5 ( Euclid’s Parallel Axiom): Given a line l and a point not on l, there is one and only one line which contains the point, and is parallel to l.

A-5H (Hyperbolic Geometry Parallel Axiom): Given a line l and a point not on l, there are at least two distinct lines which contains the point, and are parallel to l

Photo Courtesy of the Institute For Figuring.

The Network

In the name of exploration In Stitches want to see how The Sydney Hyperbolic Crochet Coral Reef travels through the community. We want to trace our network. If everyone involved in the Sydney Reef uses a word trail we can trace how we connect to our fellow crocheters.

How will we do this?

We begin with the IFF as the central node. This node is given a name ‘IFF Blast Fishing’. The IFF brought the reef to In Stitches Collective, the producers of the Sydney Reef, so In Stitches take the name Blast Fishing and add their unique name Hyperbolic. In Stiches now have the name Blast Fishing Hyperbolic. When you learn to crochet hyperbolic models from In Stiches we give you another name, for example Nitrate, which you will pass on to the people who you teach. So they will become Nitrate plus their unique name- say– Exponential and they then have the name Exponential Nitrate. Through this network of connections we can see how The Sydney Hyperbolic Crochet Coral Reef forms a life form of its own.

What’s in a name?

All the names are organised in pairs- one name is a geometric term (eg. pseudo-sphere), the other aims to draw awareness to the many contributing factors of reef degradation (eg. aquarium industry).

How do we get our names?

The first name you get from the person who taught you about the reef. Then if you email us at sydneyreef@gmail.com we will send you your unique name and more information about the project including meeting dates and patterns and where to send your hyperbolic crochet for the grand installation in 2009.

Network Concept and Visualisation - In Stitches.

Visualisation created by In Stitches from image of Red hyperbolic plane crocheted by Dr Daina Taimina

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