A beautiful crocheted coral reef on display in Dublin is a response to the threat of global warming and a fine example of living maths and a great work of art, writes KARLIN LILLINGTON

MOTHER NATURE loves maths. Principles of mathematics underlie everything from the way a leaf grows to the structure of a nautilus shell.

But it turns out that nature also likes geometries that are so strange that mathematicians spent 2,000 years trying to prove they couldn’t possibly exist. Geometries so odd, that it is only within the past decade that a mathematician figured out a way to represent that geometric world in three-dimensional form.

Perhaps it is no fluke that the mathematician who did so is a woman, and the form that she found for making this geometry literally palpable, is the mostly female craft of crochet.

The mathematician, Latvian born Dr Daina Taimina, was in Dublin this week speaking about the delights of crocheting in hyperbolic form at the Science Gallery at Trinity College. But even if you missed the event, you still have a week in which to see a most glorious manifestation of the hyperbolic world and its direct connection to nature.

The Science Gallery is filled with what it is calling a “woolly wonder”: a huge, crocheted hyperbolic coral reef that perfectly straddles the boundaries of art and science.

It turns out that when you crochet according to the laws of hyperbolic geometry, you produce woolly structures that look exactly like coral, sea anemones, jellyfish, diatoms, and the delicate frilly mantles of the beautiful sea slugs called nudibranchs.

And of course this isn’t coincidence either – it’s because scientists now understand that nature has a love affair with hyperbolic geometry.

When you see undulating edges and frills and spirals in plants and animals, you are looking at hyperbolic geometry in living 3-D.

Hyperbolic geometry occurs in a different dimension than the two we are familiar with, the geometry of the flat planes and of spheres.

On a flat plane, we know that two parallel lines will never intersect and will always remain the same distance apart into infinity, never sharing a common point.

On a sphere, lines that encircle the sphere and create two equal halves will always intersect.

So far, so familiar. But it turns out there is another geometric dimension, that of hyperbolic space, in which infinite parallel lines can intersect with a single point and yet never touch each other.

Only in the late 19th-century did French mathematician Henri Poincare find a way of visualising this geometry.

His circular Poincare disc will be instantly recognizable to anyone who was ever looked at those famous MC Escher woodcuts in which strange but perfectly interlinked figures tile a curving plane.

The Escher images are so fascinating because we can tell they represent a three-dimensional space but we are viewing it on the flat, two-dimensional surface of a piece of paper. And like all MC Escher images, it makes logical sense one moment and totally confuses the mind the next.

Interestingly, crochet (for reasons docents at the Science Gallery are happy to explain and even demonstrate with a crochet hook and ball of yarn) makes it much easier to understand the end result of the application of a hyperbolic formula to a process.

And because it ends up looking like something we know in the natural world, this strange geometric world makes more sense.

But to see an endless variety of hyperbolic forms joined into a great hyperbolic crochet coral reef is truly not just a beautiful sight to behold, but a perfect and delightful example of living mathematics.

And proof that Mother Nature always has far more up her sleeve than we understand or expect.

The coral reef is an ongoing art project created by Australian twins Margaret and Christine Wertheim of the Institute for Figuring in Los Angeles.

The woolly creation, begun and curated by the two and now added to by people all around the world (there’s a whole Irish-made reef section in the exhibit), is a response to the threat of global warming to the stunning Great Barrier Reef in Australia, an homage to the beauty of science and mathematics, and a tribute to the crafting skills of about 3,000 women (and two or three men).

Margaret Wertheim gave a fascinating talk at the Science Gallery about the genesis of the reef and its underlying mathematics (in which she noted with amusement that although there is only one exhibit in the whole thing that lights up – sea creatures crocheted from electrified “yarn” used to illuminate the inside of army tanks – it is the one that always attracts men instantly).

You can also look up a talk she gave on the crochet reef on Ted.com (search by her name).

The reef remains on view at the Science Gallery until June 11th. An extra attraction is the “Mathematics Chapel” upstairs, where two original, exceedingly beautiful Escher circular woodcuts that demonstrate his use of hyperbolic space are displayed. The woodcuts are truly a must see.

As Wertheim has written of hyperbolic geometry: “It is one thing, however, to know that something is logically possible; it is quite another to understand it.”

The crochet coral reef will help everyone, children and adults, to do just that, while gaining all the pleasures of being in the presence of a very beautiful work of art.