Are you the sort who gets your isosceles triangles in a twist, who has problems with polygons and trouble with trig? Or are you a more mathematical type? Do you start to feel edgy around anything arty and long for stern logic instead of aesthetic waffle?

Put aside your prejudices. Beyond Measure, the latest show to be staged at Kettle's Yard gallery in Cambridge, looks at the ways in which geometry has been used by everyone from artists through designers and architects to surgeons, physicists and astronomers. It explores the many ways this particular branch of mathematics can bridge the divide between science and art.

Art and geometry share a long history that runs from Plato's Academy, with its daunting over-thelintel injunction “let no man destitute of geometry enter these doors”, through the perspective plans of the great Renaissance masters, to those modern day “teach yourself to draw” manuals that, for the sake of clarity, translate the body into assemblages of circles and cylinders.

And yet we tend to see science as a search for fundamental laws. By contrast, we assume that art is more about feelings. A fault line emerges. On the one side is the intellectual; on the other, the sensual. We pit empirical analysis against sensual perception, logical truths against emotional illusions. And the development of dauntingly specialist vocabularies only widens the divide. How can we communicate if we can't speak the same language? Simple words just won't do. That's why there are whiteboards in the lifts of the Cambridge mathematics department. They are there so that colleagues can chat happily in scribbled equations for a minute or two.

The time has come to discard our relatively modern - and yet firmly outmoded - prejudices and start constructing bridges. You think that engineering is plodding? Leonardo da Vinci was an engineer. You think art is too vague? Pioneering colour theories underpin the haziest Impressionist picture. Institutions such as the Wellcome Foundation, the Dana Institute and Arts Catalyst all encourage the creative crossfertilisation of thought.

Now this show measures out another piece of shared ground - quite literally when you consider the Greek derivation of geometry: geos meaning Earth and metros meaning measure. Science and art, it yet again emphasises, have much in common. Both are means of investigation. Both involve ideas, theories and hypotheses that are tested in places where mind and hand meet: in the laboratory of the scientist, the studio of the artist, the study of the writer.

So don't expect a smartly finished show - any more than you would expect an artist's studio to be tidy. This exhibition is the gallery equivalent of those whiteboards in the lift. It is about work in progress. Don't expect polished sculptures and gilt framed pictures. Expect grubby polystyrene models and pages ripped from notebooks. This exhibition is more about thought processes than highly finished pieces. It's just a pity that the gallery has not produced a better catalogue. This show (bar a few hands-on experiences: the avian flu virus that can be thrown like a beach ball or the grow-your-own snowflake) presents the sorts of ideas that could be explored in inspiring depth in the pages of a book.

Beyond Measure does more than use art to explain or illustrate science. It explores a more fundamental level of communication. There are works of simple translation: a piece of jazz music scored in geometric shapes, for instance, or mathematics transformed into textiles, furniture and architectural models. Quantum physics, it seems, can turn into a most striking chandelier. But the conversations between art and science are often less direct, more intuitive and more feeling.

Here are the original Nobel prize-winning virus models of the British-born chemist Aaron Klug. They are displayed near the notebook pages of Buckminster Fuller, with whom he had several informative conversations concerning the viability of the geodesic dome. But apart from the structural similarities between virus and Fifties pavilion, what is most striking is the Blue Peter-style construction. Klug makes his models from lavatory rolls and drawing pins. Or a mathematics professor explores her theories through crochet. Her little woolly frills look far more like those funny pink sponge things that people hang in their showers than advanced mathematical expositions. But, just like artists who start working only when they start fiddling or writers who get stuck until they start tapping keyboards, scientists are discovering not through abstracted mental concepts. They are finding things out with their fingertips

With the introduction of nonEuclidean geometry, whole new spaces of inquiry have opened up. Reality can no longer be packaged into strict rectilinear shapes. Mathematicians have learnt a whole new alphabet of curves: the fold and cusp and swallowtail and butterfly. These describe the irregular patterns that transform established geometric theory. As the engineer Allan McRobie describes it: “My buildings may have rectilinear lines but behind are curved energy surfaces which all the time I have to hold in my head.” These surfaces shimmer like the patterns of light that he lets play across the gallery walls. A pleasing beauty becomes a by-product of scientific discovery.

Art can evoke dimensions that science can't explain. David Nash's boulder, a simple unseasoned wood sphere slipped and rolled and pushed through the landscape, carried along by rivers and streams, bobbing out to sea to be washed back to land again by currents, speaks of the passing of time and the patterns of nature in a way that a scientific model can't quite encompass.

Sometimes the conversation between the two disciplines is demonstrably useful. The plastic surgeon Tariq Ahmed becomes the latest exponent of the figurative tradition. Just as the Ancient Greeks thought about geometry as they carved their marble ideals, he uses his meticulous mathematical knowledge as he sculpts living faces, carefully transposing little rhomboids and triangles of skin. A folding Moulton bicycle looks like a piece of maths homework that you can pedal about on.

But what about that which lies beyond the functional? What about the metaphysical? Ever since the Ancient Egyptians first tried to plot their Nile flood plains in accordance with the stars and the position of sacred temples, geometry has always had a spiritual dimension. Perfect shapes and patterns evoke something transcendent. In this show, a Benedictine monk reaches beyond measure as he tries to make models of the fourth dimension. I don't want to put words in his mouth. He doesn't say he is sculpting Heaven. If he is, then it looks like a Fisher Price toy. But in a show that is constantly making us wonder, testing our intellect, pushing our conceptions, one can't help thinking why it should stop there. There is a whole new dimension of geometry that remains unexplored.

Beyond Measure is at Kettle's Yard, Castle Street, Camridge (01223 352124; www.kettlesyard.com), until June 1

BLINDED BY SCIENCE: FROM THE BANKS OF THE NILE TO A VOLCANO

Ancient Egyptians

Encompassed the “golden ratio” into the pyramids, establishing the patterns of proportion.

Leonardo da Vinci

Believed that moral and ethical meanings could emerge only through accurate scientific descriptions.

Johannes Vermeer

The 17th-century Dutch artist connected science and art in such works as The Astronomer. The details of worldly craftsmanship are explored in the context of the wider universe.

Claude Monet

Complex colour theories underlaid the Impressionist movement. The pictures might look blurred, but the artists explored the range of the visible spectrum precisely.

James Turrell

The contemporary artist who is turning a volcanic crater into an artwork while adhering to sound engineering principles.

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