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Persistent symmetry;Reviews;Mathematics;Books

GEOMETRIC PATTERNS SERIES: Tiles and Brickwork. Churches and Cathedrals. Islamic Art and Architecture. Roman Mosaic. By Robert Field pound;2.95 each. From Tarquin Publications, Stradbroke, Diss, Norfolk IP21 5JP

Harvey McGavin traces decorative motifs which have endured for millennia.

Patterns are everywhere - made by the bricks of our buildings, the tiles on our roofs and the stones of our pavements. Often the form is determined by function - bricks are staggered to make walls stronger, or tiles overlap to keep roofs waterproof.

But for thousands of years, builders and bricklayers, architects and artisans have expressed themselves through their craft, and have left a lasting impression by adding some-thing distinctive to their designs.

This series takes a detailed look at the geometrical make-up of these everyday delineations. There are no specific references to the curriculum but maths teachers will find many real-life examples of geometry to enliven classroom study.

The four slim volumes contain dozens of illustrations of decorative construction techniques, from simple grids of over-lapping bricks and chequer-board mosaics to the dazzling symmetries in the Alhambra palace in Granada and the Great Mosque at Cordoba.

It was his first encounters with these ancient tableaux on a trip to southern Spain that prompted Robert Field, retired deputy head of a school near Aldershot, to start cataloguing these configurations. On a visit to Cordoba he found a magnificent mosaic in a museum courtyard. "Unfortunately photography was not allowed," he says. "As seems so often to be the case, no postcard or reproduction of that particular design, a feast of running peltae in black, white, red and yellow, was available." He made a sketch of it in his notebook and began a painstaking record of his long-held fascination with patterns.

At Mr Field's school, projects on the Romans were enlivened by visits to sites at Bignor in West Sussex and Fishbourne in Hampshire. But you don't need Roman remains on your doorstep to appreciate the wonderful complexity of their mosaics.

Students of geometry can find examples in the architecture of every town. Churches and mosques are an often overlooked source, while modern building styles and the vogue for mosaics have shown a revival in patterned work.

Robert Field's old school boasted a broad pallet of Victorian brickwork - English garden wall and stretcher bond - but, he says, "most places will have access to patterned brickwork or tiles of some sort". New pedestrian precincts in towns often use herringbone, for example. These patterns are being used far more than they were 10 or 20 years ago. Many buildings are clad in brick - these geometric patterns are coming back into their own.

Tiles and Brickwork includes a wealth of modern-day examples. London's Docklands has many manifestations of the bricklayer's art, and there are examples from the author's home town of Farnham, Surrey, a place noted for its extravagant Victorian exteriors.

The books intersperse photographs with graphic explanations of the designs and tips on how to reproduce them. "You learn about them as you are drawing them. It's not until you actually try to work them out and reproduce them that you become aware of how interesting they are."

In addition to the mathematical applications of these books - from shape identification and simple embroidery at primary level to studying circumferences, diameters and areas at secondary - this series has cross-curricular interest.

It's impossible to study the geometrical beauty of these designs without also considering history, geography, and art and design. Often they are the last remnants of ancient civilisations in Rome, Islamic Spain or Turkey, but their origins are even older, says Mr Field. Many patterns that occur in tiles and marble floors in Roman times go back a lot further to the Greeks and near Eastern cultures.

Closer to home, the same shapes and symbols can be found in the more florid styles of Victoriana - check out your local churches and town halls.

Robert Field has kept it simple, limiting his illustrations to those that can be reproduced on squared paper. But surprisingly complex designs can be produced by overlaying straightforward patterns. This series would make a handy source of reference for designers and mathematicians - it's a thorough compendium of geometry in the outside world.

This series provides a vivid illustration of the wide applications of geometry, and would make an ideal starting point for turning the distracted doodling of disaffected pupils into an involving hands-on project.

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