Whether in art or nature, certain geometric proportions appeal naturally to the eye. Others seem inharmonious. It is a matter of scientific fact. The ancient Greeks and Romans, and the masters of the Renaissance, knew about the rules of correct proportion and applied them in their art and architecture.
Our age has distinguished itself by forgetting them. But when all the impressionisms, expressionisms and sensationalisms have run their course, visual art that obeys the timeless laws of sacred geometry will maintain its magical appeal.
The 33-year-old sculptor Charles Hadcock is almost unique in his observance of the rules of correct proportion.
His reward came last year when Passacaglia, his 20 tonne, 5 metre high abstract sculpture in cast iron, was permanently installed on Brighton beach.
Instead of inspiring derision from the customers of the nearby candyfloss and shellfish stalls, it left them wide-eyed and full of praise. Passers- by told Hadcock they loved it, but could not reason why. Hadcock's answer - "sacred geometry" - left them little wiser.
Your chance to install some of his sacred geometry in your home comes next month, when he is holding a selling exhibition of his drawings and maquettes at Imperial College, London. The exhibition includes a bronze cast of the maquette for Passacaglia.
Hadcock, an RCA graduate, has worked the back off his copy of the Architectura of Vitruvius, the 1st century AD architect and engineer who was the Renaissance's chief reference on sacred geometry. His trained eye now spots Vitruvius's celebrated "golden ratio" - that is 1:1.618 - in the most unusual places, even in the shape of polystyrene boxes for frozen fish. By chance, he bumped into the designer of the boxes, who had never heard of the golden ratio and told him: "It's the strongest, most economical shape - and it looks good".
Hadcock's use of sacred geometry is not always so obvious. He sometimes applies the "golden ratio" to the shape of the space between forms, as well as to the forms themselves, or deviates slightly from it so that the sculpture seems to be striving to achieve geometric perfection.
Despite the mysticism that has surrounded it since the Renaissance, the golden ratio is mathematically very simple. Take a pencil, draw a line, and divide it unequally with a dot, such that the proportion of the smaller bit of line to the longer bit equals the proportion of the longer bit to the line as a whole. That is the golden ratio.
If you draw a "golden rectangle" - that is, one whose long and short sides are in this ratio to one another - you will find that its interior can be divided into a perfect square plus a rectangle of the same golden proportion. If you do this repeatedly - in theory, ad infinitum - you will soon recognise the spirals of the Nautilus shell and the sunflower head.
For the mathematically inclined, the ratio is actually 1: 1.6180339... an "irrational" number; that is, one that goes on for ever. Perhaps it is magic, after all. The more practical-minded prefer the rule-of-thumb interpretation, which is 8:13.
In Hadcock's Passacaglia, one arm is 1.618 the size of the smaller arm. There is tension between the two because, although at first glance they appear to be trying to complete a circle, they are too far apart and their curves are not circular but logarithmic - the pure accelerating curve of the Nautilus.
Exhibition prices: drawings from pounds 700, maquettes from pounds 1,500. The Passacaglia maquette is pounds 3,000.
`Charles Hadcock, Drawings and Maquettes', 3-23 Feb, Tues-Sun (11am- 6pm), at the Imperial College of Science, Technology and Medicine, The Gallery, Ground Floor, Sherfield Building, Exhibition Road, London SW7 (0171-594 8442)Reuse content