When Greek writings were rediscovered during the Renaissance, tracts defining beauty and attempting to snare it in the meshes of mathematics began to appear.One writer declared that for absolute beauty the face should be one-eighth the length of the body;another that the corners of the lips must decline, forming an obtuse angle.

In the 19th century, one writer gave geometry a racist twist with his "facial angles", measuring the angle between the tip of the chin and the nose. A profile of 100° represented divinity. The European rated a noble 90°, while the 70° scored by an African was considered to be "scarcely human".

But the most influential idea was the so-called golden section, a pleasing ratio of just over 1.6 to one which was used by the Ancient Greeks. Its appeal is as strong today.

Dr Mark Lowey, of University College Hospital, has made detailed measurements of fashion models' faces. He claims the reason we classify certain people as beautiful is because they come closer to the golden section proportions than the rest of the population.

"In the Hitchhiker's Guide to the Galaxy, the answer to everything was 42, but actually it is 1.618," he says. On beautiful hands the relationship between the between shorter and longer joints is 1.618 , just as the distance from the hairline to the tip of the nose on a beautiful face is 1.618 the distance between the nose and the chin.

"Things that follow this proportion are seen as pleasing, but we have no idea why," admits Dr Lowey. Some faces can be quite a way from it and still be considered beautiful. Princess Diana, for instance, has a face with a nose that is too big and is not balanced by the mouth.

Why hasn't evolution produced a race of small-nosed, pouty-lipped clones?

Evolution hasn't produced a race of small-nosed, pouty-lipped clones. What about Glen Close or Susan Sarandon, with their strong, even slightly hooked noses and definite chins? Another beauty researcher, Dr Michael Cunningham of Elmhurst College, Illinois, has been looking at the effect of individual features in a beautiful face and has discovered that some features may or may not be desirable, depending on what the judge is looking for.

When male interviewers are selecting a woman for a job, for instance, arched expressive eyebrows and dilated pupils are seen as desirable, but they were less important on a potential date.On the other hand, men contemplating partners with a view to settling down and starting a family, found a wide smile more important than expressive eyes and eyebrows. Is the secret of Julia Robert's appeal that she would be good with children?

Cunningham also found that attractive women with mature features, such as small eyes and a large nose, received more respect ."It could be that societies where women have more power and autonomy idealise women with more mature features," he says, "while those which value submissive females may prefer baby faces". But is beauty really just a matter of sending out a message saying: ''I am ready to conceive?'' So far all the studies are limited to photos that capture some types of beauty.Yet we all know people who are attractive in the flesh, but lousy in photos.

Why? Is it to do with how fertile they look? No one knows. But the search for a better definition of beauty will continue, driven by the billion-pound beauty industry's desire to find new ways of closing the gap between the actual and the ideal.

In politics and business, personal looks are increasingly important;one estimate says that American professional women now spend up to one-third of their income on appearance.Maybe the 19th-century writer Stendhal got it right when he said: "Beauty is no more than the promise of happiness." Jerome Burne .

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