Is There a Golden Ratio?

Dentists and orthodontists have used an instrument called the Golden Divider to identify golden relationships in the human face and teeth. The instrument expands, pantograph style, maintaining a Golden Ratio between its two interlocking calipers. Dr. Robert Ricketts, in a JCO article on the Golden Divider¹, demonstrated some of the golden relationships in the face, teeth, and skull that may contribute to the beauty of the human face. In the tele­vision series, a more sophisticated mathematical and geo­metric representation of the human face was shown, based on the work of Dr. Stephen R. Marquardt, Chief of Research in Facial Imaging at UCLA.

The Golden Ratio is usually expressed as 1:1.618, which is actually an abbreviation of what is called an irra­tional or infinite number--1.6180339887498948482 . . . Since this is a mathematical construct, one won­ders if 1:1.6 would not make an adequate mea­surement, especially considering the relative crudeness of the Golden Divider. One also won­ders why we need to identify a Golden Face at all, although there is some basis for the position that the more golden relationships a face has, the more attractive it is. The Golden Ratio could be taken into consideration in plastic surgery or in making adjustments in the size and shape of teeth, but concepts of facial beauty have varied among races and over the course of time. In the 1920s, the "movie star" face had a small, thin-­lipped mouth. The preferred face among leading models today appears to have a short upper lip and a pouty mouth with protruding lips and teeth. An orthodontist would probably be unhappy with such a result.

Some of the golden relationships observed in nature may be more compelling than subjec­tive conclusions about what constitutes harmony in design. There is not, for example, universal agreement that symmetry creates the most pleas­ing design, and in some cases mere coincidence may apply to an apparent relationship. This may be true of efforts to relate the dimensions of the Egyptian pyramids to the Golden Ratio. Great as that civilization was, it dealt in cubits, not mea­surements carried to three decimal places. That does not rule out the notion that the builders of the pyramids independently chose a design whose harmony was close to the Golden Ratio. Other supposed relationships to the Golden Ratio are even more suspect. A website makes a case for the appearance of the Golden Ratio in the wagers made at thoroughbred and harness race tracks for win and place. This led to the conclu­sion: "We suggest that race wagering markets self-organize towards the Golden Section to opti­mize resource allocation of money." Don't bet on it.

Although many measurements in living things that approach the Golden Ratio seem to make agreeable combinations, it would be exceeding the extent of our present knowledge to ascribe this to a natural plan, or to demand rela­tionships as precise as 1:1.618. Still, with so many fine minds having believed in the Ratio over the past 2,500 years, its relevance cannot be ruled out. As the genetic code becomes better understood, one unexpected finding may be that there is a genetic basis for the Golden Ratio in biology and botany. Wouldn't it be a revelation if beauty were not actually in the eye of the behold­er, but in an inherited Golden Ratio?