The Biological Connection and the Divine Proportion

The normal morphology of structures related to orthodontics, dentistry, and plastic surgery are founded in basic mathematical and geometric principles. As has been suggested before in other essays, the appreciation of beauty by the human mind leads to an attraction to proportions in harmony with the Golden Section, that is 1.618 and its reciprocal 0.618.

Biologic structure develops first in terms of function, as opposed to form, because the nervous system monitors the body with physical and chemical qualities necessary for proper function. This monitoring and feedback arrangement produces structures that are economical in function. Biologists and morphologists speak of this in terms of "laws" --- the "law of conservation of energy" interpreted to be maximum performance with minimum effort; and the "law of conservation of tissue" interpreted to be a minimum amount of material employed to perform the needed task. A third law is a combination of these two which provides efficiency, a requirement for individual survival. Integration of all the functioning parts of a living body relates to the basic cellular level, and tissues ultimately behave under certain mathematical and geometric laws of space.

The normal human face is possibly the most beautifully perfect structure in all of the animal kingdom. The subject of structure, harmony, balance, and proportion from mathematical and geometric aspects are associated with the biology of growth and form. To ascertain these aspects in the human face, particular measurements are taken.

For the frontal transverse analysis, the following lengths are compared: the lateral rim of the ala of the nose (the widest part) to the chilion, a point at the angle of the mouth ( where the mouth angles up or down); a point at the lateral canthus (the outermost corner) of the eyes; a point at the base of the nasal bridge (lies right between the eyes); and a point at the border of the temple at the level of the eyebrows. A progressive phi relationship exists, with the golden proportion having the four parts in series. Taking the width of the nose as 1.0, the width of the mouth is 1.618 or phi. The next progressive phi is the lateral width of the eyes at the lateral canthus as phi squared; phi cubed is the width of the head at the temporal soft tissue (on each side of the forehead). The reciprocal of phi is the interdycron width ( innermost corners) between the two eyes. Starting with the nose, the mouth is golden and, then the eyes are golden to the mouth, making the eyes phi squared to the nose; the head width at the temple is golden to the width of the eyes, making the head phi cubed to the nose.

The same type comparisons can be made with the heights in the face, i.e. forehead to eye, eye to menton ( chin), and menton to ala (bottom) of nose, ala to forehead. Analysis of facial depth is based on the nose tip to the base of the tragus ( opening ) of the ear. This leads to the location of the cheek prominence in the face. When the teeth are considered, a second series of divine proportions presents itself. Beginning with the widths of the lower incisors and working away from them, there is harmony in the dentation patterns which emulates the same golden series seen in the frontal face transverse patterns.

So, of what significance are these divine proportions?

1. The plastic surgeon has a starting point when massive or localized reconstruction is necessary and beauty and balance are desired.

2. The orthodontist can measure spatial needs in a patient's oral picture and calculate the correction necessary to achieve the best results.

And, 3. the makeup artist can successfully apply cosmetics to the face using the guidelines set out by the line from the stomion (center of the upper lip) to the end of the canthus of the eye.

In the final analysis, in the frontal view and facial depth a natural progression takes place in a beautiful face. The face will have rhythm. "Rhythm is produced by the dynamic action of proportion on a uniform recurrence." The beautiful human face has rhythm, both transversely and vertically or in width and height.

References for Essays

American Journal of Orthodontics, May, 1982

Huntley, H. E., The Divine Proportion

Barron's Math Wizardry for Kids

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