## Introduction

As a scientist, I am quite surprised by the mathematics of facial beauty. As a plastic surgeon, I am delighted. My research has shown that the fundamental difference between an unattractive, average, attractive, and remarkably beautiful face lies within a few millimeters and a few angular degrees. With this in mind, I have developed the formula of "AH," a simple mathematical formula that allows for the first time a mathematical definition of facial beauty based on seven facial angles (A) and seven facial highlights (H).

Research in the study of a normal or average face has opened up a new world in the ability to analyze, classify, and identify faces. Normal or average faces have been studied extensively; a beautiful face has yet to be successfully analyzed mathematically and defined. Agreeably or disagreeably, the attractiveness of the male and female figure is often described in measured numbers. Why not the face? As we live in a measured world of mathematics and computers, a mathematical definition of facial beauty's time has come.

It is important to reemphasize that for well over a century, the attractiveness of a woman's figure (chest, waist, and hips) has been based on numerical measurements (e.g., 36-24-35). The hip-waist ratio has also been studied as a symbol of fertility and fecundity, important in mate selection. Female facial beauty is also numerically related to the volumetric curves and proportioned shapes of several locations on the face. Male handsomeness (to be presented in a future publication) is related to the positional angularity of the face and its volumetric proportions.

The human face can be thought of itself as an "oil painting," a true work of art. Like a beautiful portrait, a face is complimented by the skin (canvas), hair (frame), and teeth (matte). In my opinion, a beautiful face combines facial features that are (1) harmonious, (2) shapely, (3) balanced, (4) elevated, (5) symmetrical, (6) highlighted, and (7) in volumetric proportion and relationship.

1. 11.1. Seven youthful fat pads. a A 54-year-old patient, with extended supraplatysmal plane, endocoronal lift, and fibro-a tired, aging appearance. b Note the proper positioning of fatty grafting to seven the youthful facial fat pads (or "eggs") the youthful egg-shaped highlights. c One-year postoperative
2. 11.1. Seven youthful fat pads. a A 54-year-old patient, with extended supraplatysmal plane, endocoronal lift, and fibro-a tired, aging appearance. b Note the proper positioning of fatty grafting to seven the youthful facial fat pads (or "eggs") the youthful egg-shaped highlights. c One-year postoperative

Many believe that the true purpose of beauty has escaped those other than philosophers and artists. This is not true considering that beauty has a definite purpose in nature. Insect pollinators are attracted to the most beautiful or fragrant flowers, which ultimately ensures genetic survival for both parties in a symbiotic relationship. In the animal kingdom, beauty can be correlated with health, strength, and youthfulness. These qualities ensure genetic survival through preferential mate selection.

Unlike poets and artists of the past and present, my goal is to provide a mathematical definition of a beautiful face, a very important step in understanding facial beauty. Until now, a numerical classification has not been successful in assessing facial beauty. Defining a face as beautiful in an artistic context is quite simple; the difficulty lies in being able to provide a precise, objective, and mathematical definition without being surpassed by a subjective interpretation.

Whatever its reason, the quest for beauty is here to stay. A beautiful face will never be denied or ignored. Facial beauty offers its own rewards to be shared, enjoyed, studied, and remembered.