Understanding the nature and meaning of beauty is one of the key themes in the philosophical discipline known as aesthetics.
A common theory says that beauty is the appearance of things and people that are good. This has many supporting examples. Most of us judge healthy, symmetric, fertile or virile human beings as beautiful. Symmetry may be important because it is evidence that the person grew up in a healthy way, from without visible genetic defects. One traditional, subtle feature that is considered an indication of beautiful women in all cultures is a waist-to-hip ratio of about 75%. The waist-to-hip ratio (WHR) theory was discovered by psychologist Dr. Devendra Singh of the University of Texas at Austin. Physiologists have shown that this ratio accurately indicates most womens' fertility. Traditionally, in premodern ages when food was more scarce, fat people were judged more attractive than slender.
"Beauty as goodness" still has whole classes of significant counterexamples with no agreed solution. These include such things as a glacier, or a ruggedly dry desert mountain range. Many people find beauty in hostile nature, but this seems bad, or at least unrelated to any sense of goodness. Another type of counterexample are comic or sarcastic works of art, which can be good, but are rarely beautiful.
It is well known that people's skills develop and change their sense of beauty. Carpenters may view an out-of-true building as ugly, and many master carpenters can see out-of-true angles as small as half a degree. Many musicians can likewise hear as dissonant a tone that's high or low by as little as two percent of the distance to the next note. Most people have similar aesthetics about the work or hobbies they've mastered.
The earliest theory of beauty can be found in the works of early Greek philosophers from the presocratic period, like Pythagoras. The extant writings attributed to Pythagoras reveal that the Pythagorean school, if not Pythagoras himself, saw a strong connection between mathematics and beauty. In particular, they noted that objects proportioned according to the golden ratio seemed more attractive. Some modern research seems to confirm this, in that people whose facial features are symmetric and proportioned according the golden ratio are consistently ranked as more attractive than those whose faces are not.
Even mathematical formulae can be considered beautiful. is commonly considered one of the most beautiful theorems in mathematics. (see (Euler's identity)
Another connection between mathematics and beauty which played a prominent role in Pythagoras's philosophy was the way in which musical tones can be arranged in mathematical sequences, which repeat at regular intervals called octaves.
Beauty contests claim to be able to judge beauty. The millihelen is sometimes jokingly defined as the scientific unit of human beauty. This derives from the legend of Helen of Troy as presented in Christopher Marlowe's Doctor Faustus, in which her beauty was said to have launched a thousand ships. The millihelen is therefore the degree of beauty that can launch one ship.
A survey conducted by London Guildhall University of 11,000 people showed that (subjectively) good-looking people earn more. Less attractive people earned, on average, 13% less than more attractive people. While the penalty for overweight was around 5%.
More needs to be said about this, but it contains most of the useful information from the notes that were here before.