Ever think a number could be beautiful? From the bad luck of 13 to the holiness of 3, people have long ascribed mystical and abstract properties to numbers. One number in particular has been associated with beauty for nearly 2,000 years, and it's not a number you can count to: the so-called "golden section" is an irrational number approximately equal to 0.618. Dr. Stephen Marquardt, a former plastic surgeon, has used the golden section and some of its relatives to make a mask that he claims is the most beautiful shape a human face can have.
This mysterious number has a horde of related quantities and shapes, many of which have long-standing associations with beauty. Among them is the "golden ratio," which is the ratio of 1.618-to-1. This ratio can be used to build so-called golden shapes; for instance, a golden rectangle is one whose ratio of width to height is the golden ratio. These rectangles have been considered beautiful by many artists, and they have made appearances in some of history's most renowned works of art. Using the golden ratio one can also make golden triangles, pentagons and decagons. Dr. Marquardt has tapped this golden tradition in making his mask — he's used a golden ratio-based arrangement of 40 golden decagons of six different sizes, carefully aligned with the face's various features.
According to Dr. Marquardt, beauty is a mechanism to ensure humans recognize and are attracted to other humans. "Other animals recognize members of their own species and have a tremendous reaction when they do," he says, noting dogs' common reaction to other dogs. He adds that humans are highly visual creatures, so we use sight as our primary means of recognition. The most beautiful faces, he claims, are the ones that are the most easily recognizable as human. "Beauty is really just humanness," he says.
Dr. Marquardt theorizes that we discern whether a face is obviously human by unconsciously comparing it to an ideal face that lurks in the unreachable recesses of the psyche. Since we have no direct access to this ideal "most human" face, we can't say precisely what it is; however, Dr. Marquardt claims he has captured the ideal face in his beauty mask. He says, "The mask radiates, it advertises and screams: 'human, human, human.' "
Whatever the reasons, the mask fits the faces of several famous beauties fairly well (see Timeless Beauty), and Dr. Marquardt has conducted a study that indicates a broad preference among many cultural groups for faces that closely correspond to his mask.
The key to the design of the mask, he says, is the golden section, that enigmatic number that has long stood for beauty. Knowledge of the golden section, ratio and rectangle goes back to the Greeks, who based their most famous work of art on them: the Parthenon is full of golden rectangles. The Greek followers of the mathematician and mystic Pythagoras even thought of the golden ratio as divine.
Later, Leonardo da Vinci painted Mona Lisa's face to fit perfectly into a golden rectangle, and structured the rest of the painting around similar rectangles. Mozart divided a striking number of his sonatas into two parts whose lengths reflect the golden ratio, though there is much debate about whether he was conscious of this. In more modern times, Hungarian composer Bela Bartok and French architect Le Corbusier purposefully incorporated the golden ratio into their work.
Even today, the golden ratio is in human-made objects all around us. Look at almost any Christian cross; the ratio of the vertical part to the horizontal is the golden ratio. To find a golden rectangle, you need to look no further than the credit cards in your wallet.
Despite these numerous appearances in works of art throughout the ages, there is an ongoing debate among psychologists about whether people really do perceive the golden shapes, particularly the golden rectangle, as more beautiful than other shapes. In a 1995 article in the journal Perception, professor Christopher Green, of York University in Toronto, discusses several experiments over the years that have shown no measurable preference for the golden rectangle, but notes that several others have provided evidence suggesting such a preference exists.
Regardless of the science, the golden ratio retains a mystique, partly because excellent approximations of it turn up in many unexpected places in nature. The spiral inside a nautilus shell is remarkably close to the golden section, and the ratio of the lengths of the thorax and abdomen in most bees is nearly the golden ratio. Even a cross section of the most common form of human DNA fits nicely into a golden decagon. The golden ratio and its relatives also appear in many unexpected contexts in mathematics, and they continue to spark interest in the mathematical community.
-------------------- People are like pieces of a puzzle. We all fit together, but not all of us connect. Berichten: 6985 | Plaats: Zeist | Geregistreerd: Jul 2002
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