viernes, 4 de mayo de 2012

RV: Beauty by The Numbers

Fuente: REALscience
Expuesto el: lunes, 30 de abril de 2012 20:59
Autor: Michael Bradbury
Asunto: Beauty by The Numbers


Beauty may be in the eye of the beholder but what the beholder beholds is just math. We don’t see math in a pretty face but it is math that makes it appear beautiful.

Golden Spiral Made from Whirling Triangles, Based on Fibonacci Sequence

Golden Spiral Made from Whirling Triangles, Based on Fibonacci Sequence

Scientists have found the Golden Ratio throughout nature and the man-made world. It appears in the spirals of seashells and the great pyramids of Giza. It can be found in the Parthenon in Athens and all over your own body. Expressed as a number the Golden Ratio is 1.618.

It starts with the Fibonacci Numbers where every number (after the second) is the sum of the two preceding numbers. For example 1, 1, 2, 3, 5, 8, 13, 21…

The Golden Ratio is derived by dividing the Fibonacci Numbers. For example 1/1=1, 2/1=2, 3/2=1.5, 5/3=1.666…, 8/5=1.6, 13/8=1.625, 21/13=1.61538…, 34/21=1.61905…, 55/34=1.61764…, 89/55=1.61861…

Like its neighbor irrational number Pi, the Golden Ratio or Phi has no equivalent fraction and the numbers after its decimal point go on forever. Though it is irrational it is very important in nature and demonstrates a high degree of efficiency. The Golden Ratio is found in the patterns we see in sunflowers, pine cones and even pineapples. This is largely because one of the best ways to efficiently pack things tightly together is using the Fibonacci sequence. Just look at the petals of flowers and leaves on many plants. They are designed to maximize sunlight and water transport. And they all utilize the Golden Ratio.

Population can be measured with this ratio in mind and we can even tell how attractive someone is by how they fit the Golden Ratio. A recent contest in England proved that.

Florence Colgate, Most Beautiful Face of Britain

Florence Colgate, Most Beautiful Face of Britain

Over 8,000 women submitted pictures in Great Britain in hopes of being rated the most beautiful according to the Golden Ratio. Natural beauty is based on distances between prominent facial features and symmetry. It is the optimum ratio between the mouth, eyes, chin, and forehead.

18-year-old Florence Colgate took home the prize from Lorraine Cosmetics for her near-perfect symmetry and mathematically flawless face. The young seaside fish and chip fry girl who is studying for exams to study business management in college has been dubbed Britain’s most beautiful face and there is science to back up that claim.

Scientists at the St. Andrews University perception lab determined that Colgate has a perfectly proportioned face. The distance between the eyes is 44 percent of the whole width of her face. The ideal golden ratio girl would have eye distance of 46 percent. Experts also believe the relative distance between eyes and mouth should be just over a third of the measurement from hairline to chin. Colgate’s ratio is 32.8 per cent.

PhD student Carmen Lefèvre says Colgate has all the classic signs of beauty. She says, “She has large eyes, high cheekbones, full lips and a fair complexion. Symmetry appears to be a very important cue to attractiveness.”

While Colgate is the current mathematical beauty scientists have conducted several studies on attractiveness over the years and the most aesthetically pleasing people are closely aligned with the Golden Ratio. 1.618 gets repeated throughout nature and is the ideal for many body proportions.

For example, the ideal distance from the pupil of a person’s eye to the center of the chin is 1.618 times the distance from the pupil to the end of the nose. The ideal length of a face is also 1.618 times its width and 1.618 times the distance between the eyes and the person’s mouth. In other words, wherever you think classical beauty, you’re probably just responding to the beautiful symmetry and repeating mathematical perfection.

RF Mask of Facial Beauty, Designed by Stephen Marquardt, Female (L), Male (R)

RF Mask of Facial Beauty, Designed by Stephen Marquardt, Female (L), Male (R)

It is the ratio between the length of your hand and the length of your lower arm (between your elbow and your wrist). It’s also the ratio of your total height to the distance between your head and your fingertips. It can even appear deep inside your cells in the structure of DNA. The DNA molecule measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral. And a cross-section of a DNA double helix forms a decagon, which in essence is two pentagons rotated 36 degrees so each spiral of DNA double helix traces out a pentagon. And the ratio of the diagonal of a pentagon to its side is 1.618:1.

In 2007 scientists at Cambridge University found that the closer a woman’s hips to waist ratio is to 0.7 the sexier her walk is. So, a woman with 25 inch waist and 36 inch hips, has all she needs for a perfect walk. For men, a ratio of 0.9 shows a strong correlation with general health and fertility.

Jessica Alba, Modern Day Beauty, According to the Math

Jessica Alba, Modern Day Beauty, According to the Math

According to the mathematicians actress Jessica Alba’s sashay beat the competition, including Kate Moss, Angelina Jolie and even Marilyn Monroe, whose sexy strut made her famous. While the math team found Monroe was a fraction off the target ratio with 0.69, the Cambridge team said that Alba had the perfect proportions.

The report also reveals that singer Shania Twain and actresses Liz Hurley are ranked among perfectly formed celebrities.

Now there’s an app to see where you fall on the scale of stunning. The Ugly Meter uses a virtual structure to measure your eyes, nose, mouth and the size and shape of your face. It then comes up with a rating based on the measurements and spits out a score based on a 100 point scale. Ugly Meter scans a user’s photo looking for contours, symmetry and proportions.

Joe Overline, Ugly Meter App Maker

Joe Overline, Ugly Meter App Maker

Jo Overline made the app and admits that his ugly mug is just that. According to his own invention, he scores a measly 32. But he’s laughing all the way to the bank. The app he built at his company Dapper Gentlemen just knocked Angry Birds of its perch as the top-selling app in the iTunes store.

Arizona-based Overline started the $.99 app as a joke. But the $4.99 Pro version is much more scientifically robust, including using the Golden Ratio for facial symmetry.

He says Brad Pitt scores a 91 out of 100 on the Ugly Meter while a photo of Angelina Jolie gets an 86. The app suggests that her eyes are a bit too close together although the perfect size for her head.

While holding a smartphone up to a photo removes a lot of the scientific validity that went into building the app, it shows that mathematical proportion and symmetry underlie what we commonly view as beautiful.


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