The "Golden Ratio." Mathematically Explains Beauty.

"Truth is Beauty; Beauty Truth..."

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Classic face of Mona meets Golden Ratio parameters.In antinquity, the problem was interestingBones of the hand fit the explanationMake my Day!Unforgettable GraceThe Great Mosque of Kairouan is a classic example of the Ratio's principlesBook design never departs far from Ratio's guiding lightCliff, everyone's favorite Peter Pan.  His face gaily sticks to the idea,  Cliff's perfect bone structure has enabled him to defy ageingClassic Bone Structure helps Taylor survive hard life with good looks even today
Classic face of Mona meets Golden Ratio parameters.
Classic face of Mona meets Golden Ratio parameters.
In antinquity, the problem was interesting
In antinquity, the problem was interesting
Bones of the hand fit the explanation
Bones of the hand fit the explanation
Make my Day!
Make my Day!
Unforgettable Grace
Unforgettable Grace
The Great Mosque of Kairouan is a classic example of the Ratio's principles
The Great Mosque of Kairouan is a classic example of the Ratio's principles
Book design never departs far from Ratio's guiding light
Book design never departs far from Ratio's guiding light
Cliff, everyone's favorite Peter Pan.  His face gaily sticks to the idea,  Cliff's perfect bone structure has enabled him to defy ageing
Cliff, everyone's favorite Peter Pan. His face gaily sticks to the idea, Cliff's perfect bone structure has enabled him to defy ageing
Classic Bone Structure helps Taylor survive hard life with good looks even today
Classic Bone Structure helps Taylor survive hard life with good looks even today

Kids - Don't Forget Your Sums!

Good Looks Subjective? Bah! It's All 2 Plus 2.

Kids about to sit their exams might seriously consider there are few fields of life or human endeavour that excludes the application of mathematics. Not only do we use math every day going about our ordinary lives, man’s greatest triumphs like conquering the globe and landing on the moon could never have been accomplished without starting with 1 plus 1, (equals 2, should any of today’s youngsters be counting on their fingers!). More prosaically, today’s OAP’s would be lost without calculating to the last red cent what they can spend today in Safeway or Tesco; state pensioners in Britain will be dying of malnutrition soon if some administration doesn’t allot them a living wage instead of allowing sociopathic bankers and the thieving establishment to steal it all.

Long has groaned-on the argument of whether beauty is determined in the eye of the observer - is subjective - or whether there are classical, objective parameters which determine attractiveness. There is no doubt there are many factors when assessing what makes a person of the opposite - or indeed the same - sex appealing to us while another leaves us disinterested or even repelled. But sticking to the purely physical - as in a lovely painting - mathematicians tell us there is a formula - a ratio - that apparently applies to all objects in nature, outside and in, such as a beautiful man or woman, a flower, butterfly or tree, that shows certain measurements common to all, most of us find compelling. And it can be taken further to explain all we find lovely in architecture and other man-made structures as well. Among many others, Michelangelo is said to have been guided by this magical calculation - the Golden Ratio - in his magisterial works “David,” and his design of the temples.

The Golden Ratio is based on the long understood Fibonacci Numbers ratio. Those who passed their “A” levels may remember that this ratio depends on each number in a sequence consisting of the sum of the two previous numbers, hence: 1,1,2,3,5,8,13,21,34,55,89, and so on. I won’t list the equivalent fractions which lead up to the golden ratio as it might put you off or become boring, suffice it to show that it is this number - phi=1.618033 recurring, and the fractions that lead to its conclusion, that act as a template to explain beauty, and to create it in a myriad ways.

Perhaps an easy way to explain the principles of the golden ratio, or golden section as it is sometimes called, is to merely say it describes the common, most practical and pleasing, ratio of the smaller quantities of anything to the larger, or whole. This phenomenon, and the often complex formulaic explanations that describe, it has been the subject of debate for at least 2,500 years and is common knowledge to mathematicians, architects, painters and rocket scientists who have consciously or unconsciously been guided by its principles in much of their work.

Architects tell us they see the Ratio in the pleasing dimensions of the Acropolis and the Parthenon as well as the Great Mosque of Kairouan and many other religious buildings…in fact, the ratio is so common here it is sometimes referred to as the Divine Ratio.

The Ratio can also explain classical beauty, according to its adherents: Among male film stars, Clint Eastwood has often been said as possessing the face with the best and most regular measurements and those which fit into the Ratio’s parameters perfectly. Elizabeth Taylor and Grace Kelly have often been quoted as possessing two of the most desirable faces of all time. It is often argues that this is subjective, but if that were true, Ma and Pa Kettle would have just as many raving over their winsomeness. There is no doubt that there are faces and bodies which appeal to the majority - many more than their contemporaries - all can be explained by this ratio of the smaller parts to the whole (see pic).

Evolutionists tell us attraction for a man by a woman is based on his physical strength and size; confidence, and, today, in his ability to perform well socially and in the acquisition department - because this type is more likely to be a good defender and provider of her children. (The once premium attractions of tooth and fang have been replaced in the modern male by the appeal of the ruthless business tyro, whereas the desirable qualities of the female have remained mainly the same). For a man, a good breeder is the number one choice: a healthy body, wide hips for child bearing, good breasts for feeding kids, and a healthy, vibrant expression. We translate all this into meaning beauty, while the Golden Ratio describes the ideal mathematically, showing that the most desired partners are those with the correct distribution of smaller parts in ratio to the whole.

Anatomists say the whole complexity of bones, nerves, the circulation system and body shape agrees with the Ratio. Biologists point out that so do the blueprints for veins, leaves and the dimensions of plants. There’s a reason, apparently, why we gaze at the mighty oak, the spreading chestnut (and chest!); the seductive willow and the beauty of rose and orchid. As well as the color and scent, it’s the aesthetic proportions that appeal to us. No wonder so much money is spent on plastic surgery!

 

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Comments 22 comments

msorensson profile image

msorensson 6 years ago

Great hub. I enjoyed it. Thank you.


diogenes profile image

diogenes 6 years ago from UK and Mexico Author

Kind of you to say, Bob


diogenes profile image

diogenes 6 years ago from UK and Mexico Author

Kind of you to say, Bob


Hello, hello, profile image

Hello, hello, 6 years ago from London, UK

Unusual subject but intriging and something to think about it Thank you.


diogenes profile image

diogenes 6 years ago from UK and Mexico Author

Hi, HH, nice to hear from you as ever...Bob


HellKatz profile image

HellKatz 6 years ago

Interesting read, Diogenes.

>>>No wonder so much money is spent on plastic surgery!


HellKatz profile image

HellKatz 6 years ago

.....Plastic surgery, is for the shallow thinking.


billyaustindillon profile image

billyaustindillon 6 years ago

It is amazing how the Golden Ratio replicates through nature - Nautilus shares and pine cones are just two that are amazing. The work of Fibonacci in this area is of course telling and Gann's Natures law. Great hub - a big rated up!


diogenes profile image

diogenes 6 years ago from UK and Mexico Author

Cheers guys,..Bob


Nell Rose profile image

Nell Rose 6 years ago from England

Hi, Bob, this has always fascinated me. Ever since I read that the ratio is in plants and snails shells etc. It certainly makes you think. thanks nell

p.s. forgot to say, that did you know they know believe by measuring the Mona Lisa's face, and putting it over a picture of Leonardo, that they are one and the same?? Mona's a man! clever guy!! lol


Amanda Severn profile image

Amanda Severn 6 years ago from UK

Hi Bob, as always, an entertaining read! I don't think I've ever been overly conscious of Fibonacci when painting, but there is a general convention amongst most of the artists I know, whereby the picture is divided in to thirds, so that the principle subject will fall at a point either a third of the way across, or a third of the way down. It's only a very rough rule of thumb, but it invariably produces a more pleasing picture. (Hey, maybe that is Fibonacci......!)


soumyasrajan 6 years ago from Mumbai India and often in USA

very nice article on Golden ratio diogenes! Enjoyed it!

Amanda Severn what you do is indeed golden ratio. 1/3 division is a rough estimate of golden ratio 1/1.1618033..

I learnt first about golden ratio in a Mathematics class and while reading a book on measure of beauty by a mathematician.

Later I took a short course one week course in art appreciation in a fine art college in Mumbai where they talked about it. It was very pleasing. I did understand that our eyebrows bend at this ratio and our lips divide our chin in this ratio etc. Then I learnt about this phenomena in a biology class also.

Finally once a Jain follower (an ancient religion in India which preaches nonviolence and nature preservation ) once told me that in their religion they fast on some fixed dates of each month because they want to be fasting on the day which divides their life into golden ratio. That may occur on these dates. This was preached to them 1000's of years back by their first monks. It is indeed pleasant to see that nature, human behavior is so diverse at the same time it has all these common themes appearing every where.


soumyasrajan 6 years ago from Mumbai India and often in USA

oh! I put an extra 1. That should have been 1/6.18033...


soumyasrajan 6 years ago from Mumbai India and often in USA

Oh! error again. It is 1/1.618033..


diogenes profile image

diogenes 6 years ago from UK and Mexico Author

Hi Brain-dead Billy Bob: you might think that!...Bob


Royo1234 profile image

Royo1234 5 years ago from Galway, Ireland.

Very well written. I enjoyed this.


diogenes profile image

diogenes 5 years ago from UK and Mexico Author

Thanks for visit Royo...Bob


eugeneteddy20 profile image

eugeneteddy20 5 years ago from Miri,Sarawak,Malaysia

nice hub.i like the title a lot.keep it up


diogenese 5 years ago

Many thanks...Bob


Sophia Angelique 4 years ago

I have always believed that beauty is a mathematically concept. Those who examine these things point out that a people are considered beautiful is their faces have equal proportions on both sides. Most don't as left side and right side tend to be different. I also think that space arrangement has a lot to do with balance, rhythm, etc. (well, all the artistic rules) that are, essentially, mathematical. :)


diogenes 4 years ago

Yip..a formula for everything...Bob


mike 4 years ago

please include a link in your hub to this article

http://wwww.science-and-mathematics.blogspot.com/2...

its a good article

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