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Mystery of golden ratio explained
Duke University ^ | Dec 21, 2009 | Unknown

Posted on 12/21/2009 3:53:49 AM PST by decimon

DURHAM, N.C. -- The Egyptians supposedly used it to guide the construction the Pyramids. The architecture of ancient Athens is thought to have been based on it. Fictional Harvard symbologist Robert Langdon tried to unravel its mysteries in the novel The Da Vinci Code.

"It" is the golden ratio, a geometric proportion that has been theorized to be the most aesthetically pleasing to the eye and has been the root of countless mysteries over the centuries. Now, a Duke University engineer has found it to be a compelling springboard to unify vision, thought and movement under a single law of nature's design.

Also know the divine proportion, the golden ratio describes a rectangle with a length roughly one and a half times its width. Many artists and architects have fashioned their works around this proportion. For example, the Parthenon in Athens and Leonardo da Vinci's painting Mona Lisa are commonly cited examples of the ratio.

Adrian Bejan, professor of mechanical engineering at Duke's Pratt School of Engineering, thinks he knows why the golden ratio pops up everywhere: the eyes scan an image the fastest when it is shaped as a golden-ratio rectangle.

The natural design that connects vision and cognition is a theory that flowing systems -- from airways in the lungs to the formation of river deltas -- evolve in time so that they flow more and more easily. Bejan termed this the constructal law in 1996, and its latest application appears early online in the International Journal of Design & Nature and Ecodynamics.

"When you look atwhat so many people have been drawing and building, you see these proportions everywhere," Bejan said. "It is well known that the eyes take in information more efficiently when they scan side-to-side, as opposed to up and down."

Bejan argues that the world – whether it is a human looking at a painting or a gazelle on the open plain scanning the horizon – is basically oriented on the horizontal. For the gazelle, danger primarily comes from the sides or from behind, not from above or below, so their scope of vision evolved to go side-to-side. As vision developed, he argues, the animals got "smarter" by seeing better and moving faster and more safely.

"As animals developed organs for vision, they minimized the danger from ahead and the sides," Bejan said. "This has made the overall flow of animals on earth safer and more efficient. The flow of animal mass develops for itself flow channels that are efficient and conducive to survival – straighter, with fewer obstacles and predators."

For Bejan, vision and cognition evolved together and are one and the same design as locomotion.The increased efficiency of information flowing from the world through the eyes to the brain corresponds with the transmission of this information through the branching architecture of nerves and the brain.

"Cognition is the name of the constructal evolution of the brain's architecture, every minute and every moment," Bejan said. "This is the phenomenon of thinking, knowing, and then thinking again more efficiently. Getting smarter is the constructal law in action."

While the golden ratio provided a conceptual entryway into this view of nature's design, Bejan sees something even broader.

"It is the oneness of vision, cognition and locomotion as the design of the movement of all animals on earth," he said. "The phenomenon of the golden ratio contributes to this understanding the idea that pattern and diversity coexist as integral and necessary features of the evolutionary design of nature."

In numerous papers and books over past decade, Bejan has demonstrated that the constructal law (www.constructal.org) predicts a wide range of flow system designs seen in nature, from biology and geophysics to social dynamics and technology evolution.

###

Bejan's research is supported by the National Science Foundation.


TOPICS: Arts/Photography; History
KEYWORDS: godsgravesglyphs
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1 posted on 12/21/2009 3:53:50 AM PST by decimon
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To: decimon; SunkenCiv

Shaping up ping.


2 posted on 12/21/2009 3:54:22 AM PST by decimon
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Comment #3 Removed by Moderator

To: shibumi

“You gotta get a load of this” ping.


4 posted on 12/21/2009 4:00:00 AM PST by Salamander (I'm sure I need some rest but sleepin' don't come very easy in a straight white vest.....)
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To: decimon

Thanks for the early morning exercise in thinking. It seems a long time since the non-political side of my brain got a workout.


5 posted on 12/21/2009 4:00:34 AM PST by Marylander (Obama is a pill ... and a pain.)
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To: Marylander

http://goldennumber.net/index.htm


6 posted on 12/21/2009 4:04:30 AM PST by Salamander (I'm sure I need some rest but sleepin' don't come very easy in a straight white vest.....)
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To: decimon
Great thread! Thanks.


7 posted on 12/21/2009 4:05:52 AM PST by paulycy (Demand Constitutionality.)
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To: decimon
The full article with pictures and formulas included

http://www.constructal.org/en/art/DN%201067.pdf

8 posted on 12/21/2009 4:09:08 AM PST by CaptainK (...please make it stop. Shake a can of pennies at it.)
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To: decimon

for later


9 posted on 12/21/2009 4:11:02 AM PST by muir_redwoods (Obama: The Fresh Prince of Bill Ayers)
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To: decimon

This would explain the 16:9 TV screen ratio......


10 posted on 12/21/2009 4:16:40 AM PST by G Larry (DNC is comprised of REGRESSIVES!)
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To: decimon

Either that or God created it that way.


11 posted on 12/21/2009 4:21:02 AM PST by reg45 (Be calm everyone. The idiot children are in charge!)
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To: G Larry

The 16:9 TV has a 1.56 ratio, not 1.5.


12 posted on 12/21/2009 4:23:43 AM PST by reg45 (Be calm everyone. The idiot children are in charge!)
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To: decimon

bttt


13 posted on 12/21/2009 4:27:49 AM PST by silverleaf (More folks being invited to the White House for Holiday parties than are being sent to Afghanistan)
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To: reg45

“the golden ratio describes a rectangle with a length roughly one and a half times its width”

Do you suppose 1.56 falls within “roughly”?


14 posted on 12/21/2009 4:30:43 AM PST by G Larry (DNC is comprised of REGRESSIVES!)
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To: decimon

British units such as pounds per square inch are more meaningful than the abstracted metric system. I suppose the golden ratio is the visual part of this brain estimation breakdown of an object.


15 posted on 12/21/2009 4:52:25 AM PST by JudgemAll (control freaks, their world & their problem with my gun and my protecting my private party)
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To: decimon

Isn’t this the same as a square root 5 rectangle?


16 posted on 12/21/2009 4:55:36 AM PST by rbosque (11 year Freeper! The real reason the left wants to disarm us is becoming clearer.)
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To: reg45; G Larry
The 16:9 TV has a 1.56 ratio, not 1.5.

The golden ratio is 1.618

17 posted on 12/21/2009 4:56:24 AM PST by Oztrich Boy (Life is a tragedy for those who feel, but a comedy to those who think. - Horace Walpole)
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To: decimon

Are people so afraid of math now that articles avoid showing numbers containing decimal points?


18 posted on 12/21/2009 5:05:11 AM PST by posterchild (Endowed by my Creator with certain unalienable rights.)
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To: decimon

36 - 24 - 36?


19 posted on 12/21/2009 5:07:24 AM PST by Made In The USA (The only thing better than bacon, is bacon wrapped in bacon.)
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To: decimon

Bejan sounds like a crackpot.His theories are all hand-waving nonsense.


20 posted on 12/21/2009 5:07:50 AM PST by 1955Ford
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To: G Larry

Perhaps. Roughly speaking, it could be said that 1.56 is roughly within the rough estimate of 1.5. It could be a bit tough to say how rough, because, roughly speaking, ‘roughly 1.5’ is difficult to be precise about.


21 posted on 12/21/2009 5:11:15 AM PST by RoadGumby (For God so loved the world)
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To: Made In The USA

“36 - 24 - 36?”

(1.5 ratio) This is the funniest post of the day


22 posted on 12/21/2009 5:12:44 AM PST by 1955Ford
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To: decimon
Nice ratio.....

2:me = :-)



23 posted on 12/21/2009 5:13:20 AM PST by domeika
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To: decimon

I was with him until he started talking about the “flow of animals”. I sense a flow of a different sort.


24 posted on 12/21/2009 5:14:39 AM PST by Fresh Wind ("...a whip of political correctness strangles their voice"-Vaclav Klaus on GW skeptics)
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To: Made In The USA
36 - 24 - 36?

Well, in the horizontal...

25 posted on 12/21/2009 5:17:34 AM PST by decimon
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To: decimon

Someone got cause and effect confused.


26 posted on 12/21/2009 5:21:24 AM PST by ctdonath2 (It from fit.)
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To: Oztrich Boy
The golden ratio is approximately 1.618.

The article says one and a half - that's 1.5.

When I googled "golden ratio" - it said 1.618, so therefore the article is either wrong or conflating two different ratios. The 1.618 value is related to the Fibonacci sequence which approaches it asymptotically.

27 posted on 12/21/2009 5:30:36 AM PST by reg45 (Be calm everyone. The idiot children are in charge!)
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To: decimon

For later.


28 posted on 12/21/2009 5:31:32 AM PST by PalmettoMason (But...Obama INHERITED bad presidential poll numbers from Bush. It's BUSH'S fault!)
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To: G Larry

I guess that the value of 1.5 is for the benefit of the victims of modern education.


29 posted on 12/21/2009 5:36:43 AM PST by reg45 (Be calm everyone. The idiot children are in charge!)
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Comment #30 Removed by Moderator

Comment #31 Removed by Moderator

To: JudgemAll

I always liked Pounds, shillings and pence. Was it 12 pence = 1 shilling and 20 shillings = 1 pound ?


32 posted on 12/21/2009 5:49:50 AM PST by Eric in the Ozarks (Impeachment !)
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To: rbosque
(1 + √5)/2
33 posted on 12/21/2009 5:56:40 AM PST by reg45 (Be calm everyone. The idiot children are in charge!)
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To: reg45

Well, I guess 1.5 is approximately 1.618! :-0


34 posted on 12/21/2009 5:59:24 AM PST by biff
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To: reg45

16/9=1.777777777777


35 posted on 12/21/2009 5:59:41 AM PST by dangerdoc
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To: Eric in the Ozarks
how much is a sovereign?
36 posted on 12/21/2009 6:00:40 AM PST by dangerdoc
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To: paulycy
As it occurs in nature...


37 posted on 12/21/2009 6:01:42 AM PST by Joe 6-pack (Que me amat, amet et canem meum)
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To: Joe 6-pack

Beautiful.


38 posted on 12/21/2009 6:03:36 AM PST by paulycy (Demand Constitutionality.)
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To: dangerdoc

You are right, I must have been half asleep when I did the calculation of 1.56.


39 posted on 12/21/2009 6:14:07 AM PST by reg45 (Be calm everyone. The idiot children are in charge!)
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To: dangerdoc

You are right, I must have been half asleep when I did the calculation of 1.56.


40 posted on 12/21/2009 6:14:15 AM PST by reg45 (Be calm everyone. The idiot children are in charge!)
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To: decimon

I guess they have nothing useful to do at Duke.


41 posted on 12/21/2009 6:15:56 AM PST by Leftism is Mentally Deranged
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To: 1955Ford

So would 39-24-39 be more golden?


42 posted on 12/21/2009 6:17:51 AM PST by reg45 (Be calm everyone. The idiot children are in charge!)
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To: dangerdoc

Define “Quid.”


43 posted on 12/21/2009 6:28:45 AM PST by Eric in the Ozarks (Impeachment !)
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To: decimon

bfltr


44 posted on 12/21/2009 6:50:20 AM PST by mnehring
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To: Eric in the Ozarks

That which comes before pro quo.


45 posted on 12/21/2009 6:52:15 AM PST by dangerdoc
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To: dangerdoc

And a heypenny back at cha.


46 posted on 12/21/2009 6:55:26 AM PST by Eric in the Ozarks (Impeachment !)
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To: domeika

What pretty eyes you have....


47 posted on 12/21/2009 7:04:23 AM PST by Calamari (Pass enough laws and everyone is guilty of something.)
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To: domeika

They’re fake. Natural breasts are pear shaped, not shaped like two hemispheres.


48 posted on 12/21/2009 7:12:31 AM PST by Screaming_Gerbil (The light at the end of the tunnel might be a muzzle flash...)
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To: reg45

I took geometry in college but it was a 5 week summer course. We never did explore phi. I wish we had.


49 posted on 12/21/2009 7:17:24 AM PST by rbosque (11 year Freeper! The real reason the left wants to disarm us is becoming clearer.)
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To: Screaming_Gerbil

does it really matter?

it is all an illusion.

There are no straight lines at the Parthenon.


50 posted on 12/21/2009 7:18:10 AM PST by longtermmemmory (VOTE! http://www.senate.gov and http://www.house.gov)
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