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The Golden Ratio


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#1    Alisdair.MacDonald

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Posted 28 July 2013 - 12:25 PM

"Why are the objects that contain the Golden Ratio so pleasing? Much reliable evidence has shown that objects that meet the requirements of the Golden Ratio are attractive and pleasing to the human eye. Throughout history, many experts have tried to find reasonable explanations for this question.

Two thousand years ago, ancient Greeks discovered the magic of this ratio from the Golden Rectangle. The Golden Rectangle is a rectangle that meets the Golden Ratio requirements and contains an infinite number of proportional Golden Rectangles within itself. The ancient Greeks were attracted by this special number and its unique characteristics."

http://library.think.../phisecrets.htm

My question:

Is there evidence to suggest that we are hard wired to perceive aesthetic beauty in a certain way, or are these claims simply theories?

Can anyone find examples of the golden ratio actually happening in nature?


#2    vitruvian12

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Posted 28 July 2013 - 03:01 PM

The Fibonacci series can be found in many flower petal layouts and seed layouts like the sun flower and a pine cone.  It also describes the spiral of some sea shells.


#3    Alisdair.MacDonald

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Posted 28 July 2013 - 03:13 PM

View Postvitruvian12, on 28 July 2013 - 03:01 PM, said:

The Fibonacci series can be found in many flower petal layouts and seed layouts like the sun flower and a pine cone.  It also describes the spiral of some sea shells.

I am familiar with the Fibonacci series. I will have to check this out. Thanks!


#4    Zaphod222

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Posted 28 July 2013 - 06:06 PM

View PostAlisdair.MacDonald, on 28 July 2013 - 12:25 PM, said:

My question:
Is there evidence to suggest that we are hard wired to perceive aesthetic beauty in a certain way, or are these claims simply theories?

Interesting topic. Personally, I don´t believe this is an "either or" proposition. I think like the "nature or nurture" discussion, this is not a question of one or the other, but of both factors being there.

Clearly, there is evidence that we are hard-wired to enjoy some things (think voluptuous young females...)
And just as clearly, there is evidence that we can learn to enjoy some very weird things (think lutefisk or vegemite...)

The golden ratio might be so pleasing because it relates to the perfect human shape (e.g. the Da Vinci man). Just an idea.

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#5    Harte

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Posted 28 July 2013 - 10:12 PM

View PostAlisdair.MacDonald, on 28 July 2013 - 12:25 PM, said:

"Why are the objects that contain the Golden Ratio so pleasing? Much reliable evidence has shown that objects that meet the requirements of the Golden Ratio are attractive and pleasing to the human eye. Throughout history, many experts have tried to find reasonable explanations for this question.

Two thousand years ago, ancient Greeks discovered the magic of this ratio from the Golden Rectangle. The Golden Rectangle is a rectangle that meets the Golden Ratio requirements and contains an infinite number of proportional Golden Rectangles within itself. The ancient Greeks were attracted by this special number and its unique characteristics."

http://library.think.../phisecrets.htm

My question:

Is there evidence to suggest that we are hard wired to perceive aesthetic beauty in a certain way, or are these claims simply theories?

Quote

Now a US academic believes he has discovered the reason why it pleases the eye. According to Adrian Bejan, professor of mechanical engineering at Duke University, in Durham, North Carolina, the human eye is capable of interpreting an image featuring the golden ratio faster than any other.
Source

View PostAlisdair.MacDonald, on 28 July 2013 - 12:25 PM, said:

Can anyone find examples of the golden ratio actually happening in nature?
There's this webpage called "Google."

Here's what it says about this.

Harte

Posted Image
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#6    DieChecker

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Posted 28 July 2013 - 11:41 PM

Interesting link Harte...

Here at Intel we make processors on 12 inch wafers. And, the individual processors on the wafers are called die. And, I am employed to check these die. That is why I am the DieChecker.

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#7    jaylemurph

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Posted 28 July 2013 - 11:48 PM

View PostHarte, on 28 July 2013 - 10:12 PM, said:

Source


There's this webpage called "Google."

Here's what it says about this.

Harte

"Google", you say? Sounds dirty to me. One might even be tempted to Google themselves, which is clearly obscene.

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Posted Image

Deeply venial

#8    Harte

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Posted 29 July 2013 - 01:38 AM

Not to mention humiliating.

H.

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#9    Mario Dantas

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Posted 29 July 2013 - 12:12 PM

Hello,

Since 2007, i have made pictures of an odd structure in central Greenland. This structure was, apparently, a golden mean rectangle. I have proposed since then that this rectangle was Plato´s rectangular and oblong plain:

Quote

I will now describe the plain, as it was fashioned by nature and by the labours of many generations of kings through long ages. It was for ditch were incredible, and gave the impression that a work of such extent, in addition to so many others, could never have been artificial. Nevertheless whole of the plain, and was ten thousand stadia in length. It received the streams which came down from the mountains, and winding round the plain the plain, and again let off into the ditch leading to the sea: these canals were at intervals of a hundred stadia, and by them they brought down the to the city. Twice in the year they gathered the fruits of the earth-in winter having the benefit of the rains of heaven, and in summer the water Euclidean plane geometry, a rectangle is any quadrilateral with four right angles. It can also be defined as an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°). It can also be defined as a parallelogram containing a right angle. A rectangle with four sides of equal length is a square. The term oblong is occasionally used to refer to a non-square rectangle.[1][2][3] A rectangle with verticesABCD would be denoted as Posted ImageABCD.
http://en.wikipedia.org/wiki/Rectangle

There was, some years ago, a great controversy on the internet regarding this subject (object).The image below has vanished from Google earth, according to specialists. Nevertheless, there is still an "invisible" golden mean rectangle in the center of Greenland (see links with dates).


Posted Image




https://lh4.googleus...V5WY/s800/z.png
https://lh5.googleus...s%20%289%29.jpg
https://lh3.googleus.../s800/AAAAB.jpg
https://lh3.googleus...lantis%20A2.jpg
https://lh5.googleus...The%20Plain.jpg
https://lh3.googleus...lantis%20A3.jpg
https://lh3.googleus...A/s800/ASFT.jpg
https://lh5.googleus...s%20%283%29.jpg
https://lh5.googleus...0%28NOOP%29.jpg
https://lh6.googleus...s%20%289%29.jpg
https://lh3.googleus...ywY/s800/A2.jpg
https://lh3.googleus...mail_fig04a.gif
https://lh5.googleus...mail_fig04a.gif
https://lh4.googleus...Island%202.jpeg
https://lh4.googleus...Island%202.jpeg
https://lh3.googleus...0/oijoijoij.jpg
https://lh4.googleus...lantis%20A4.jpg
https://lh5.googleus...lantis%20A1.jpg
https://lh5.googleus...lantis%20A2.jpg
https://lh6.googleus...00/Atlantis.jpg
https://lh5.googleus...opography1.jpeg
https://lh5.googleus...20mountain5.jpg
https://lh4.googleus...0Plain%204.jpeg

1. Catalog of Images
https://picasaweb.google.com/106047243612755133722

2. Was Atlantis in Greenland?
http://a7lan7is.blogspot.com

#10    Mario Dantas

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Posted 29 July 2013 - 12:47 PM

Posted Image


A golden rectangle is one whose side lengths are in the golden ratio, Posted Image, which is Posted Image (the Greek letter phi), where Posted Image is approximately 1.618.


http://en.wikipedia....olden_rectangle





I forgot to mention that Plato´s rectangle plain´s side lengths are also in the golden ratio, that is 1.618... which makes it a golden mean rectangle!

Width across its Centre               2000    Stadia
Length along the Sea                   3000    Stadia

(data taken from Ulf Richter´s work http://www.black-sea...com/richter.pdf)


  3000 / 2000  ----------- ratio = 1.5

Edited by Mario Dantas, 29 July 2013 - 01:02 PM.

1. Catalog of Images
https://picasaweb.google.com/106047243612755133722

2. Was Atlantis in Greenland?
http://a7lan7is.blogspot.com

#11    Alisdair.MacDonald

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Posted 29 July 2013 - 03:38 PM

View PostHarte, on 28 July 2013 - 10:12 PM, said:

Source


There's this webpage called "Google."

Here's what it says about this.

Harte

I'd rather let the pros handle it. Like yourself.


#12    vitruvian12

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Posted 29 July 2013 - 03:38 PM

View PostMario Dantas, on 29 July 2013 - 12:47 PM, said:


Posted Image


A golden rectangle is one whose side lengths are in the golden ratio, Posted Image, which is Posted Image (the Greek letter phi), where Posted Image is approximately 1.618.


http://en.wikipedia....olden_rectangle





I forgot to mention that Plato´s rectangle plain´s side lengths are also in the golden ratio, that is 1.618... which makes it a golden mean rectangle!

Width across its Centre    2000    Stadia
Length along the Sea    3000    Stadia

(data taken from Ulf Richter´s work http://www.black-sea...com/richter.pdf)


  3000 / 2000  ----------- ratio = 1.5

Doesn't your previous quote say the plain was 10 000 stadia in length?
I cant make any sense of the sat. photo.

Edited by vitruvian12, 29 July 2013 - 03:40 PM.


#13    Mario Dantas

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Posted 29 July 2013 - 04:37 PM

Hi vitruvian12,

I don´t know what happened while i was editing my first post, everything just went upside down...

Here is the quote of Plato´s Critias:

Quote

I will now describe the plain, as it was fashioned by nature and by the labours of many generations of kings through long ages. It was for line followed the circular ditch. The depth, and width, and length of this ditch were incredible, and gave the impression that a work of such extent, in addition to so many others, could never have been artificial. Nevertheless feet, and its breadth was a stadium everywhere; it was carried round the whole of the plain, and was ten thousand stadia in length. It received the streams which came down from the mountains, and winding round the plain likewise, straight canals of a hundred feet in width were cut from it through the plain, and again let off into the ditch leading to the sea: these canals were at intervals of a hundred stadia, and by them they brought down the in ships, cutting transverse passages from one canal into another, and to the city. Twice in the year they gathered the fruits of the earth-in winter having the benefit of the rains of heaven, and in summer the water which the land supplied by introducing streams from the canals.

http://classics.mit....to/critias.html

He says that the ditch was 10.000 stadia in length, not the plain:

Quote

and where falling out of the straight line followed the circular ditch. The depth, and width, and length of this in addition to so many others, could never have been artificial. Nevertheless I must say what I was told. It was excavated to the depth of a hundred, feet, and its breadth was a stadium everywhere; it was carried round the whole of the plain, and was ten thousand stadia in length.


Regarding the satellite image on Google Earth, it is supposed to be a rectangular shape. Although i have given up to show any similarity with a rectangle, it is there still:

Posted Image

Posted Image

Posted Image



Sorry for the typos...


Regards,
Mario Dantas

Edited by Mario Dantas, 29 July 2013 - 05:10 PM.

1. Catalog of Images
https://picasaweb.google.com/106047243612755133722

2. Was Atlantis in Greenland?
http://a7lan7is.blogspot.com

#14    Harte

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Posted 29 July 2013 - 08:25 PM

I see that now 1.5 = 1.618...

Close enough?

Hardly.

1.5, after all, is rational.  Phi is irrational.

I guess that doesn't matter to some people though.

Harte

Posted Image
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#15    DieChecker

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Posted 29 July 2013 - 08:45 PM

View PostMario Dantas, on 29 July 2013 - 12:12 PM, said:

Since 2007, i have made pictures of an odd structure in central Greenland. This structure was, apparently, a golden mean rectangle. I have proposed since then that this rectangle was Plato´s rectangular and oblong plain:

I still can't believe you've spent 6 years working on a google maps compilation error artifact. There is no evidence Greenland has moved noticably in the last 100,000 years.

Here at Intel we make processors on 12 inch wafers. And, the individual processors on the wafers are called die. And, I am employed to check these die. That is why I am the DieChecker.

At times one remains faithful to a cause only because its opponents do not cease to be insipid. - Friedrich Nietzsche

Qualifications? This is cryptozoology, dammit! All that is required is the spirit of adventure. - Night Walker




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