Golden Section

May 15, 2012

The Golden Section / Golden Ratio

 


GoldenNumber.Net explores the appearance of Phi, 1.618 (also known as the Golden Ratio, Golden Mean, Golden Section or Divine Proportion, in mathematicsgeometrylife and the universe and shows you how to apply it, and its applications are limitless:

The Golden Section is a ratio based on a the number Phi, 1.618…

The Golden Section or Ratio is is a ratio or proportion defined by the number Phi (= 1.618033988749895… )

It can be derived with a number of geometric constructions, each of which divides a line segment at the unique point where:

the ratio of the whole line (A) to the large segment (B)

is the same as

the ratio of the large segment (B) to the small segment (C).

Sectioning a line to form the Golden Section, based on phi, the golden ratio

In other words, A is to B as B is to C.

This occurs only where A is 1.618 … times B and B is 1.618 … times C.


This ratio has been used by mankind for centuries

Its use may have started as early as with the Egyptians in the design of the pyramids,

Phi, the golden ratio, as found in the Great Pyramid of Egypt The Great Pyramid of Egypt

 

The Greeks recognized it as
“dividing a line in the extreme and mean ratio”
The Renaissance artists
knew it as the
Divine Proportion
The Parthenon illustrates design based on phi, the golden ratio The Last Supper by Leonardo Da Vinci makes extensive use of phi, the golden ratio or Divine proportion in its composition and design
and used it for beauty
and balance in the
design of architecture,
perhaps as early as the Parthenon
and used it for beauty
and balance in the
design of art

 

It appears in the design of Notre Dame in Paris

Phi, the golden ratio is found in design of Notre Dame cathedral in Paris

and continues today in many examples of art, architecture and design.

It also appears in the physical proportions of the human body, movements in the stock market and many other aspects of life and the universe.

Dr. Stephen Marquardt has discovered a template for human beauty using the Golden Section, with obvious relevance in the plastic surgery industry. Marquardt’s analysis takes ethnicity into account, and illustrates variations that are are both numerous and subtle.

See the other sections and pages of this site listed above and to the right for a broad sampling of the many appearances and applications of the golden ratio.

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Leave a Comment

{ 12 comments… read them below or add one }

NF Hannibal September 12, 2012 at 12:07 pm

This is good stuff – I have been trying to find a good source to educate myself in the concepts of sacred geometry, looks like I have found it!

Reply

patrick November 20, 2012 at 1:33 am

Get Robert Ludlow’s book “Sacred Geometry”. It’s a brilliant primer and workbook on the subject

Reply

SIMONA October 21, 2012 at 5:16 am

Instructive and interesting

Reply

Sammy January 24, 2013 at 3:53 pm

Awesome

Reply

ebonygrace March 27, 2013 at 10:17 am

love this site

Reply

vector louis April 21, 2013 at 10:43 am

The golden ratio is unique and amazing because I think it is somewhat like a snake biting its own tail which is part of the symbol of world in Taros. Euclid defined this ratio as follows: If we divide a line such that the ratio of the small portion to the large one is equal to the the ratio of the large portion to the whole line. I think it is like the snake and it represents the harmony and beauty of the multiverse which has no origin and ends.

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giovanni borello July 1, 2013 at 12:09 pm

very informational and understandable

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oscar borello July 2, 2013 at 6:46 pm

very instructive and easy to understand

Reply

Tom July 17, 2013 at 4:03 pm

Did you know the golden section proportions are found in the Holy Bible?? The old testament fits into the large section and the new testament fits into the smaller section. That’s how you know the Holy Bible was divinely inspired by God, and is the truth to all the universe.

If you need further proof, just divide 66 (the number of books in the bible) by 1.618 (the Golden ratio number) and you get (40.7) The book of Matthew… exactly where the Bible divides in two.

Furthermore, the complete sum of one Golden section box equals 33. The complete sum of Jesus at the age he died was 33! Two golden spirals added up equals 66. The bible has 66 books. The Bible is actually the DNA of God in words.

Reply

Kim September 30, 2013 at 12:14 am

Where did you find this out?

Reply

Matguwapo August 26, 2013 at 7:57 pm

This is the best golden section/ratio explanation

Reply

musoke godfrey October 15, 2013 at 3:38 am

the golden section is great art

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