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 mathematics, geometrylife 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.


  1. NF Hannibal says

    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!

  2. vector louis says

    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.

      • says

        A : B=B : C simply means that the ratio of length A (the entire line) to that of B (the longer segment) is the same ratio as that of length B to that of C (the shorter segment). It expresses mathematically the one and only way to divide a line so that its sections are in the same ratio to one another. The dividing point occurs at 0.618… of the line’s length, the reciprocal of 1.618… This results in ratios of A to B of 1.618:1 and B to C of 1.618:1 By contrast, if you cut a line in half, the ratio of the entire length to the sectioned pieces is 2:1 while the ratio of the pieces are 1:1. Cut it in thirds and the ratio A to B is 3:2 and B to C is 2:1. Only the golden ratio pf 1.618 results in the same ratio for all the segments.

  3. Tom says

    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.


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