What is phi Φ, or the “Golden Ratio”?
Also known as “the Divine Proportion”, the Golden Ratio or, phi ( Φ ) has been the mystery, cause, hope and fixation of many of the world’s foremost mathematicians, artists, architects, musicians, scientists, theologians, philosophers and mystics.
Here is briefly the basic mathematical understanding of “phi”, or the Golden Ratio:
AB/CB = CB/AC = 1.618…
“The golden section is a line segment sectioned into two according to the golden ratio. The total length a+b is to the longer segment a as a is to the shorter segment b.” from WikiPedia
Rather than get into a very long, protracted explanation, I’ll attempt to reveal certain features, and provide links to more authoritative sources on each subject.
phi in Art
Leonardo da Vinci’s illustrations in De Divina Proportione (On the Divine Proportion) and his views that some bodily proportions exhibit the golden ratio have led some scholars to speculate that he incorporated the golden ratio in his own paintings. Some suggest that his Mona Lisa, for example, employs the golden ratio in its geometric equivalents.
phi in Philosophy
The Golden Mean can be construed as the basis of philosophy and Sacred Geometry, one of the Transcendental Numbers, and is typically derived from Fibonacci Numbers.
phi in Music
The Fibonacci series, coming from phi, or “The Golden Ratio”, appears in the foundation of aspects of art, beauty and life. Even music has a foundation in the series, as:
- There are 13 notes in the span of any note through its octave.
- A scale is comprised of 8 notes, of which the
- 5th and 3rd notes create the basic foundation of all chords, and are based on whole tone which is
- 2 steps from the root tone, that is the
- 1st note of the scale.
phi in Architecture
Its use started as early as with the Egyptians in the design of the pyramids. When the basic phi relationships are used to create a right triangle, it forms the dimensions of the great pyramids of Egypt, with the geometry shown below creating an angle of 51.83 degrees, the cosine of which is phi, or 0.618.
phi in Math
Euclid, the Greek mathematician of about 300BC, wrote the Elements which is a collection of 13 books on Geometry (written in Greek originally). It was the most important mathematical work until this century, when Geometry began to take a lower place on school syllabuses, but it has had a major influence on mathematics.