As a mathematical and natural phenomenon, the Golden Ratio has links with the Fibonacci sequence, the Stradivarius Violin, and the Vitruvian Man. The golden ratio has been widely used throughout the visual art, architecture, and music fields, by Mozart and Le Corbusier, among others, however it is rarely utilized within the field of dance.
The relationship of the highly subjective field of dance and the pragmatic field of mathematics has not yet fully been explored.
The mean and extreme ratio, later named the Golden Ratio, was first clearly defined mathematically circa 300 BCE by Euclid of Alexandria.
In Book VI of his Elements, Euclid describes the ratio:
A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less.
In the beginning of the 20th Century, Mark Barr termed the Golden Ratio, phi, after the Greek architect responsible for the many Parthenon sculptures such as “Athena Parthenos”, Phidias 2 6. Use of phi, or the Greek letters, Φ and φ, is now commonly used as a reference point when discussing the properties of the Golden Ratio.
There have been connections forming between dance and mathematics education as well as mathematics and dance definition which have furthered both fields.
Why the Golden Ratio? The Golden Ratio is considered to be the “mathematical concept which is at the centre of … discussion,” by many mathematicians and math historians alike.
The Golden Ratio, while being a relatively simple mathematical concept, can be linked to numerous natural phenomena and artistic expressions throughout history: from the number and arrangement of petals on flowers to the beautiful works of music composed by Mozart; from the structures of the galaxies to the evolution of deep sea creatures; from the design of the soccer ball to the architecture of the Taj Mahal. Golden Ratio can be seen in a wide variety of natural and artistic mediums internationally and throughout history.
The Golden Ratio as a Series of Numbers
The sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, . . . , in which each term (starting with the third) is equal to the sum of two preceding terms, was appropriately dubbed the Fibonacci sequence in the nineteenth century, by the French mathematician Edouard Lucas (1842-1891).
Golden Ratio in Music
Mozart, one of the most timeless and well-known composers in history, was known to show very high interest in mathematics. There are even math equations jotted down in the margins of many of his compositions.
The Golden Ratio can be mathematically defined as a number, a ratio, a series of numbers, and many other forms. Often related to nature and works of art, the Golden Ratio will also be defined by these occurrences. The arrangement of flower petals’ growth and the design of the pentagram are a few of the natural and artistic expressions of the Golden Ratio.
The process of relating the mathematical, natural, and artistic expressions of the Golden Ratio is comprised of three phases:
- Utilizing the four main components of the Laban Movement Analysis – Body, Space, Effort, and Shape – the mathematical expressions can be related to movement constraints.
- Relating the natural expressions of the Golden Ratio into choreographic structure.
- By relating the existing artistic expressions of the Golden Ratio to choreographic methods to create choreographic ideas.