**The Golden Ratio / The Golden Spiral / The Fibonacci Sequence**

“The knowledge of which geometry aims is – the knowledge of the eternal.”

–Plato

Plato suggested there are *ideal and perfect forms*, and – sometimes – they emerge in Nature/The World/Reality/The Universe.

Some other great thinkers in history who, at some point have also felt likewise, include (among others):

- Euclid (Euclid wrote about/defined The Golden Ratio in his
*Elements,*circa 300 B.C.) - Fibonacci (Fibonacci noticed the mathematical sequence behind The Golden Ratio in his mathematical treatise,
*Liber Abaci*(1202 AD)) - Aristotle (who also preached about The Golden Ratio)
- Einstein
- Godel
- Penrose
- Galileo
- Newton
- Hawking

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**THE FIBONACCI SEQUENCE**

The Fibonacci sequence is:

**0, 1, 1, 2, 3, 5, 8, 13, 21, 34… (etc.)**

Each number in the recursive sequence is the sum of the two preceding numbers.

The numbers of the sequence are also intimately connected with the golden ratio, or

**1 : 1.61803**…*(etc. The number is infinite, and non-repeating)*.

For example – in mathematical terms, the closest *rational approximations* to The Golden Ratio *(1 : 1.6)* are: 2/1, 3/2, 5/3, 8/5. The higher in the sequence, *the closer two consecutive numbers of the sequence, divided by each other approaches the golden ratio* (approximately 1 : 1.618).

1:1.6 is also known as *phi* – or the Greek φ – or The Golden Ratio (also The Golden Section).

**The Fibonacci Rectangle**

**Golden Spiral and Golden Rectangle**

**Golden Spiral and Golden Rectangle Combined:**

Nautilus shells and animal horns also use the Golden Ratio/Fibonacci Sequence.

*The StoryAlity Syntagm:*

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### A BRIEF HISTORY OF THE GOLDEN RATIO:

According to Priya Hemenway in *“Divine Proportion: Phi In Art, Nature, and Science”* (2005) the timeline of The Golden Ratio runs thus:

- Phidias (490–430 BC) – within the Parthenon statues
- Plato (427–347 BC) – in
*Timaeus*, describes the Platonic solids, which are related to The Golden Ratio. - Euclid (c. 325–c. 265 BC), in
*Elements*, gave the first recorded definition of The Golden Ratio - Fibonacci (1170–1250) in
*Liber Abaci* - Luca Pacioli (1445–1517) – called the golden ratio the “divine proportion” in his
*Divina Proportione*, which was illustrated by Leonardo Da Vinci. - Michael Maestlin (1550–1631) – published the first approximation of the (inverse) Golden Ratio as a decimal
- Johannes Kepler (1571–1630) proved that the golden ratio was the limit of the ratio of consecutive Fibonacci numbers, and describes the golden ratio as a “precious jewel”:

- (These two `geometric treasures’ are combined in the Kepler triangle.)
- Charles Bonnet (1720–1793) points out that in the spiral phyllotaxis of plants going clockwise and counter-clockwise were frequently two successive Fibonacci series.

- Martin Ohm (1792–1872) is believed to be the first to use the term
*goldener schnitt*(golden section) to describe this ratio, in 1835. - Édouard Lucas (1842–1891) gives the numerical sequence now known as the Fibonacci sequence its present name.
- Mark Barr (American mathematician) in 1909 suggests the Greek letter phi (φ), the initial letter of Greek sculptor Phidias’s name, as a symbol for the golden ratio.
- Roger Penrose (1931-) discovered a symmetrical pattern that uses the golden ratio in the field of aperiodic tilings, which led to new discoveries about quasicrystals.

(Hemenway 2005 pp 20-21)

*Vitruvian Man* – by Leonardo Da Vinci

**Divine Proportions:**

**An analysis of the story structure of the Top 20 ROI (return on investment) Films:**

“The knowledge of which geometry aims is – the knowledge of the eternal.”

–Plato

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JT Velikovsky

High ROI Film/Story/Screenplay Analyst

*The above is an adapted excerpt from my doctoral thesis: “ Understanding And Exploring The Relationship Between: Creativity; Theories Of Narratology; Screenwriting; And Narrative Fiction Feature Film-Making Practices.” It is presented here for the benefit of fellow screenwriting and filmmaking researchers.*

*JT Velikovsky is a produced feature film screenwriter and million-selling transmedia **writer-director-producer. He has been a professional story analyst for major film **studios, film funding organizations, and the national writer’s guild. For more see: **http://on-writering.blogspot.com/*

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**REFERENCES**

[1] Priya Hemenway, *Divine Proportion: Phi In Art, Nature, and Science.* New York: Sterling. (2005) pp. 20–21

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