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

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

–Plato

Okay so first maybe watch this (just to get in the mood):

Okay. And, so – 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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High-RoI Story/Screenplay/Movie and Transmedia Researcher

*The above is (mostly) an adapted excerpt, from my doctoral thesis: “ Communication, Creativity and Consilience in Cinema”. It is presented here for the benefit of fellow screenwriting, filmmaking and creativity researchers. For more, see https://aftrs.academia.edu/JTVelikovsky*

*JT Velikovsky is also 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 for 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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It would be interesting to learn what each of the top 20 ROI films have in common about their stories.

Hi Phil

See what you think of al the common elements listed, in:

https://storyality.wordpress.com/an-index-to-this-blog/

Cheers

JT

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