Fibonacci in Applied Arts

This is an excerpt from Master Fibonacci: The Man Who Changed Math. All citations are catalogued on the Citations page.

Fibonacci in Industrial Design & Commercial Art

(Previous Section: Fibonacci in Film)

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According to Ukrainian mathematician, inventor, and engineer Alexey Stakhov, many commercial products created today exhibit the Golden Rectangle shape in their design, including match boxes, lighters, books, credit cards, and suitcases (Stakhov 21). However, others insist some of these pop-culture beliefs are misconceptions because, for example, credit cards’ “aspect ratio is defined by the ISO/IEC 7810 standard as 85.60 mm x 53.98 mm, a ratio of 1.5858:1, which differs by 2% from the Golden Mean (Salingaros, “Applications”). In addition, the television, film, and computer industries do not consistently adhere to a Golden Mean standard aspect ratio; one would think that they would “try to utilize a human preference for a specific aspect ratio.” Computer screens, for example, are manufactured according to “the unofficial but ubiquitous standard of 4:3 ≈ 1.33:1.” Salingaros concedes that the MacBook Pro computer’s 15-inch screen does have 1,440×900 pixels, and thus an aspect ratio of 8:5 = 1.60:1. … within 1.1% of the Golden Mean,” but “the perfectionist Steve Jobs could have easily used 1,440×890 pixels for an aspect ratio of 1.6180:1 if he had wished to use the Golden Mean” (Salingaros, “Applications”).

 

Apple Logo Fibonacci Golden Ratio
Apple Logo

The production and arrangement of floor tiles has benefited from Phi (Φ) (1.618) which informed the development of the 1970s Penrose Tiles, allowing surfaces to be tiled in five-fold symmetry (Hom). “In the 1980s, phi (φ) (0.618) appeared in quasicrystals, a then-newly discovered form of matter whose utility for industrial purposes has only just begun to be enthusiastically investigated” (Hom).

In visual arts and architecture, the Golden Section is the dynamic bearer of harmony (Stefanovic). Some have proposed that Fortune 500 companies and major companies all over the world design logos and products using the Golden Section, conceivably to satisfy consumers’ inherent preference for aesthetic harmony. Apple for example, was said to have used the Golden Ratio to design its logo and many of its products (a claim which has just as often been debunked) and it’s been said that Twitter used it to create their new profile page (Brandon).

Video Game Design

In 1984 two university undergraduates working out of a dormitory in Jesus College, Cambridge employed vector math to create video-game simulations of space in the spaceship game, “Elite.” David Braben and Ian Bell chose not to manually plot star systems by typing coordinates of star and planets into a database; instead, Braben attempted randomly-generated numbers. However, this method led to random arrangements of the game space object representations every time the game was loaded. To overcome this problem, Braben “used the Fibonacci sequence as a seed from which identical galaxies would be generated each time the game was played, all within a computer program a fraction of the size of a photograph taken with a mobile phone today” (Parkin).

More recently, Vigil Games’ senior designer Mike Birkhead explained in the 2012 article, “Tips from a Combat Designer: Fibonacci Game Design,” how he uses Fibonacci sequence numbers to limit the options for players, such as the number of weapons players are allowed to have in a game, how many talent trees, or how many monsters can be spawned in an encounter. He usually limits the choices to three or five (Fibonacci numbers). “When I think about adding something to the game I constrain myself within Fibonacci’s beautiful sequence, for it forces me to REALLY commit to ‘just one more,’ as now it is NOT just one more, but in fact several more” (Birkhead). He finds that this self-imposed limitation upon design choices empowers him to create programs and games more confidently and efficiently.

FIBONACCI IN LITERARY ARTS

Poetry

Aristotle maintained that poetic verse expresses a beautiful impression by deliberate rhythmic, numerical

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relations (Stakhov 40). Just as a red rose blossoms in a well-orchestrated sequence of botanical processes governed somehow by the Golden Ratio (some say), so, too, may the literary artist deliberately conduct a poetic symphony according to elements related to the Fibonacci numbers.

Two ways the Golden Ratio and Fibonacci numbers can be used to compose poetry are: 1) There can be poems about the Golden Ratio or the Fibonacci numbers themselves or about geometrical shapes or phenomena that are closely related to them; and 2) The Golden Ratio or Fibonacci numbers can be utilized in constructing the form, pattern, or rhythm of a poem. (Livio 198)

In Fascinating Fibonaccis, author Trudi Hammel Garland composed a limerick comprised of five lines with the number of beats in each line being two or three, and the total number of beats being thirteen (all Fibonacci numbers):

A fly and a flea in a flue (3 beats)
 Were imprisoned, so what could they do? (3beats)
 Said the fly, “Let us flee!” (2 beats)
 “Let us fly!” said the flea,  (2 beats)
 So they fled through a flaw in the flue. (3 beats) 
 (Livio 198)

Fibs
14 Fibs of Gregory K.
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Gregory K. Pincus coined the term “Fib” in 2006 to refer to a six-line, twenty syllable poem using the Fibonacci numbers and since then has maintained a popular blog, written a children’s book, and has recently authored a novel, The 14 Fibs of Gregory K. (Pincus). The number of syllables in each line of a Fib is the sum of the previous two lines: 1, 1, 2, 3, 5, 8. “The constrained form makes you very conscious of word choice,” he says (Pincus). Since 2006, Mary-Jane Grandinetti has edited “The Fib Review,” an online poetry journal that specializes in only one particular poetry form – the Fibonacci poem. “Submissions are carefully selected for publication based on their poetic value and their adherence to the Fibonacci number sequence whether in syllable count, word count or any other experimental genre yet to be created” (Grandinetti).

There is no restriction for the subject of the Fibonacci poem, but the form of the Fibonacci poem is based on the structure of the Fibonacci number sequence. The poem, therefore, consists of lines with 1, 1, 2, 3, 5, 8 (and so on) syllables or words that a writer places in each line of the poem. As a literary device, it is a formatted pattern in which meaning is offered in any organized way, providing the number sequence remains the constancy of the form (Grandinetti).

“Fibonacci Salute” is a poem both inspired by and containing Fibonacci numbers in the text:

Fibonacci Salute

One finds
one self alone suddenly where there were
two when repeated percussion strikes spark
three-dimensional (make that
five or
eight) fires with fangs in swiftest motion, scythe-like, as in an unlucky
thirteen lightning strike, deal mortal blows until every
 
twenty-one gun salute cracking the still, chill air cackles, “He’ll never see
thirty-four.”

Shelley Allen

 

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Master Fibonacci: The Man Who Changed Math

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Paperback: 128 pages
Author: Shelley Allen, M.A.Ed.
Publisher: Fibonacci Inc.; 1st edition (2019)
Language: English