Fibonacci numbers in popular culture

The Fibonacci numbers form a sequence of integers, mathematically defined by

F(0)=0; F(1)=1; F(n) = F(n - 1) + F(n - 2) for n > 1.

This results in the following sequence of numbers:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, ...

so that each new number is the sum of the previous two, after seeding the sequence with the starting pair 0, 1.

Dividing the larger number by its smaller neighbor yields a number that approaches the golden ratio.

The Fibonacci numbers, and in conjunction the golden ratio, are a popular theme in culture. They have been mentioned in novels, films, television shows, and songs. The numbers have also been used in the creation of music, visual art, and architecture.

Architecture

Chimney of Turku Energia, Turku, Finland featuring Fibonacci sequence in 2m high neon lights. By Italian artist Mario Merz for an environmental art project (1994)

• The sequence has been used in the design of a building, the Core, at the Eden Project, near St Austell, Cornwall, England.

Cinema

• In the Tamil Science fiction film Enthiran when Chitty The Robot was asked whether 24,157,817 is a Fibonacci Number, Chitty replies in affirmative and says that it is the 22nd Fibonacci Number. However, it is actually the thirty-seventh Fibonacci Number; the twenty-second Fibonacci Number is 17,711.
• In the film Dopo Mezzanotte (After Midnight), the sequence appears as neon numbers on the dome of the Mole Antonelliana in Turin, Italy, and is also used to select numbers in a lottery, ultimately winning it.
• Along with the golden rectangle and golden spiral, the Fibonacci sequence is mentioned in Darren Aronofsky's independent film π. They are used to find the name of God.(1998)
• In The Da Vinci Code, the numbers are used to unlock a safe. They are also placed out of order in a message to indicate that the message is also out of order (anagram).
• In Mr. Magorium's Wonder Emporium (2007), Magorium hires accountant Henry Weston (Jason Bateman) after an interview in which he demonstrates knowledge of Fibonacci numbers.
• In 21 (2008), the first eight numbers of the sequence are written in icing on a birthday cake which has twenty-one candles.
• In the Japanese film L: change the WorLd the child character, Near, is said to be a mathematical genius and is seen arranging candies in a pattern that the protagonist, L, says corrosponds with fibonacci numbers.

Comic strips

• In a strip of FoxTrot by Bill Amend, characters Jason and Marcus take one nacho from a bowl, one more nacho, then two nachos, three nachos, five nachos, eight nachos, etc., calling it 'Fibonacho.'
• In the strip "Alone" of the online comic xkcd by Randall Munroe, a male and female stick figure are seen together in an intimate situation. The male voices over, explaining his obsessive tendency to count numbers and find patterns. When he realizes that she is touching him in a pattern corresponding to the Fibonacci Sequence, his appreciation for her increases tremendously.
• In a strip of Frazz by Jef Mallett, Frazz and a student are discussing her knitted hat. The student says, "Mom sewed on sparlky here and here. Two sparlkies here. Three sparklies here. Eight sparklies here. Thirteen sparklies..." To which Frazz replies, "Oh, Fabonacci sequins."

Human Development

John Waskom postulated that stages of human development followed the Fibonacci sequence, indicating that the unfolding psychology of human life would ideally be a "living proof" of the Golden Mean. This theory was developed and published by Norman Rose in two articles. The first article laid out the general theory: Design and Development of Wholeness: Waskom's Paradigm; The Educational Forum, 55, 3 (Spring 1991), 243-259 (viewable at http://whizkidz.org/design/DevelopmentDesign.pdf). The second article laid out the applications and implications of the theory to the topic of moral development: Moral Development: The Experiential Perspective; Journal of Moral Education, 21, 1 (Winter, 1992), 29-40 (viewable at http://whizkidz.org/design/MoralDevelopment.pdf).

Literature

• The Fibonacci sequence plays an important role in the plot of the children's book The Wright 3 by Blue Balliett.
• The Fibonacci sequence plays a small part in the bestselling novel and film The Da Vinci Code.
• The Fibonacci sequence plays a part in unravelling the Atlantis Code in Stel Pavlou's bestselling novel Decipher.
• A part of the Fibonacci sequence is used as a code in Matthew Reilly's novel Ice Station.
• In Philip K. Dick's novel VALIS, the Fibonacci sequence (as well as the Fibonacci constant) are used as identification signs by an organization called the "Friends of God".
• In the collection of poetry alfabet by the Danish poet Inger Christensen, the Fibonacci sequence is used to define the number of lines in each poem.
• The Fibonacci sequence is one of many mathematical topics in Scarlett Thomas's novel PopCo whose main character has an affinity for mathematics.
• The Fibonacci sequence is one of the main sources of math-based magic for the main character, Reason Cansino, in Justine Larbalestier's trilogy, Magic or Madness
• The Fibonacci sequence is mentioned in the children's book Math Curse by Jon Scieszka.
• It was briefly included (and recognized by Charles Wallace) in the television film adaptation of A Wrinkle in Time.
• The Fibonacci sequence is frequently referenced in the 2001 book The Perfect Spiral by Jason S. Hornsby.
• The Fibonacci sequence is mentioned In the movie The Oxford Murders. In the movie a professor and a grad student work together to try to stop a potential series of murders seemingly linked by mathematical symbols.
• The Fibonacci sequence and golden ratio are briefly described in John Fowles's 1985 novel A Maggot
• The Fibonacci sequence is explored in Emily Gravett's 2009 book The Rabbit Problem

Music

• Rap group Black Star's song, Astronomy (8th Light) from the 1998 album Mos Def & Talib Kweli are Black Star, features the Fibonacci sequence in the chorus:

Now everybody hop on the one, the sounds of the two

It's the third eye vision, five side dimension

The 8th Light, is gonna shine bright tonight

• Tool's song "Lateralus" from the album of the same name features the Fibonacci sequence symbolically in the verses of the song. The syllables in the first verse count 1, 1, 2, 3, 5, 8, 5, 3, 13, 8, 5, 3. The missing section (2, 1, 1, 2, 3, 5, 8) is later filled in during the second verse. The time signatures of the chorus change from 9/8 to 8/8 to 7/8; as drummer Danny Carey says, "It was originally titled 9-8-7. For the time signatures. Then it turned out that 987 was the 16th number of the Fibonacci sequence. So that was cool."
• Ernő Lendvaï analyzes Béla Bartók's works as being based on two opposing systems, that of the golden ratio and the acoustic scale. In the third movement of Bartok's Music for Strings, Percussion and Celesta, the opening xylophone passage uses Fibonacci rhythm as such: 1:1:2:3:5:8:5:3:2:1:1.
• The Fibonacci numbers are also apparent in the organisation of the sections in the music of Debussy's Image, Reflections in Water, in which the sequence of keys is marked out by the intervals 34, 21, 13 and 8.
• Polish composer Krzysztof Meyer structured the values in his Trio for clarinet, cello and piano according to the Fibonacci sequence.
• American musician BT also recorded a song titled Fibonacci Sequence. The narrator in the song goes through all the numbers of the sequence from 1 to 21 (0 is not mentioned). The track appeared on a limited edition version of his 1999 album Movement in Still Life, and is also featured on the second disc of the Global Underground 013: Ibiza compilation mixed by Sasha.
• Voiceover and recording artist, Ken Nordine described Fibonacci numbers in a word jazz piece called Fibonacci Numbers on his album A Transparent Mask.
• American musician Doctor Steel has a song titled "Fibonacci Sequence" on his album People of Earth.

Visual arts

Martina Schettina: Fibonaccis Dream, 2008, 40 x 40 cm

• Artist Mario Merz made the Fibonacci sequence a recurring theme in his work. Examples are the Chimney of Turku Energia, in Turku, Finland, featuring the start of the Fibonacci sequence in 2m high neon lights, and the the representation of the first Fibonacci numbers with red neon lights on one of the four-faced dome of the Mole Antonelliana in Turin, Italy, part of the artistic work Il volo dei Numeri ("Flight of the numbers").
• Fibonacci numbers have also been used in knitting to create aesthetically appealing patterns.
• The artist Martina Schettina uses Fibonacci numbers in her paintings. Her "Mathemagic paintings" were shown at the Museumsquartier Vienna in 2010.

Television

• The scientist character Walter Bishop in the television show Fringe recites the Fibonacci sequence to fall asleep. It is later revealed to be the key sequence identifying a series of safe deposit boxes he had maintained.
• Square One Television's Mathnet series had a storyline that featured a parrot belonging to a deceased individual who was fascinated by the Fibonacci numbers. When "1, 1, 2, 3" is said in the parrot's presence, it responds "5, eureka!" This proves to be the key to case; tiles in a garden wall are found to follow the Fibonacci sequence, with a secret compartment hidden behind the lone misplaced tile.
• The Criminal Minds episode "Masterpiece" in season 4 features a serial killer who uses Fibonacci sequences to choose both the amount of victims at a given time and the location of their hometowns.
• Aliens use Fibonacci's sequence in the Taken episode "God's Equation".
• In the Disney Channel T.V. show So Weird, The Fibonacci sequence is used to build a house. The house becomes a nexus for lost spirits, Fiona is given a choice to use it to free her father as well as the builder of the house, but ultimately chooses to free the spirits and destroys the nexus.
• The Fibonacci sequence is a main plot theme in the 2012 television show, Touch, produced by Fox Network and starring Kiefer Sutherland.

See also

• Numerology

External links

• Subhash Kak, The Golden Mean and the Physics of Aesthetics, Archive of Physics, (2004).
• Math for Poets and Drummers – Rachael Hall surveys rhythm and Fibonacci numbers and also the Hemachandra connection. Saint Joseph's University, 2005.
• Rachel Hall, Hemachandra's application to Sanskrit poetry, (undated; 2005 or earlier).
• Fibonacci Numbers and The Golden Section in Art, Architecture and Music, which lists a number of academic sources.