Fibonacci numbers in popular culture

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

: $,F(0)\; =\; 0;\; F(1)\; =\; 1;\; F(n)\; =\; F(n\; -\; 1)\; +\; F(n\; -\; 2)\; mbox\{\; for\; \}\; n\; >\; 1.$

So after the two initial numbers, each number is the sum of the two preceding numbers:

: $,0,\; 1,\; 1,\; 2,\; 3,\; 5,\; 8,\; 13,\; 21,\; 34,\; dots$

This sequence has appeared many times in popular culture. Fibonacci numbers have been mentioned in novels, films, episodes of television shows, and songs. The numbers have also been used in the creation of music and visual art.

Architecture

* The sequence has been used in the design of a building, the Core, at the Eden Project, near St Austell, Cornwall, England. [cite book |last=Smith |first=Peter |title=Sustainability at the Cutting Edge, Second Edition: Emerging Technologies for low energy buildings |year=2007 |publisher=Elsevier |isbn=0750683007 |pages=p. 151|tle= date=December 2007]

Cinema

* 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" (1998)
* 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 "" (2007), a child sets up marshmallows in the shape of a grid showing a Fibonacci Spiral.
* In "21" (2008), the first eight numbers of the sequence are written in icing on a birthday cake which has twenty-one candles.

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.

Music

* MC Paul Barman structured the rhymes in his song "Enter Pan-Man" according to the Fibonacci sequence.
* BT released a dance song in 2000 entitled "Fibonacci Sequence," which features a sample of a reading of the sequence over a frenetic breakbeat. He also used the Fibonacci sequence as a compositional structure in his 2006 album "This Binary Universe."
* 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. [cite web | author=Di Carlo, Christopher| year=2001| title=Interview with Maynard James Keenan | format=HTML | url=http://www.cdicarlo.com/paper_04maynard.htm | accessdate=2007-05-22] [. An exposition of how the fibonacci sequence appears in Lateralus set to pictures from the Hubble telescope: http://youtube.com/watch?v=wS7CZIJVxFY]
* The ratios of justly tuned octave, fifth, and major and minor sixths are ratios of consecutive Fibonacci numbers.
* Ernő Lendvai analyzes Béla Bartók's works as being based on two opposing systems, that of the golden ratio and the acoustic scale. [*cite book |last=Lendvai |first=Ernő |authorlink=Ernő Lendvai |title=Béla Bartók: An Analysis of his Music |others=introd. by Alan Bush |date=1971 |publisher=Kahn & Averill |location=London |isbn=0900707046 |oclc=240301] 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.Smith, Peter F. "The Dynamics of Delight: Architecture and Aesthetics" (New York: Routledge, 2003) p. 83, ISBN 0-415-30010-X]
* 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.
* American composer Casey Mongoven has developed a style of music characterized by the Fibonacci numbers and the golden ratio.
* Polish composer Krzysztof Meyer structured the values in his "Trio for clarinet, cello and piano" according to the Fibonacci sequence. [Weselmann, Thomas (2003) "Musica incrostata". Poznan]
* A song from the Clock Radio service by They Might Be Giants entitled "Turtle Songs of North America" describes to a fictional Tudlow Turtle whose 'gasping' mating call follows the Fibonacci sequence, causing it to pass out after making as many as 55 or 89 gasps.
* Ima Robot's song "Fibonacci" has lyrics "1, 2, 3, 5, 8, 13, 21.... FIBONACCI!".

Visual arts

* In a FoxTrot comic, Jason and Marcus are playing football. Jason yells, "Hut 0! Hut 1! Hut 1! Hut 2! Hut 3! Hut 5! Hut 8! Hut 13!" Marcus yells, "Is it the Fibonacci sequence?" Jason says, "Correct! Touchdown, Marcus!"
* The Fibonacci sequence is featured in an xkcd comic strip. [cite web|url=http://xkcd.com/289/|title=Alone|accessdate=2008-04-24]
* Marilyn Manson uses the sequence overtly in a watercolor painting entitled "Fibonacci" during his Holy Wood era, which uses bees as focal points. More discreetly, Manson used the sequence in the interior album art of "Antichrist Superstar" in his depiction of "The Vitruvian Man", in the vein of Leonardo DaVinci's work which was also based on the sequence.
* Artist Mario Merz made the Fibonacci sequence a recurring theme in his work. [cite web|url=http://www.guardian.co.uk/news/2003/nov/13/guardianobituaries.italy|title=Obituary: Mario Merz|accessdate=2008-09-14]
* Fibonacci numbers have also been used in knitting to create aesthetically appealing patterns. [cite web|url=http://www.diynetwork.com/diy/na_knitting/article/0,2025,DIY_14141_4956504,00.html|title=Fibonacci Accessories: Scarf|accessdate=2007-12-31]
* In the PLAYSTATION 3 video game , in one of the game's early cutscenes a young girl named Sunny can be heard singing the Fibonacci sequence while cooking eggs.
* In "Fringe" on FOX Television, the September 16, 2008 episode closes with Walter Bishop reciting the Fibonacci sequence while trying to fall asleep.
* In the online game "RuneScape", one of the quests involves entering the first few numbers of the Fibonacci sequence into a safe.

See also

* Golden ratio

References

External links

* Subhash Kak, " [http://uk.arxiv.org/abs/physics/0411195 The Golden Mean and the Physics of Aesthetics] ", Archive of Physics, (2004).
* [http://www.sju.edu/~rhall/Rhythms/Poets/arcadia.pdf Math for Poets and Drummers] - Rachael Hall surveys rhythm and Fibonacci numbers and also the Hemachandra connection. Saint Joseph's University, 2005.
* Rachel Hall, " [http://www.sju.edu/~rhall/Multi/rhythm2.pdf Hemachandra's application to Sanskrit poetry] ", (undated; 2005 or earlier).
* " [http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibInArt.html Fibonacci Numbers and The Golden Section in Art, Architecture and Music] ", which lists a number of academic sources.