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Fibonacci numbers in popular culture

From Wikipedia, the free encyclopedia

The Fibonacci numbers are a sequence of integers, starting with 0, 1 and continuing 1, 2, 3, 5, 8, 13, ..., each new number being the sum of the previous two. The Fibonacci numbers, often presented in conjunction with 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.

YouTube Encyclopedic

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  • Doodling in Math: Spirals, Fibonacci, and Being a Plant [1 of 3]
  • The Fibonacci Sequence: Nature's Code
  • Flat Earth Symbolism, And The Fallen Angels Have Always Run The Illuminati 7
  • Doodling in Math: Spirals, Fibonacci, and Being a Plant [Part 3 of 3]
  • Doodling in Math Class: Spirals, Fibonacci, and Being a Plant [2 of 3]

Transcription

Voiceover:Say [unintelligible], you're in math class and your teacher's talking about ... Well, who knows what your teacher's talking about. Probably a good time to start doodling. And you're feeling spirally today, so yeah. Oh, and because of overcrowding in your school, your math class is taking place in greenhouse number three. Plants. Anyway. You've decided there are three basic types of spirals. There's the kind where, as you spiral out, you keep the same distance. Or you could start big but make it tighter and tighter as you go around, in which case the spiral ends. Or you could start tight but make the spiral bigger as you go out. The first kind is good if you really want to fill up a page with lines. Or if you want to draw curled up snakes. You can start with a wonky shape to spiral around but you've noticed that, as you spiral out, it gets rounder and rounder. Probably something to do with how the ratio between two different numbers approaches one as you repeatedly add the same number to both. But you can bring the wonk back by exaggerating the bumps and it gets all optical illusiony. Anyway, you're not sure what the second kind of spiral is good for, but I guess it's a good way to draw snuggled up slug cats, which are a species you've invented just to keep this kind of spiral from feeling useless. This third spiral, however, is good for all sorts of things. You could draw a snail or a nautilus shell. And elephant with a curled up trunk, the horns of a sheep, a fern frond, a cochlea in an inner ear diagram, an ear itself. Those other spirals can't help but be jealous of this clearly superior kind of spiral. But I draw more slug cats. Here's one way to draw a really perfect spiral. Start with one square and draw another next to it that is the same height. Make the next square fit next to both together, that is each side is length two. The next square has length three. The entire outside shape will always be a rectangle. Keep spiraling around, adding bigger and bigger squares. This one has side length one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13. And now 21. Once you do that you can add a curve going through each square, arcing from one corner to the opposite corner. Resist the urge to zip quickly across the diagonal, if you want a nice smooth spiral. Have you ever looked at the spirally pattern on a pine cone and thought, "Hey, sure are "spirals on this pine cone?" I don't know why there's pine cones in your greenhouse. Maybe the greenhouse is in a forest. Anyway, there's spirals and there's not just one either. There's one, two, three, four, five, six, seven, eight going this way. Or you could look at the spirals going the other way and there's one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13. Look familiar? Eight and 13 are both numbers in the Fibonacci series. That's the one where you start by adding one and one to get two, then one and two to get three, two and three to get five. Three plus five is eight, five plus eight is 13, and so on. Some people think that instead of starting with one plus one you should start with zero and one. Zero plus one is one, one plus one is two, one plus two and three, and it continues on the same way as starting with one and one. Or, I guess you could start with one plus zero and that would work too. Or why not go back one more to negative one and so on? Anyway, if you're into the Fibonacci series, you probably have a bunch memorized. I mean, you've got to know one, one, two, three, five. Finish off the single digits with eight and, ooh with 13, how spooky. And once you're memorizing double digits, you might as well know 21, 34, 55, 89 so that whenever someone turns a Fibonacci number you can say, "Happy Fib Birthday." And then, isn't it interesting that 144, 233, 377? But 610 breaks that pattern, so you'd better know that one too. And oh my goodness, 987 is a neat number and, well, you see how these things get out of hand. Anyway, 'tis the season for decorative scented pine cones and if you're putting glitter glue spirals on your pine cones during math class, you might notice that the number of spirals are five and eight or three and five or three and five again. Five and eight. This one was eight and thirteen and one Fibonacci pine cone is one thing, but all of them? What is up with that? This pine cone has this wumpy weird part. Maybe that messes it up. Let's count the top. Five and eight. Now let's check out the bottom. Eight and 13. If you wanted to draw a mathematically realistic pine cone, you might start by drawing five spirals one way and eight going the other. I'm going to mark out starting and ending points for my spirals first as a guide and then draw the arms. Eight one way and five the other. Now I can fill in the little pine coney things. So there's Fibonacci numbers in pine cones but are there Fibonacci numbers in other things that start with pine? Let's count the spirals on this thing. One, two, three, four, five, six, seven, eight. And one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13. The leaves are hard to keep track of, but they're in spirals too. Of Fibonacci numbers. What if we looked at these really tight spirals going almost straight up? One, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21. A Fibonacci number. Can we find a third spiral on this pine cone? Sure, go down like this. And one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13 (muttering) 19, 20, 21. But that's only a couple examples. How about this thing I found on the side of the road? I don't know what it is. It probably starts with pine, though. Five and eight. Let's see how far the conspiracy goes. What else has spirals in it? This artichoke has five and eight. So does this artichoke looking flower thing. And this cactus fruit does too. Here's an orange cauliflower with five and eight and a green one with five and eight. I mean, five and eight. Oh, it's actually five and eight. Maybe plants just like these numbers though. Doesn't mean it has anything to do with Fibonacci, does it? So let's go for some higher numbers. We're going to need some flowers. I think this is a flower. It's got 13 and 21. These daisies are hard to count, but they have 21 and 34. Now let's bring in the big guns. One, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34. And one, two, three, four, five, six, seven, eight, nine, 10, 11, (muttering) 17, 24, (muttering) 42, 53, 54, 55. I promise, this is a random flower and I didn't pick it out specially to trick you into thinking there's Fibonacci numbers in things, but you should really count for yourself next time you see something spirally. There's even Fibonacci numbers in how the leaves are arranged on this stalk, or this one, or the Brussels sprouts on this stalk are a beautiful delicious three and five. Fibonacci is even in the arrangement of the petals on this rose, and sunflowers have shown Fibonacci numbers as high as 144. It seems pretty cosmic and wondrous, but the cool thing about the Fibonacci series and spiral is not that it's this big complicated mystical magical super math thing beyond the comprehension of our puny human minds that shows up mysteriously everywhere. We'll find that these numbers aren't weird at all. In fact, it would be weird if they weren't there. The cool thing about it is that these incredibly intricate patterns can result from utterly simple beginnings.

Architecture

Cinema

  • In The Phantom Tollbooth (1970), Milo (Butch Patrick) is given a set of numbers to identify in order to gain entry to the "Numbers Mine", and correctly answers noting that it is the Fibonacci sequence.
  • Along with the golden rectangle and golden spiral, the Fibonacci sequence is mentioned in Darren Aronofsky's independent film Pi (1998). They are used to find the name of God.
  • In The Da Vinci Code (2006), 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 L: Change the World (2008), Near is seen arranging sugar cubes in a Fibonacci sequence.
  • In 21 (2008), the first seven numbers in the Fibonacci Sequence are drawn in icing on Ben's (Jim Sturgess) birthday cake. The 8th term, 21, is left out. Ben and Miles (Josh Gad) quickly figure it out.
  • In Nymphomaniac (2013), the character Seligman (Stellan Skarsgård) notes that when Joe (Charlotte Gainsbourg) loses her virginity, the boy who deflowers her does so in a sequence of thrusts that are Fibonacci numbers.
  • In Arrival (2016), character Ian Donnelly (Jeremy Renner) checks if the aliens have communicated with humans in any of the following approaches: "shapes, patterns, numbers, fibonacci".

Comic strips

  • In the February 8, 2009, edition 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 a strip of Frazz by Jef Mallett, Frazz and a student are discussing her knitted hat. The student says, "Mom sewed one sparkly here and here. Two sparklies here. Three sparklies. Five sparklies. Eight sparklies. Thirteen..." To which Frazz replies, "Fibonacci sequins, of course."

Finance

Human development

John Waskom postulated that stages of human development followed the Fibonacci sequence, and that the unfolding psychology of human life would ideally be a "living proof" of the Golden Mean. This theory was originally developed and published by Norman Rose in two articles. The first article, which laid out the general theory, was entitled "Design and Development of Wholeness: Waskom's Paradigm."[3] The second article laid out the applications and implications of the theory to the topic of moral development, and was entitled "Moral Development: The Experiential Perspective."[4]

Literature

  • The Fibonacci sequence plays a small part in Dan Brown's bestselling novel (and film) The Da Vinci Code.
  • 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.
  • It was briefly included (and recognized by Charles Wallace Murry) 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.
  • A youthful Fibonacci is one of the main characters in the novel Crusade in Jeans (1973). He was left out of the 2006 movie version, however.
  • 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.
  • The Rabbit Problem is also described in Marina Lewycka's book Various Pets Alive and Dead.
  • Ice Station (1998), a novel by Australian writer Matthew Reilly, involves a partially completed access code, the remaining numbers of which can only be found by extrapolating a Fibonacci pattern.
  • The Fibonacci sequence is used by a serial killer to attract the protagonist Special Agent Pendergast in the Douglas Preston/Lincoln Child novel Two Graves (2012).
  • Eleanor Catton's novel The Luminaries (2013), winner of the 2013 Man Booker Prize, is structured around an inverse Fibonacci sequence, with each part of the book half the length of the one preceding it.

Music

Roll Karti Jaise Barrel
Fibonacci Wala Spiral
[When you twerk, you roll as a barrel. As if tracing out a Fibonacci's Spiral.]

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, 13, 13, 8, 5, 3. The missing section (2, 1, 1, 2, 3, 5, 8) is later filled in during the second verse.[5][6] 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."[7]
Fibonacci intervals (counting in semitones) in Bartók's Sonata for Two Pianos and Percussion, 3rd mov. (1937).[8] Playⓘ
  • Ernő Lendvai analyzes Béla Bartók's works as being based on two opposing systems, that of the golden ratio and the acoustic scale.[9] In the third movement of Bartók'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.[10]
  • The Fibonacci numbers are also apparent in the organisation of the sections in the music of Claude Debussy's Image, Reflections in Water, in which the sequence of keys is marked out by the intervals 34, 21, 13 and 8.[10]
  • Italian composer and mathematical-physicist Matteo Sommacal wrote in 2002 the eight-movement suite Fibonacci's Piranhas,[11][12] for piano 4, 5 and 6 hands, which makes an extensive use of the Fibonacci numbers for deriving and developing the whole melodic, rhythmic and harmonic structure of the piece.[13]
  • Polish composer Krzysztof Meyer structured the values in his Trio for clarinet, cello and piano according to the Fibonacci sequence.[14]
  • Fibonacci's name was adopted by a Los Angeles-based art rock group The Fibonaccis, that recorded from 1981 to 1987.
  • 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.[15]
  • Voiceover and recording artist Ken Nordine described Fibonacci numbers in a word jazz piece called "Fibonacci Numbers" on his album A Transparent Mask.[16]
  • Australian electronic group Angelspit uses the Fibonacci in the song "Vermin". The lyrics start with, "1, 2 3 5 8, Who do we decapitate?" and continues through a few more iterations of the sequence.
  • Avant garde composer Elliott Sharp used Fibonacci numbers in his compositions.[17]
  • Fred Frith composed an instrumental "Ruins" for the avant-rock group Henry Cow using Fibonacci numbers to establish beat and harmony.[18]
  • Composer Dave Soldier's opera with Komar and Melamid, Naked Revolution, contains a soprano aria titled "Sing of Nature, Sing of Numbers" with lyrics and music based on the Fibonacci series, sung in character by Isadora Duncan.
  • In 2001, American musician Doctor Steel recorded the song "Fibonacci Sequence" from the album People of Earth.[19]
  • In 2018, shortly before his death, Russian hip hop artist Detsl recorded the song "Fibonacci" (in English)[20]

Visual arts

Martina Schettina: Fibonaccis Dream, 2008, 40 x 40 cm
Petra Paffenholz: Fibonacci Cubes, 2014, 10 cm to 6.8 m[21]
  • Artist Mario Merz made the Fibonacci sequence a recurring theme in his work.[22] Examples are the Chimney of Turku Energia, in Turku, Finland, featuring the start of the Fibonacci sequence in 2 m high neon lights, and the representation of the first Fibonacci numbers with red neon lights on one face 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.[23]
  • The artist Martina Schettina uses Fibonacci numbers in her paintings.[24][25] Her Mathemagic paintings were shown at the Museumsquartier Vienna in 2010.[26]
  • Visual artist Marisa Ferreira used the Fibonacci numeral sequence to create the geometric shapes of her piece Rear Window, installed from February to August 2015 on the façade of Oslo Central Station, Norway. The artist used the sequence to express the walking pattern and rhythm of footsteps of pedestrian traffic in and out of the station.[27]
  • Grace DeGennaro uses the Fibonacci sequence to accumulate the intricate patterns of dots in her paintings "to create a visible record of time."[28]
  • German artist and architect Claus Bury used the Fibonacci numeral sequence in his sculptural projects.[29]

Television

  • Fibonacci numbers appear in the series The Good Place, first in the main character Eleanor's horoscope on the day she dies and as the area code on the afterlife's neighborhood.
  • 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 solving the 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 number of victims he kills at a given time, as well as the location of their hometowns.
  • Aliens use Fibonacci's sequence in the Taken episode "God's Equation".
  • In the Disney Channel TV show So Weird, the Fibonacci sequence is used to build a house. The house becomes a nexus for lost spirits. One character, 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. It revolves around a number sequence 318 5296 3287 9.5 22 975 6 1188 1604 55124... and on. These numbers are calculated from using the Fibonacci sequence in some way to reveal patterns in both natural and artificial systems, essentially allowing the characters to predict the future.
  • In the CBS show Numb3rs episode "Thirteen", a Fibonacci sequence is embedded in a numeric code left behind by a serial killer.
  • On the animated TV show Adventure Time, the sequence of 8, 13, 21, is shown on the back of the Enchiridion in certain episodes.
  • In the Cartoon Network special The Powerpuff Girls: Dance Pantsed, one of the kidnapping victims is named Fibonacci Sequins (voiced by Ringo Starr).
  • In episode 11 of the Japanese anime series Aguu: Tensai Ningyou, a Fibonacci sequence is rapidly fired back-and-forth in a battle of wits between two archenemies.
  • In episode 14 of the Japanese anime adaptation of Banana Fish, the Fibonacci sequence is mentioned during an IQ test.

References

  1. ^ Smith, Peter (December 2007). Sustainability at the Cutting Edge, Second Edition: Emerging Technologies for low energy buildings. Elsevier. p. 151. ISBN 978-0-7506-8300-5.
  2. ^ The Engineer, "Eden Project gets into flower power"[permanent dead link].
  3. ^ The Educational Forum, 55, 3 (Spring 1991), 243-259 http://whizkidz.org/design/DevelopmentDesign.pdf)
  4. ^ Journal of Moral Education, 21, 1 (Winter, 1992), 29-40 http://whizkidz.org/design/MoralDevelopment.pdf
  5. ^ Di Carlo, Christopher (2001). "Interview with Maynard James Keenan". Archived from the original on 2013-01-12. Retrieved 2007-05-22.
  6. ^ . An exposition of how the fibonacci sequence appears in Lateralus set to pictures from the Hubble telescope: https://www.youtube.com/watch?v=wS7CZIJVxFY
  7. ^ Norris, Chris (2001). "Hammer Of The Gods". Archived from the original on 2011-11-01. Retrieved 2007-04-25.
  8. ^ Maconie, Robin (2005). Other Planets, 26 & 28. ISBN 0-8108-5356-6. Citing Lendvai (1972). "Einführung in die Formen- und Harmonienwelt Bartóks" (1953), Béla Bartók: Weg und Werk, p.105-49. Bence Szabolcsi, ed.
  9. ^ *Lendvai, Ernő (1971). Béla Bartók: An Analysis of his Music. introd. by Alan Bush. London: Kahn & Averill. ISBN 0-900707-04-6. OCLC 240301.
  10. ^ a b Smith, Peter F. The Dynamics of Delight: Architecture and Aesthetics (New York: Routledge, 2003) p. 83, ISBN 0-415-30010-X
  11. ^ M. Sommacal, Fibonacci's Piranhas - 5th Movement, performed by Valeria Di Matteo
  12. ^ M. Sommacal, Fibonacci's Piranhas - 5th Movement, performed by Taglieri Genitoni Duo, live recording, "Concerti e Colline", Nizza Monferrato, 31 January 2012
  13. ^ M.G. Ortore, "Musica, Fisica e Matematica: intervista a Matteo Sommacal", Ticonzero, Article 61, April 2015, ISSN 2420-8442
  14. ^ Weselmann, Thomas (2003) Musica incrostata. Poznan
  15. ^ BT - Fibonacci Sequence on YouTube
  16. ^ Fibonacci Numbers: Ken Nordine at Amazon.com.
  17. ^ Ambrose, P. Elliott Sharp's Instrumental Vision The Morning News, October 4, 2005
  18. ^ Romano, Will (2014). Prog Rock FAQ: All That's Left To Know About Rock's Most Progressive Music (e-book ed.). Milwaukee, Wisconsin: Backbeat Books. p. 315. ISBN 978-1-61713-587-3.
  19. ^ Doctor Steel's Fibonacci Sequence on YouTube
  20. ^ Detsl aka Le Truk - Fibonacci on YouTube
  21. ^ "FIBONACCI CUBES". PETRA PAFFENHOLZ. Retrieved 15 July 2017.
  22. ^ "Obituary: Mario Merz". The Guardian. London. 2003-11-13. Retrieved 2008-09-14.
  23. ^ "Fibonacci Accessories: Scarf". Archived from the original on 2007-12-22. Retrieved 2007-12-31.
  24. ^ Ingmar Lehman: „Fibonacci-numbers in visual arts and literature" (German)(last called on November 7, 2009)
  25. ^ 2009: Martina Schettina:Mathemagische Bilder - Bilder und Texte. Vernissage Verlag Brod Media, Wien 2009, ISBN 978-3-200-01743-6 (German)
  26. ^ About the exhibition, interview on Radio Ö1 Archived 2011-06-05 at the Wayback Machine(recalled at February 28, 2010)
  27. ^ "Rear Window 2015". Marisa Ferreira. Retrieved 6 June 2015.
  28. ^ Friedman, Samantha (June 2009). "Patterning: Selections from the Kentler Flatfiles". Kentler International Drawing Space. Retrieved December 23, 2018.
  29. ^ Posamentier, Alfred S.; Lehmann, Ingmar (2010-12-30). The Fabulous Fibonacci Numbers. Prometheus Books. ISBN 978-1-61592-022-8.

External links

This page was last edited on 10 April 2024, at 20:18
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