Fibonacci
Portrait by unknown artist
Born	c. 1170
Died	c. 1250 (aged around 80)
Nationality	Italian
Fields	Mathematician
Known for	Fibonacci number Fibonacci prime Brahmagupta–Fibonacci identity Fibonacci polynomials Fibonacci pseudoprime Fibonacci word Reciprocal Fibonacci constant Introduction of digital notation to Europe Pisano period Practical number

Leonardo Pisano Bigollo (c. 1170 – c. 1250)^[1] also known as Leonardo of Pisa, Leonardo Pisano, Leonardo Bonacci, Leonardo Fibonacci, or, most commonly, simply Fibonacci, was an Italian mathematician, considered by some "the most talented western mathematician of the Middle Ages."^[2]

Fibonacci is best known to the modern world for ^[3] the spreading of the Hindu–Arabic numeral system in Europe, primarily through the publication in 1202 of his Liber Abaci (Book of Calculation), and for a number sequence named the Fibonacci numbers after him, which he did not discover but used as an example in the Liber Abaci.^[4]

Life[link]

Leonardo Fibonacci was born around 1170 to Guglielmo Bonacci, a wealthy Italian merchant. Guglielmo directed a trading post (by some accounts he was the consultant for Pisa) in Bugia, a port east of Algiers in the Almohad dynasty's sultanate in North Africa (now Bejaia, Algeria). As a young boy, Leonardo traveled with him to help; it was there he learned about the Hindu–Arabic numeral system.^[5]

Recognizing that arithmetic with Hindu–Arabic numerals is simpler and more efficient than with Roman numerals, Fibonacci traveled throughout the Mediterranean world to study under the leading Arab mathematicians of the time. Leonardo returned from his travels around 1200. In 1202, at age 32, he published what he had learned in Liber Abaci (Book of Abacus or Book of Calculation), and thereby popularized Hindu–Arabic numerals in Europe.

Leonardo became an amicable guest of the Emperor Frederick II, who enjoyed mathematics and science. In 1240 the Republic of Pisa honored Leonardo, referred to as Leonardo Bigollo,^[6] by granting him a salary.

In the 19th century, a statue of Fibonacci was constructed and erected in Pisa. Today it is located in the western gallery of the Camposanto, historical cemetery on the Piazza dei Miracoli.^[7]

[edit] Liber Abaci

In the Liber Abaci (1202), Fibonacci introduces the so-called modus Indorum (method of the Indians), today known as Arabic numerals (Sigler 2003; Grimm 1973). The book advocated numeration with the digits 0–9 and place value. The book showed the practical importance of the new numeral system, using lattice multiplication and Egyptian fractions, by applying it to commercial bookkeeping, conversion of weights and measures, the calculation of interest, money-changing, and other applications. The book was well received throughout educated Europe and had a profound impact on European thought.

Fibonacci sequence[link]

Liber Abaci also posed, and solved, a problem involving the growth of a population of rabbits based on idealized assumptions. The solution, generation by generation, was a sequence of numbers later known as Fibonacci numbers. The number sequence was known to Indian mathematicians as early as the 6th century,^[8][9][10] but it was Fibonacci's Liber Abaci that introduced it to the West.

In the Fibonacci sequence of numbers, each number is the sum of the previous two numbers, starting with 0 and 1. This sequence begins 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 ... ^[11]

The higher up in the sequence, the closer two consecutive "Fibonacci numbers" of the sequence divided by each other will approach the golden ratio (approximately 1 : 1.618 or 0.618 : 1).

In popular culture[link]

• Fibonacci's name was adopted by a Los Angeles-based art rock group, The Fibonaccis, that recorded from 1981 to 1987.
• Stock traders frequently look to the "Fibonacci retracement" when predicting future share prices.
• 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.

19th century statue of Fibonacci in Camposanto, Pisa.

Bibliography[link]

Fibonacci wrote the following books:

• Liber Abaci (1202), a book on calculations (English translation by Laurence Sigler, Springer, 2002)
• Practica Geometriae (1220), a compendium on geometry and trigonometry.
• Flos (1225), solutions to problems posed by Johannes of Palermo
• Liber quadratorum, ("The Book of Squares") on Diophantine equations, dedicated to Emperor Frederick II. See in particular the Brahmagupta–Fibonacci identity.
• Di minor guisa (on commercial arithmetic; lost)
• Commentary on Book X of Euclid's Elements (lost)

See also[link]

• List of topics named after Fibonacci
• Brahmagupta–Fibonacci identity
• Elliott wave principle
• Engel expansion
• Fibonacci search technique
• Golden ratio
• Hylomorphism (computer science)
• Pisano period
• Practical number
• Primefree sequence
• Verner Emil Hoggatt, Jr.

Notes[link]

References[link]

• Goetzmann, William N. and Rouwenhorst, K.Geert, The Origins of Value: The Financial Innovations That Created Modern Capital Markets (2005, Oxford University Press Inc, USA), ISBN 0-19-517571-9.
• Grimm, R. E., "The Autobiography of Leonardo Pisano", Fibonacci Quarterly, Vol. 11, No. 1, February 1973, pp. 99–104.
• A. F. Horadam, "Eight hundred years young," The Australian Mathematics Teacher 31 (1975) 123-134.

External links[link]

• Fibonacci Biography
• Who was Fibonacci? by Ron Knott.
• Goetzmann, William N., Fibonacci and the Financial Revolution (October 23, 2003), Yale School of Management International Center for Finance Working Paper No. 03-28
• Fibonacci at Convergence
• O'Connor, John J.; Robertson, Edmund F., "Leonardo Pisano Fibonacci", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Fibonacci.html .

This article's factual accuracy is disputed. Please help to ensure that disputed facts are reliably sourced. See the relevant discussion on the talk page. (December 2011)

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Keith J. Devlin
Keith Devlin (2011)
Born	East Hull, England
Nationality	English and American
Fields	Mathematics
Institutions	Stanford University, Kings College London, University of Bristol, University of Manchester, University of Aberdeen, University of Oslo, University of Heidelberg, University of Bonn, University of Toronto, University of Lancaster, Colby College, St. Mary's College of California
Alma mater	Kings College London, University of Bristol
Doctoral advisor	Frederick Rowbottom[1]

Keith J. Devlin is a British mathematician and popular science writer. He has lived in the United States since 1987 and has dual American-British citizenship.

Biography[link]

Devlin earned a B.Sc. (Special) in Mathematics at Kings College London and a Ph.D. in Mathematics at the University of Bristol under the supervision of Frederick Rowbottom.^[1] He is co-founder and Executive Director of Stanford University's Human-Sciences and Technologies Advanced Research Institute (H-STAR), a co-founder of Stanford Media X university-industry research partnership program, and a Senior Researcher in the Center for the Study of Language and Information (CSLI). He is a commentator on National Public Radio's Weekend Edition Saturday, where he is known as "The Math Guy."^[2]

As of 2011, he is the author of 31 books and over 80 research articles.^[3] Several of his books are aimed at an audience of the general public, as opposed to much academic work.

His recent research work has focused on the development of new tools and protocols to assist intelligence analysis and the development and use of videogames in mathematics education.

Devlin is also creator of the concept "soft mathematics," introduced in the final chapter of his book Goodbye, Descartes.

Research publications[link]

• Devlin, Keith I.; Jensen, R. Björn (1975), "Marginalia to a theorem of Silver", ISILC Logic Conference (Proc. Internat. Summer Inst. and Logic Colloq., Kiel, 1974), Lecture notes in mathematics, 499, Berlin, New York: Springer-Verlag, pp. 115–142, DOI:10.1007/BFb0079419, ISBN 978-3-540-07534-9, MR 0480036, http://books.google.com/books?id=9UHU_bq-wc8C&dq=Marginalia+to+a+theorem+of+Silver  [First proof of Jensen's covering theorem; Keith J. Devlin is credited as Keith I. Devlin in the paper.]

List of books[link]

This list is incomplete; you can help by expanding it.

• Mathematics Education for a New Era: Video Games as a Medium for Learning. A K Peters. 2011. ISBN 978-1-56881-431-5. 
• The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern. Basic Books. 2008. ISBN 978-0-465-00910-7. 
• The Numbers Behind NUMB3RS: Solving Crime with Mathematics. Plume. 2007. ISBN 0-452-28857-6.  with coauthor Gary Lorden
• The Math Instinct: Why You're a Mathematical Genius (Along with Lobsters, Birds, Cats, and Dogs). Thunder's Mouth Press. 2006. ISBN 1-56025-839-X. 
• The Millennium Problems: the Seven Greatest Unsolved Mathematical Puzzles of Our Time. Basic Books. 2002. ISBN 0-465-01730-4. 
• The Math Gene: How Mathematical Thinking Evolved and Why Numbers Are Like Gossip. Basic Books. 2000. ISBN 0-465-01619-7. 
• Mathematics: The New Golden Age. Columbia University Press. 1999. ISBN 0-231-11639-X. 
• The Language of Mathematics: Making the Invisible Visible. Holt Paperbacks. 1998. ISBN 0-8050-7254-3. 
• Mathematics: The Science of Patterns. Holt Paperbacks. 1996. ISBN 0-8050-7344-2. 
• The Joy of Sets: Fundamentals of Contemporary Set Theory. Springer. 1993. ISBN 0-387-94094-4. 
• Logic and Information. Cambridge University Press. 1991. ISBN 0-521-49971-2. 
• Constructibility. Springer. 1984. ISBN 3-540-13258-9. 
• The Man of Numbers: Fibonacci's Arithmetic Revolution. Walker Publishing Co. 2011. ISBN 978-0-8027-7812-3. 

Awards[link]

• Joint Policy Board for Mathematics Communications Award^[4]
• In 2007 he received Wonderfest's Carl Sagan Prize for Science Popularization.^[5]
• 2004 International Pythagoras Prize in Mathematics, in the category Best Expository Text in the Mathematical Sciences for the Italian translation of The Millennium Problems^[6]

References[link]

1. ^ ^{a b} Devlin, K. (1973). "Some weak versions of large cardinal axioms". Annals of Mathematical Logic 5 (4): 291–325. DOI:10.1016/0003-4843(73)90010-7.  edit
2. ^ Archive of The Math Guy series from NPR's Weekend Edition accessed 2007-11-09
3. ^ http://www.stanford.edu/~kdevlin/
4. ^ Keith Devlin at Stanford University
5. ^ "Sagan Prize Recipients". wonderfest.org. 2011 [last update]. http://wonderfest.org/sagan-prize/sagan-prize-recipients/. Retrieved 10 September 2011. 
6. ^ Stanford Report—2 November 2005

External links[link]

• Official website including his curriculum vitae
• Devlin's Angle — column at the Mathematical Association of America
• Radio interview on Philosophy Talk
• The Unfinished Game, Google Authors talk, 9 October 2008.
• Keith Devlin at the Mathematics Genealogy Project

Doctor Steel
Doctor Steel with his robot band
Background information
Birth name	Unknown
Origin	Los Angeles, California, U.S.
Genres	Steampunk, Industrial, Hip-Hop, Electronic, Jazz, Alternative
Occupations	Singer songwriter, Internet Personality
Instruments	Singing, Accordion
Years active	1999 - 2011
Labels	Self-published

Doctor Steel (full name, Doctor Phineas Waldolf Steel), was a self-published American musician and internet personality located in Southern California, prominent in the Dieselpunk, Steampunk, Goth, and Rivethead scenes. He performed on rare occasions with a "backup band", claiming that a fictitious robot band had malfunctioned. Shows incorporated puppetry, multimedia and performances by female members ("Nurses" and "Scouts") of his street team, The Army of Toy Soldiers. Steel had begun to break into the mainstream media, having made a brief appearance on the Tonight Show,^[1] been interviewed by Suicide Girls^[2] as well as numerous genre magazines and podcasts^{[3][4][5][6][7][8][9]} and been the subject of an article in Wired Magazine regarding allegations that Dr. Horrible had copied his style.^[10] Steel has frequently been cited as an archetypal example of Steampunk music.^{[11][12][13][14]}

Musical career[link]

Steel began publicly performing in 1999, essentially busking on the streets of Los Angeles. A few years later, he began performing at venues like The Key Club and the CIA. His live shows combined music with puppetry and video projection that reflect the stories and meanings of the songs.^[4]

In 2001 and 2002, the albums Dr. Steel (2001),^[15] Dr. Steel II: Eclectic Boogaloo (2001),^[16] and People of Earth (2002)^[17] were released digitally to iTunes, Amazon and other stores. The Dr. Steel Collection (2004)^[18] was the first CD release, featuring many tracks which were released on other albums, slightly altered. The Dr. Steel Collection also features the track "Land of the Lost," about the 1970s version of the show by the same name. Some attempts were made to get the song into the soundtrack of 2009 movie version of Land of the Lost, but they were unsuccessful.

Steel's second CD release was The Dr. Steel Read-A-Long album (2006).^[19] It was a limited distribution and quickly sold out. The album art included a recreation of the sleeve of read-along records, and the disc design resembled that of a vinyl record. In 2007, Steel re-released the first three albums, once again in digital format.

Steel's music can often be heard on a number of steampunk radio broadcasts that stream worldwide, such as The Clockwork Cabaret.^[20] His song "Boogieman Boogie" was also included in a compilation of steampunk music released by Gilded Age Records.^[21]

Musical style[link]

Steel's music is eclectic in genre, often combining the noise and distortion of industrial with aspects of European folk, classical, and even jazz,^[22] as well as hip-hop and opera. Many songs feature samples from vintage public service announcements and educational films, such as Duck and Cover. Rue Morgue Magazine described the sound as "Industrial Hip-Hop Opera".^[3][8][23]

Doctor Steel's 'mad scientist' persona

Steel cited, as some of his musical influences, Igor Stravinsky, Tom Waits, Pink Floyd, Queen, Mike Patton, Nine Inch Nails, Danny Elfman, Beck, and John Zorn.^[24]

Stage persona[link]

On stage, and in all public performances and interviews, Steel maintained the appearance of a mad scientist bent on conquering the world and becoming the future World Emperor. He claimed to be a former toymaker who, in a fit of rage over being fired for creating drastic designs such as babies with buzzsaws for hands,^[25] burned down the factory he worked at and was committed to a psychiatric institution.^[26] This back-story relates that Steel escaped the sanitarium and retreated to a deserted island laboratory, where he became bent on world conquest in order to create a "Utopian Playland" where his toy designs could be enjoyed.^[5][27] As a mad scientist, Steel is obsessed with conspiracy theories,^[28] giant robots,^[29] baking cupcakes and "mind control cookies", and experimenting with hamsters.^[30]

In appearance, Steel drew on the mad scientist archetype, dressing in a white PVC lab coat^[31] (with comically large black buttons), black PVC gloves, black boots, shaved head, sinister goatee,^[32] and antique welder's goggles. When not in his "mad scientist" costume, Steel typically dressed in a very aristocratic neo-Victorian steampunk style,^[14] while still retaining his goggles. He was never seen without the goggles.^[33]

Retirement[link]

In 2010, Dr. Steel announced plans to begin work on a new album, entitled "Toymonger."^[34] However, in July 2011, after a long period of silence from him, it was announced that Doctor Steel had retired from the music industry, and a personal letter from Steel to the current head of the Army of Toy Soldiers in January 2012 confirmed this.^[35] (However, there was no other "official" or public announcement.) The Army of Toy Soldiers have decided to continue on as an organization, switching their focus from promoting the entertainer to promoting the philosophy he presented, such as the importance of creativity and building one's own Utopian Playland.

Promotional videos and web videos[link]

Screencap from Building a Utopian Playland, showing a faux news conference.

Doctor Steel appeared in numerous short videos released on his website and on his YouTube channel. One such is a six minute "propaganda" film called Building a Utopian Playland, which ostensibly outlined his plans for world domination. Another is a series called The Dr. Steel Show, set in his fictitious lab on his fictitious private island. Episode 3, which is the official music video for his song, "Back and Forth", and featured video clips sent in by Toy Soldiers, was showcased on MTV's website as a part of their online video series, Steampunk Infiltrates The Mainstream.^[36] Steel also appeared in a video with fellow internet personality Agamemnon Tiberius Vacuum.

Steel also released what he called "public service announcements" covering philosophical subjects such as transhumanism, freedom of thought, and subjective reality. (As a transhumanist, Dr. Steel has also been interviewed on his views by the Institute for Ethics and Emerging Technologies,^[7] and has even published a paper on the subject.^[37][38]) Finally, the Toy Soldiers Unite website features a series of videos called Ask Dr. Steel, in which Steel himself answers questions asked by Toy Soldiers.^[39] In May 2010, Doctor Steel's videos were featured in one of Veronique Chevalier's Red Velvet Variety Shows.

In May 2010, Dr. Steel released a music video to his song, "Childhood Don't a-Go-Go", directed by Tony Leonardi III.

Controversy[link]

Dr. Horrible's Sing-Along Blog[link]

In 2008, Joss Whedon released a short musical film online entitled Dr. Horrible's Sing-Along Blog. Fans of Steel, and Steel himself,^[40] noted the similarities between Dr. Steel and Dr. Horrible:

• both featured singing mad scientists who produced web videos;
• both had an "Ask Dr. ___" segment;
• the name of the production was similar to the title of one of Steel's albums, Dr. Steel Read-A-Long.

This attracted the attention of national media and was reported in Wired magazine, in which Dr. Horrible co-writer Maurissa Tancharoen responded, "All we have to say on the subject is we've never heard of Dr. Steel before." "There’s room for everyone in this party," she added.^[10]

Army of Toy Soldiers[link]

Example of Steel's "propaganda" artwork, resembling WWII recruitment posters (also illustrative of a fan club uniform)

The "Army of Toy Soldiers" is Steel's fan club (and former street team). The army plays into the Dr. Steel fiction, in that it is allegedly a tool in his plan for global domination. Toy Soldiers have "uniforms" with patches and color schemes, but are encouraged to design their own uniform so long as the required patches and colors are used.

The Toy Soldier Army has three main regiments: Toy Soldiers, Nurses, and Toy Scouts. The Nurse and Scout regiments are reserved for those who are female or identify as female within the Army, whereas people of any gender can be in the Toy Soldier regiment. The Army is further divided into divisions based upon geographical location and on creative interests ("Special Ops"). There are no ranks—all Toy Soldiers are considered equal. However, Toy Soldiers who go "above and beyond" may be awarded the honorary title of "Yellow Jacket" personally by Doctor Steel.

Toy Soldiers promote Dr. Steel's philosophy individually through "missions", while larger group events are known as "operations" or "invasions".^[41] Some Soldiers use their connections and access to the media for promotion, while others may choose to "propagandize" their school or workplace. Toy Soldiers have frequently done charity and volunteer work in uniform or in the name of Dr. Steel, such as starting local clothing or toy drives and even donating to drives such as Toys for Tots and Adopt a Highway. The Toy Soldiers have their own holiday, "Toy Soldier Day,"^[42] which is observed every year on March 4 (a play on "march forth"), and simultaneous invasions of Disney theme parks worldwide take place on the nearest Saturday to this day.^[43] Since 2010, the Toy Soldiers have participated in the Doo Dah Parade in Pasadena, CA^[44][45] and have become "veteran crowd favorites."

Since the announcement of Dr. Steel's retirement, the Army of Toy Soldiers have continued on as an organization dedicated to spreading the philosophy Dr. Steel presented, such as making fun the top priority and striving to achieve one's creative potential.

Promotional material ("Propaganda")[link]

Promotional material for Dr. Steel and the Toy Soldiers is referred to as "propaganda".^[41] The decision to use a term with such charged connotations was a deliberate satirical allusion to famous groups in the past who had plans for world domination,^[6] in order to spotlight or "hang a lampshade"^[46] on the tricks of mass manipulation.^[47] Some of the material was designed and created by Steel himself (such as the "propaganda posters", designed to resemble WWII propaganda posters),^[48] but Steel encouraged his fans to design their own propaganda as well.

References in popular culture[link]

Other than the instances noted above, Dr. Steel, his likeness and members of his fan club occasionally noticeably appear in popular media:

2007

• In the 2007 cult mocumentary, American Zombie, by director Grace Lee,^[49] one of the zombies (Ivan, played by Austin Basis) has several of Dr. Steel's propaganda posters hung in his bedroom. Screencap 1Screencap 2

2009

• During ACTFur On-Air's video coverage of MiDFur 2009, "2, The Ranting Gryphon" was asked if he was related in some way to Dr. Steel, since he bore a resemblance to the Doctor, to which he replied promptly, 'I'm not saying anything'.^[50]

2010

• In the film Battle, by director LaRon Austin,^[51] one of the supporting actresses is shown to be one of Dr. Steel's Toy Scouts (as seen midway through the trailer).

• In the January 12 episode of the hit television show Paranormal State, entitled Darkness Falls, paranormal researcher Eilfie Music is seen wearing a Dr. Steel pin.^[52][53][54]

• In several episodes of Current TV's Viral Video Film School, a Dr. Steel propaganda poster can be seen on the wall just to the left of the speaker.^[55][56]

• Dr. Steel's logo appears in strip 198 (August 18, 2010) of the webcomic Peter Is The Wolf.^[57]

2011

• On June 14, on what they called, "Titanic Takeover Tuesday", hacker group LulzSec launched DDoS attacks on multiple gamer websites.^[58] In response to "butthurt gamers", they cryptically posted a link on their Twitter page the next day to a YouTube recording of Dr. Steel's "Lullabye-Bye."^[59] (Note: Neither Dr. Steel nor the Toy Soldiers condone hacking attacks, and it is against the Terms of Service for the official Toy Soldier fan club website, "Toy Soldiers Unite.")^[60]

Discography[link]

• Dr. Steel (2001)
• Dr. Steel II: Eclectic Boogaloo (2001)
• People of Earth (2002)

See also[link]

• List of YouTube personalities
• Viral video

References[link]

External links[link]

Wikiquote has a collection of quotations related to: Doctor Steel

• Doctor Steel's MySpace
• Doctor Steel's YouTube channel
• Toy Soldiers Unite (Official fan site)
• Doctor Steel at TV Tropes