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	Fibonacci word - Wikipedia, the free encyclopedia
		The Fibonacci word is a specific infinite sequence of binary digits (or symbols from any two-letter alphabet).
		The word is related to the famous sequence of the same name (the Fibonacci sequence) in the sense that addition of integers in the inductive definition is replaced with string concatenation.
		The Fibonacci word is a famous example of a Sturmian word.
	en.wikipedia.org /wiki/Fibonacci_word (147 words)

	Fibonacci (Site not responding. Last check: 2007-10-14)
		Fibonacci was a contemporary of Jordanus but he was a far more sophisticated mathematician and his achievements were clearly recognised, although it was the practical applications rather than the abstract theorems that made him famous to his contemporaries.
		Fibonacci proves that the root of the equation is neither an integer nor a fraction, nor the square root of a fraction.
		Fibonacci was also the teacher of the "Cossists", who took their name from the word 'causa' which was first used in the West by Fibonacci in place of 'res' or 'radix'.
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Fibonacci.html (1979 words)

	Fibonacci Rabbit
		Fibonacci Rabbit Generator Fibonacci Rabbit Generator, the proposal by..exponential growth is organised by the Fibonacci series.
		The Fibonacci Rabbit sequence - the Golden String Fibonacci numbers leads us directly to the Fibonacci Rabbit sequence, but this time we..this process and is the one we call the the Fibonacci Rabbit sequence or the Golden..explore the non-repeating properties of the Fibonacci Rabbit sequence.
		Fibonacci and Crochet or the Infinite Fibonacci Word or the Fibonacci Rabbit Sequence.
	www.fibonacci-market-scanner.com /fibonacci-pages/Fibonacci-Rabbit.htm (1185 words)

	Fibonacci Sequence Rabbit
		The Rabbit Tree and The Logic of Life's Beginning the perfect balance point of the infinite Fibonacci sequence is evident in the fact..logic governs the family structure of the Rabbit Tree.
		Fibonacci go our thanks for his rabbit problem; and to our readers, thanks..approaches to calculating the Fibonacci sequence use recursion and must calculate..
		The Fibonacci sequence is a recursive sequence where the..nature of the sequence.
	www.fibonacci-market-scanner.com /fibonacci-pages/Fibonacci-Sequence-Rabbit.htm (710 words)

	Fibonacci
		Fibonacci was also known by the nickname "Bigollo", which may be taken to mean loafer, and may have expressed the general lack of interest in the purely theoretical mathematics Fibonacci showed interest in.
		Fibonacci ended his travels in approximately 1200 and settled down in Pisa, where for the next twenty five years he composed a number of texts in which he did important work in number theory and the solution of algebraic equations among other important things.
		Fibonacci did not express his mathematics in the form of equations as is done today, but he did however word them in such a way as to be directly translatable into modern equations: an example from the Liber quadatorum [3, p.
	www.math.rutgers.edu /courses/436/436-s99/Papers1999/oneill.html (2163 words)

	more word origins 8
		Today the word is used to describe the distance a periodic function varies from its central value, and the magnitude of a complex number.
		The French shortened the word to "are" as a name for a measure of land equal to one hundred squre meters.
		The word was introduced to mathematics by J. Sylvester in 1850 to describe a smaller matrix made by eliminating one row and one column from a larger matrix.
	www.pballew.net /arithme8.html (6258 words)

	FIBONACCI
		Fibonacci was probably the greatest genius of number theory during the 2000 years between Diophantus and Fermat.
		Fibonacci, also known as Leonardo of Pisa, was born in Pisa, home of the famous leaning tower (inclined at an angle of 16.5 degrees to the vertical).
		Fibonacci is thought to be a contraction of Filiorm Bonacci ("of the family of Bonacci") or Filius Bonacci ("son of Bonacci").
	faculty.evansville.edu /ck6/bstud/fibo.html (4484 words)

	Data Compression -- Section 3
		While the Fibonacci codes are not asymptotically optimal, they compare well to the Elias codes as long as the number of source messages is not too large.
		Fibonacci codes have the additional attribute of robustness, which manifests itself by the local containment of errors.
		That is, the Fibonacci representation is reversed and 1 is appended.
	www.ics.uci.edu /~dan/pubs/DC-Sec3.html (4346 words)

	Fibonacci (Site not responding. Last check: 2007-10-14)
		Fibonacci treats numbers such as sqrt(10) in the fourth section, both with rational approximations and with geometric constructions.
		Among those included is the calculation of the sides of the pentagon and the decagon from the diameter of circumscribed and inscribed circles; the inverse calculation is also given, as well as that of the sides from the surfaces.
		Fibonacci proved that a congruum must be divisible by 24 and he also showed that for x, c such that x
	alas.matf.bg.ac.yu /~mm97106/math/fibo/standrew.htm (2306 words)

	Fibonacci Numbers, the Golden section and the Golden String
		Fibonacci and the original problem about rabbits where the series first appears, the family trees of cows and bees, the golden ratio and the Fibonacci series, the Fibonacci Spiral and sea shell shapes, branching plants, flower petal and seeds, leaves and petal arrangements, on pineapples and in apples, pine cones and leaf arrangements.
		Here is a brief biography of Fibonacci and his historical achievements in mathematics, and how he helped Europe replace the Roman numeral system with the "algorithms" that we use today.
		These General Fibonacci series are called the G series but the Fibonacci series and Phi again play a prominent role in their mathematical properties.
	www.mcs.surrey.ac.uk /Personal/R.Knott/Fibonacci/fib.html (1912 words)

	Index to On-Line Encyclopedia of Integer Sequences (Site not responding. Last check: 2007-10-14)
		Fibonacci numbers, generalized: (1) A001584 A005189 A006207 A006208 A006209 A006210 A006211 A006603 A006604 A015440 A015441 A015442
		Fibonacci numbers, number of ways to write n as a sum of: A000119, A000121, A013583, A083853, A076739, A080888, A003107, A007000
		Fibonacci word (or binary sequence): A003849, A005614, A003842*, A005713, A036299, A076662
	www.research.att.com /~njas/sequences/Sindx_Fi.html (1393 words)

	The Mathematical Magic of the Fibonacci Numbers
		This page looks at some patterns in the Fibonacci numbers themselves, from the digits in the numbers to their factors and multiples and which are prime numbers.
		We can see this with the Fibonacci numbers too: there are 11 Fibonacci numbers in the range 1-100, but only one in the next 3 ranges of 100 (101-200, 201-300, 301-400) and they get increasingly rarer for large ranges of size 100.
		In other words, we are looking at this formula and explaining it in terms of generations, the original rabbit forming generation 1 and her daughters being generation 2 and so on:
	www.mcs.surrey.ac.uk /Personal/R.Knott/Fibonacci/fibmaths.html (12257 words)

	Evolution discussion (Site not responding. Last check: 2007-10-14)
		Charles Darwin did not avoid using the word because he did not want to offend and incite the religious majority of his day.
		Leonardo Fibonacci (circa 1200) recognized this progression of numbers in a study of rabbit population growth.
		They form the beginning of the so-called Fibonacci series, in which each number is the sum of the two that precede it.
	bcornet.homestead.com /files/evolution_discussion.htm (4798 words)

	Online 1911 Encyclopedia Britannica
		With over 44 million words, we know you will find this text as enriching and exciting as we do!
		LEATHER (a word which appears in all Teutonic l...
		LEG (a word of Scandinavian origin, from the Ol...
	encyclopedia.jrank.org /LAP_LEO/index.html (142 words)

	Fibonacci Numbers and The Golden Section in Art, Architecture and Music
		Joerg Wiegels of Duesseldorf told me that he was astonished to see the Fibonacci numbers glowing brightly in the night sky on a visit to Turku in Finland.
		The pitches of his notes are often based on powers of Phi and their order is fixed by a number sequence, such as the Fibonacci numbers, or R(n) - the number of Fibonacci representations of n or on many other sequences that are described here on my Fibonacci site.
		Ted Froberg explains how he used the Fibonacci numbers "mod 7" (that is the remainders when we divide each Fibonacci number by 7) to make a "theme" which he then harmonizes and has made into a Fibonacci waltz.
	www.mcs.surrey.ac.uk /Personal/R.Knott/Fibonacci/fibInArt.html (4985 words)

	s30wen (Site not responding. Last check: 2007-10-14)
		The combinatorial properties of the Fibonacci infinite word are of great interest in some aspects of mathematics and physics, such as number theory, fractal geometry, formal language, computational complexity, quasicrystals etc. In this note, we introduce the singular words of the Fibonacci infinite word and discuss their properties.
		We establish two decompositions of the Fibonacci word in singular words and their consequences.
		By using these results, we discuss the local isomorphism of the Fibonacci word and the overlap properties of the factors.
	www.maths.tcd.ie /EMIS/journals/SLC/opapers/s30wen.html (134 words)

	String Rewriting and the Fibonacci Word
		Wherever you encounter (read) an "a," you counter with (write) an "ab." Perusing the first word, we read in the "a," and we write (in another place, as it were) an "ab." That "a" was the whole of the first word, so this stage is over.
		At the next stage, the word to be examined consists of "ab." We peruse the word at hand, and rewrite everything we find there, according to the rules that have been provided.
		This differs from the Thue-Morse Word solely in the rule for the letter, "b." It is, in fact, even simpler here than was the comparable rule for the letter, "b," in the Thue-Morse Word.
	www.washingtonart.net /whealton/fibword.html (3432 words)

	A division property of the Fibonacci word (Site not responding. Last check: 2007-10-14)
		The Fibonacci word e is the limit sequence of the infinite sequence (e
		Any non trivial permutation of a finite number of the above factors will produce an infinite word which is greater than e in the lexicographic order.
		An extension of this result to the case of standard Sturmian words is also given.
	liafa.jussieu.fr /web9/rapportrech/description_en.php?idrapportrech=280 (102 words)

	The Fibonacci Rabbit sequence - the Golden String
		First we re-examine Fibonacci's original Rabbit problem and see how it can generate an infinite sequence of two symbols and in a later section we see how the same sequence is very simply related to Phi also.
		Though the numbers are not the Fibonacci numbers, they have a similar method of construction (add the last two and then add 1).
		The Fibonacci Tree, Hofstadter and the Golden String K P Togneti, G Winley, T van Ravenstein in Applications of Fibonacci Numbers, 3rd International Conference, (editor: G Bergum), pages 325-334.
	www.mcs.surrey.ac.uk /Personal/R.Knott/Fibonacci/fibrab.html (3887 words)

	Fibonacci Numbers, the Golden section and the Golden String
		Here we show there is an interesting way of representing all integers in a binary-like fashion but using only powers of Phi instead of powers of 2 (binary) or 10 (decimal).
		One that has been used a lot is based on a nice formula for calculating which angle has a given tangent, discovered by James Gregory.
		Sometimes we find series that for quite a few terms look exactly like the Fibonacci numbers, but, when we look a bit more closely, they aren't - they are Fibonacci Forgeries.
	www.ee.surrey.ac.uk /Personal/R.Knott/Fibonacci (1912 words)

	[No title] (Site not responding. Last check: 2007-10-14)
		Poets don't try to put the Fibonacci numbers into their poetry, but it seems that the sequence is not only pleasing visually--in art and architecture--but is also pleasing to listen to--in poetry and music!
		The middle line of the poem consists of 3 to 5 words which are -ing words.
		Write the lyrics and show where the numbers are in the words or meter of the song.
	www.mste.uiuc.edu /courses/ci431kt/modules/hightshoe/stupoet.html (389 words)

	What is Fibonacci numbers? - A Word Definition From the Webopedia Computer Dictionary
		Beginning with 0 and 1, the sequence of Fibonacci numbers would be 0,1,1, 2, 3, 5, 8, 13, 21, 34, etc. using the formula n = n(-1) + n(-2), where the n(-1) means "the last number before n in the series" and n(-2) refers to "the second last one before n in the series.”
		In computer programming, Fibonacci numbers give a model for designing recursive programming algorithms where the time for any routine is the time within the routine itself, plus the time for the recursive calls.
		The Fibonacci numbers were originally defined by the Italian mathematician Fibonacci, also known as Leonardo da Pisa, in the 13th century to model the growth of rabbit populations.
	www.webopedia.com /TERM/F/Fibonacci_numbers.html (427 words)

	Memory as a macroscopic ordered state (Site not responding. Last check: 2007-10-14)
		In other words, the empirical background of the Geissler-Stroud-theory and the relationships of this theory to the results in Table 3, all this is exactly that what would be needed for perfect information processing in terms of communication theory.
		Combinatorics of words is the study of arrangement of such strings, and there are literally thousands of combinatorial problems that arise in computer science.
		However, new (by neglecting a lot of nonsense with quasi-religious appeal) is the claim, supported by proven empirical facts of psychology and neurophysiology, that our brain uses the golden mean as the clock cycle of thinking and hence the powers of the golden mean and the FW as principle of coding.
	www.volkmar-weiss.de /publ10-e.html (6590 words)

	Some Properties of the singular words of the Fibonacci word - WEN (ResearchIndex)
		Abstract: The combinatorial properties of the Fibonacci infinite word are of great interest in some aspects of mathematics and physics, such as number theory, fractal geometry, formal language, computational complexity, quasicrystals etc. In this note, we introduce the singular words of the Fibonacci infinite word and discuss their properties.
		WEN Z.-X. and WEN Z.-Y. Some Properties of the Singular Words of the Fibonacci Word.
		4 Fibonacci morphisms and sturmian words (context) - S'e'ebold - 1991 ACM DBLP
	citeseer.ist.psu.edu /wen94some.html (403 words)

	fibonacci - OneLook Dictionary Search
		Fibonacci : Dictionary of Philosophical Terms and Names [home, info]
		Fibonacci, Fibonacci, Fibonacci : Eric Weisstein's World of Mathematics [home, info]
		Phrases that include fibonacci: fibonacci sequence, fibonacci number, fibonacci numbers, fibonacci series, leonardo fibonacci, more...
	www.onelook.com /?w=fibonacci (116 words)

	Political Theory Daily Review
		The woman who coined the word 'metrosexual' explains how men can reclaim their masculinity.
		Those who extol the virtues of laziness are actually terribly busy.
		From Alternet, an interview with Douglas Massey, author of Return of the "L" Word: A Liberal Vision for the New Century.
	www.politicaltheory.info (1934 words)

	Lyndon Words and Singular Factors of Sturmian Words (ResearchIndex)
		Lyndon Words and Singular Factors of Sturmian Words
		Abstract: Two different factorizations of the Fibonacci infinite word were given independently in [10] and [6].
		In a certain sense, these factorizations reveal a self-similarity property of the Fibonacci word.
	citeseer.ist.psu.edu /126868.html (262 words)

	Mozart Guided Reading (Site not responding. Last check: 2007-10-14)
		Students will print copies of the Mozart Guided Reading I questions, Mozart Guided Reading II questions, and Fibonacci and Pythagoras Guided Reading questions.
		Students will search Fibonacci II and Pythagoras II to read about links between math and music.
		Students will use a word processing program to complete a free write response to these questions: What I've learned, what I think about what I've learned, and what I'd still like to learn.
	www.thesolutionsite.com /lpnew/lesson/1095/capital2hsA4.html (377 words)

	Reply from On-Line Encyclopedia (Site not responding. Last check: 2007-10-14)
		ID Number: A005614 URL: http://www.research.att.com/projects/OEIS?Anum=A005614 Sequence: 1,0,1,1,0,1,0,1,1,0,1,1,0,1,0,1,1,0,1,0,1,1,0,1,1,0,1,0,1,1, 0,1,1,0,1,0,1,1,0,1,0,1,1,0,1,1,0,1,0,1,1,0,1,0,1,1,0,1,1,0, 1,0,1,1,0,1,1,0,1,0,1,1,0,1,0,1,1,0,1,1,0,1,0,1,1,0,1,1,0,1, 0,1,1,0,1,0,1,1,0 Name: Infinite Fibonacci word (start with 1, apply 0->1, 1->10, iterate).
		Melancon, Factorizing infinite words using Maple, MapleTech journal, vol 4, no. 1, 1997, pp.
		Shallit, Characteristic words as fixed points of homomorphisms E.
	www.research.att.com /projects/OEIS?Anum=A005614 (215 words)

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