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Topic: Fibonacci sequence

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Fibonacci number

Prime number

Binary numeral system

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1 (number)

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	The Fibonacci sequence and the golden mean
		Fibonacci was one of the first Europeans to use Arabic numbers, whose use he explained in his 1202 Liber abaci.
		Seeds in a flower head are often arranged in spiral patterns that are related to Fibonacci numbers (for example, the number of spirals that curve to the left and the number of spirals that curve to the right will be adjacent numbers in the Fibonacci sequence).
		Fibonacci numbers are also important in art and music.
	www.ualr.edu /lasmoller/fibonacci.html (543 words)

	Fibonacci numbers
		For those sequences that end in 1, their sums, not counting the last 1 is a sequence of 1's and 2's that sum to n-1, and all such actually.
		Hence the number of sequences of 1's and 2's that sum to n and end in a 1 is f(n-1).
		Similarly, the number of sequences of 1's and 2's which sum to n and end in a 2 is f(n-2).
	www.cut-the-knot.org /arithmetic/Fibonacci.shtml (913 words)

	7 The Fibonacci Sequence (Site not responding. Last check: 2007-10-02)
		There are many interesting sequences to be found in the Mandelbrot set.
		The resulting sequence is 1, 2, 3, 4, 5, 6,...
		I think that this sequence is destined to become very important in mathematics.
	math.bu.edu /DYSYS/FRACGEOM2/node7.html (247 words)

	Fibonacci sequence
		Similarly, the whorls on a pine cone, the numbers of rings on the trunks of palm trees, the patterns of snail shells, and the genealogy of the male bee all follow a sequence of Fibonacci numbers.
		An interesting use of the Fibonacci sequence is for converting miles to kilometers.
		The Fibonacci sequence is a special case of the Lucas sequence.
	www.daviddarling.info /encyclopedia/F/Fibonacci_sequence.html (740 words)

	* Fibonacci Sequence - (Stock Market): Definition
		Fibonacci Sequence: is the sequence of numbers as follows: {0, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233...}.
		The sequence of numbers (0, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233...), discovered by the Italian mathematician Leonardo de Pisa in the 13th century and the mathematical basis of the Elliott Wave Theory,...
		After development of the sequence the ratio between one number and it's preceding number is 1.618 and in the opposite direction is 0.618.
	en.mimi.hu /stockmarket/fibonacci_sequence.html (322 words)

	The Circle of Life
		Fibonacci was the nickname of the great 13th century Italian mathematician Leonardo of Pisa.
		In the Fibonacci sequence, the quantities themselves appear in the growth of various natural organisms, for example, a sunflower may have 21 left and 34 right whorls.
		Much as the Fibonacci sequence starts with two "1"s, the first point at the top of the circle may be taken to be both conception and birth.
	www.rahul.net /raithel/otfw/91circle.html (3828 words)

	World Mysteries - Science Mysteries, Fibonacci Numbers and Nature
		The sequence, in which each number is the sum of the two preceding numbers is known as the Fibonacci series: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181,...
		Fibonacci was known in his time and is still recognized today as the "greatest European mathematician of the middle ages." He was born in the 1170's and died in the 1240's and there is now a statue commemorating him located at the Leaning Tower end of the cemetery next to the Cathedral in Pisa.
		These numbers are precisely those of the Fibonacci sequence (the bigger the numbers, the better the approximation) and the choice of the fraction depends on the time laps between the appearance of each of the seeds at the center of the flower.
	www.world-mysteries.com /sci_17.htm (4159 words)

	Fibonacci Numbers (Site not responding. Last check: 2007-10-02)
		Fibonacci numbers and the Fibonacci sequence are prime examples of "how mathematics is connected to seemingly unrelated things." Even though these numbers were introduced in 1202 in Fibonacci's book Liber abaci, they remain fascinating and mysterious to people today.
		Fibonacci, who was born Leonardo da Pisa "son of Bonaccio", gave a problem in his book whose solution was the Fibonacci sequence as we know it today.
		The Fibonacci sequence can also be used to test for primality, namely with the Lucas N+1 primality test.
	jwilson.coe.uga.edu /emt669/Student.Folders/Morris.Stephanie/EMT.669/Essay.3/Fibonacci.Essay.html (888 words)

	Fibonacci sequence
		A mathematical sequence consists of a series of numbers, usually starting at 0 or 1, all of which are derived from preceeding ones according to formal rules.
		One of the most well-known sequences was one derived by the Italian medieval mathematician known today as Fibonacci.
		Fibonacci himself used the cute (pre-Australian cute) example of the multiplication of rabbits in his book.
	www.fuzzygalore.biz /articles/fibonacci_seq.shtml (601 words)

	Leonardo Fibonacci Numbers, Sequence, Golden Ratio
		Fibonacci's influence was more limited than one might have hoped and apart from his role in spreading the use of the Hindu-Arabic numerals and his rabbit problem, Fibonacci's contribution to mathematics has been largely overlooked.
		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'.
		Fibonacci is perhaps best known for a simple series of numbers, introduced in Liber abaci and later named the Fibonacci numbers in his honour.
	www.leonardo-fibonacci-numbers.com (1256 words)

	The On-Line Encyclopedia of Integer Sequences
		The Fibonacci sequence, like any additive sequence, naturally tends to be geometric with common ratio not a rational power of 10; consequently, for a sufficiently large number of terms, Benford's law of first significant digit {i.e., first digit 1 =< d =< 9 occurring with probability log_10(d+1) - log_10(d)} holds.
		Sequence in context: A000044 A107358 A039834 this_sequence A020695 A069041 A109609
		Adjacent sequences: A000042 A000043 A000044 this_sequence A000046 A000047 A000048
	www.research.att.com /~njas/sequences/A000045 (2443 words)

	The Fibonacci Sequence
		Fibonacci was best known for a series of numbers, introduced in Liber abaci, and later named the Fibonacci numbers.
		He arrived at this sequence when competing in a mathematical competitions which were commonplace in Fibonacci's day.
		It is possible to determine the general solution of the Fibonacci Sequence using difference equations.
	www.bath.ac.uk /~erc20/fibonaccisequence.html (385 words)

	Fibonacci Sequence
		This gives a sequence (the Fibonacci sequence) in which "each number is the sum of the two preceding numbers".
		Thus, the sequence progresses: 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597...
		SOFP shows the sequence in which florets are laid down (half the spirals are omitted).
	protea.worldonline.co.za /fibon.htm (666 words)

	Modified Fibonacci Series
		Fibonacci Numbers can be easily had by using starting numbers other than 0 and 1.
		Not surprisingly, the general rule is that the nth number of all of the different, modified Fibonacci series, all differ between the adjacent series by the (n-2)th number of the original Fibonacci series.
		What you might not have guessed is the manner in which the nth number in the cumulative sequence is less than the n+2 number in the regular sequence by the second number in the regular sequence.
	www.halexandria.org /dward094.htm (720 words)

	Fibonacci sequence
		Now, on to what Fibonacci is widely known for around the world: The Fibonacci Sequence.
		When you look at the sequence and pick a number you will notice it is composed of the previous two numbers added together.
		One important number that was found as a result of the Fibonacci sequence is 1.61803.
	iluvkids.myweb.uga.edu /Fibonaccisequence.html (324 words)

	Fibonacci Trader
		After the first several numbers in the sequence, the ratio of any number to the next higher is approximately.618 to 1 and to the next lower number approximately 1.618 to 1.
		Between alternate numbers in the sequence, the ratio is approximately.382, whose inverse is 2.618.
		Fibonacci Retracements are displayed by first drawing a trend line between two extreme points (i.e., a significant trough and peak).
	www.elliottwaves.biz /fibonacci_trader.htm (746 words)

	Mathwords: Fibonacci Sequence
		The sequence of numbers 1, 1, 2, 3, 5, 8, 13, 21, 34,.
		This sequence is encountered in many settings, from population models to botany.
		Note: The sequence of ratios of consecutive terms has the Golden Mean as its limit.
	www.mathwords.com /f/fibonacci_sequence.htm (62 words)

	Fibonacci, Fibonacci Numbers, Fibonacci Sequence
		In the Fibonacci Sequence (0, 1, 1, 2, 3, 5, 8,...), each number is the sum of the two previous numbers (ie: 2+3=5, 3+5=8,...
		The Fibonacci Spiral is inherent in the Fibonacci numbers and the Golden Ratio.
		It has been cited as a generative form in nature, describing the patterns and growth sequences of natural objects ranging from the shell of the nautilus on a micro-level, to galaxies on a macro-level.
	mathematicianspictures.com /FIBONACCI/Fibonacci.htm (350 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 (1948 words)

	Fibonacci number sequence
		In his day, Fibonacci was very famous: Frederick II, the Emperor of the Holy Roman Empire, the King of Sicily and Jerusalem, and descendant of two of the noblest families in Europe, travelled to Pisa in Italy to meet Fibonacci in 1225 AD.
		Now, though, the only monuments to Fibonacci are a small statue across the river from the Leaning Tower of Pisa (of which Fibonacci helped to design) and two street names that bare his name: one in Florence and one in Pisa.
		This sequence of numbers illustrates the ratio between the second Fibonacci numbers away from the Golden Mean on Figure 175; namely those of 4.236 and.236.
	www.futures-investor.co.uk /fibonacci_number_sequence.htm (2862 words)

	Ward Melville HS - Fibonacci
		Fibonacci we noticed a very distinct pattern in the wording of his answers, mainly having to do with one of his mathematical masterpieces.
		On the head of a Coneflower, the seeds are arranged are in accordance with the sequence because of the spirals they form throughout from the center to the outside edge.
		When the sequence is graphed it becomes apparent that there is a ration between each number and the one preceding it, which is almost identical to Phi or approximately 1.6.
	www.3villagecsd.k12.ny.us /wmhs/Departments/Math/OBrien/fibonacci.html (1412 words)

	FIBONACCI (Site not responding. Last check: 2007-10-02)
		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)

	Using Fibonacci to determinate market goals (Site not responding. Last check: 2007-10-02)
		Many contributions were applied to mathematics science by Fibonacci, but the most relevant discover was denominated by the French mathematician, Edouard Lucas, as Fibonacci Sequence in the XIX Century.
		Fibonacci proved that this sequence could be found in the evolution of many natural phenomenons.
		Then we could find and additive sequence with the properties of the Fibonacci Sequence, because each number is the sum of the immediately two before, and moreover, each number is 1,618 times the number before.
	www.fxstreet.com /education/technical/using-fibonacci-to-determinate-market-goals (1106 words)

	Fibonacci and Crochet
		Sequence: 0, 1, 1, 2, 3, 5, 8...
		The Fibonacci sequence of numbers is quite useful for planning a pleasing-to-the-eye sequence of colors.
		Another way to use the sequence is in determining the length of your afghan.
	www.crochetcabana.com /specialty/fibonacci_and_crochet.htm (1440 words)

	FIBONACCI OR FORGERY? (Site not responding. Last check: 2007-10-02)
		The Fibonacci sequence is the very famous sequence in which each number is the sum of the two previous numbers.
		The point of this essay is that there exist sequences which start off like a Fibonacci sequence, but end up being an all new sequence.
		Another type of Fibonacci sequence is one in which the nth term is the sum of the squares of n-1 and n-2, so we have
	jwilson.coe.uga.edu /emt669/Student.Folders/Lewis.Millard/fibonacci/Fib.html (533 words)

	PlanetMath: Fibonacci sequence
		th Fibonacci number is generated by adding the previous two.
		Thus, the Fibonacci sequence has the recurrence relation
		This is version 16 of Fibonacci sequence, born on 2001-11-04, modified 2007-04-22.
	planetmath.org /encyclopedia/FibonacciSequence.html (99 words)

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