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Topic: Fibonacci number program

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	Fibonacci numbers (Python) - LiteratePrograms
		The Fibonacci numbers are the integer sequence 0, 1, 1, 2, 3, 5, 8, 13, 21,..., in which each item is formed by adding the previous two.
		Fibonacci number programs that implement this definition directly are often used as introductory examples of recursion.
		This may be useful, for example to find the Fibonacci number closest to a given number.
	en.literateprograms.org /Fibonacci_numbers_(Python) (667 words)

	Fibonacci number - Wikipedia, the free encyclopedia
		The Fibonacci numbers are named after Leonardo of Pisa, known as Fibonacci, although they had been described earlier in India.
		Fibonacci numbers are used by some pseudorandom number generators.
		The Fibonacci polynomials are another generalization of Fibonacci numbers.
	en.wikipedia.org /wiki/Fibonacci_number (3898 words)

	Science News Online (6/12/99): Fibonacci at Random (Site not responding. Last check: )
		Fibonacci numbers come up surprisingly often in nature, from the number of petals in various flowers to the number of scales along a spiral row in a pine cone.
		The hundredth Fibonacci number, for example, is roughly equal to the hundredth power of the golden ratio.
		He found that the hundredth term in such a sequence, for example, is approximately equal to the hundredth power of the number 1.13198824....
	www.sciencenews.org /pages/sn_arc99/6_12_99/bob1.htm (1142 words)

	Untitled Document (Site not responding. Last check: )
		Write a program with a function with the following input: the number of bed knobs per unit, the number of units per line and the number of lines.
		The program will ask the user if he or she wants to continue after each area calculation is made.
		A user can then request that the numbers be printed from a lower limit to a higher limit up to the 20th number in the series.
	www.intuitor.com /student/Q2_Comp_Sci_Program_Assignments.html (684 words)

	Fibonacci Sunflowers
		Fibonacci, aka as Leonard of Pisa, lived in the1200's and was largely responsible for introducing Northern Europe to the Arabic number and decimal positioning system we use today.
		Each number from the 3rd on is the sum of the previous two numbers.
		If you count the apparent number of arms in these spirals, you'll find that they always equal two adjacent Fibonacci numbers whose ratios to the succeeding numbers are slightly above and below phi.
	www.delphiforfun.org /Programs/FiboSunflower.htm (634 words)

	The Math Forum - Math Library - Golden Ratio/Fibonacci (Site not responding. Last check: )
		Fibonacci numbers are closely related to the golden ratio (also known as the golden mean, golden number, golden section) and golden string.
		Explore applications of the Fibonacci series: Fibonacci ratios, Binet revisited, one over eighty-nine (examining the decimal expansion of 1/89), apartment buildings (an explanation of why the number of combinations for each set of a certain group of apartment buildings is a Fibonacci number), nature, Leonardo da Vinci.
		Fibonacci and his original problem about rabbits that gave the series its name; the family trees of bees; the golden ratio and the Fibonacci series; the Fibonacci Spiral and sea shell shapes; branching plants; flower petal and seed-heads; and the leaf...more>>
	mathforum.org /library/topics/golden_ratio (2460 words)

	Fibonacci number program - Wikipedia, the free encyclopedia
		In many beginning computer science courses, an introduction to the concept of recursion often includes a program to calculate and print Fibonacci numbers (or computing the factorial of a number).
		In simple terms, each number is the sum of the previous two numbers, with the first and second term 0 and 1 respectively.
		The Fibonacci sequence is also a popular introductory program for recursion (along with factorials) in computer science classes.
	en.wikipedia.org /wiki/Fibonacci_number_program (2090 words)

	Fibonacci
		Fibonacci numbers 2 3 5 8 13 and 21 are drawn in fl.
		Apart from the numbers needed to specify the width of the trunk and the spacing of the rings, the only parameters used were the golden angle and the direction of winding.
		You can find the Fibonacci numbers by counting the helical series of scars on many small coniferous trees, on their cones, and in the helical arrangement of leaves on plants.
	www.branta.connectfree.co.uk /fibonacci.htm (5852 words)

	Fibonacci number program problem - Dev Shed
		The funny thing is, whatever nth number of the sequence you want, fib(n) will end up calling fib(1) the number of times of that number in the sequence.
		The eighth number in the sequence is 21.
		For the fibonacci problem in Haskell, it is possible to use tree recursion without the combinatorial overhead because the language processor automagically memoizes the results of repeated calls - any calls for previously calculated values are replaced with a table lookup.
	forums.devshed.com /other-programming-languages-139/fibonacci-number-program-problem-341613.html (2040 words)

	Fibonacci.html
		Fibonacci was an Italian mathematician whose name is accredited to the following set of numbers:
		Fibonacci numbers are extremely closely related to the
		And without the Greeks observing nature to determine Phi, we would have no clue as to how Fibonacci numbers could be calculated (or at least no so early in history).
	members.tripod.com /~Colincool/Pages/Fibonacci.html (327 words)

	Phi & Fibonacci Anomalies
		Note: The Fibonacci series spiral on the left is slightly different from the perfect spiral generated by Phi (1.61804...) because of the approximations early in the series leading to Phi.
		The DNA molecule, the program for all life, is based on the golden section.
		34 and 21, of course, are numbers in the Fibonacci series and their ratio, 1.6190476 closely approximates phi, 1.6180339.
	evolutionoftruth.com /div/fibomyst.htm (591 words)

	Computing Excersice - 1st Week (Site not responding. Last check: )
		Abdussalam Shehu S. Fibonacci numbers is a sequence of numbers defined as follows: The first two numbers are both 1, the next number is obtained as the sum of the previous two and so on.
		So I kep on increasing the number of dicimal places for the fibonacci number up to the point where I was able to get the exact 1000th number.
		A very interesting observation was that the number of decimal places is (208) exactly equal to the power of 10 in the in the 1000th fibonacci, implying that the 1000th fibonacci number have 209 digits!
	www.aims.ac.za /~shehu/fibonacci.html (250 words)

	Mathematics Archives - Numbers
		In the section on applications there are a number of interactive programs that convert rationals (or quadratic irrationals) into a simple continued fraction, as well as the converse.
		All numbers are not created equal; that certain constants appear at all and then echo throughout mathematics, in seemingly independent ways, is a source of fascination.
		A prime k-tuplet is a sequence of consecutive prime numbers {p1, p2,..., pk} such that, in some sense, pk - p1 is as small as possible.
	archives.math.utk.edu /subjects/numbers.html (1310 words)

	Fibonacci numbers
		Fibonacci originally defined this sequence to characterize the growth in size of rabbit populations;
		But there are enough other applications that a qurterly journal is devoted to the study of Fibonacci (and related) sequences
		the time consumed in computing fib is clearly proportional to the number of calls made to fib; this turns out to grow exponentially in n, so that for n=40, over 300 million calls are made
	www.willamette.edu /~fruehr/dsa/lectures/examples4.html (153 words)

	Illuminations: Fibonacci Nim
		Students also learn about the Fibonacci representation, which is a method for representing a numeral as a sum of Fibonacci numbers.
		The program can be downloaded to student calculators, or you can download it to a calculator with projection capabilities and display the results on the overhead projector.
		If you wish to convert a number, n, from base 10 to base b by the repeated subtraction method, the first p powers of b are needed.
	illuminations.nctm.org /LessonDetail.aspx?ID=L694 (2063 words)

	The Religion of Vague
		Directly related to the golden number is the golden rectangle, in which the ratio of the rectangle’s length to its width is equal to phi.
		The Fibonacci sequence goes: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, etc., in which each number is equal to the sum of the two preceding numbers: 1+1=2; 1+2=3; 2+3=5; 3+5=8; 5+8=13; 8+13=21; 13+21=34; 21+34=55; 34+55=89; 55+89=144; 89+144=233.
		Thus Fibonacci numbers are a kind of golden ratio in disguise, and they, too, pop up in the most unexpected places.
	www.rae.org /goldennumber.html (874 words)

	A Formula for the nth Fibonacci number
		the n-th Fibonacci number is the sum of the (n-1)th and the (n-2)th.
		Numbers which are real have zero as their complex part so the real number 3 is the same as the complex number 3 + 0 i and has "coordinates" (3,0).
		Numbers which are purely imaginary have a real-part of zero and so are of the form 0+yi always lying exactly on the y axis (the imaginary axis).
	www.mcs.surrey.ac.uk /Personal/R.Knott/Fibonacci/fibFormula.html (4000 words)

	Math Forum - Ask Dr. Math Archives: College Number Theory
		I am trying to find a method (one that can be programmed on a PC) to convert the decimal part of a real number to a fraction represented by integers for the numerator and denominator.
		Apparently almost any number can be made into a palindromic number by reversing the digits and adding and then repeating the steps until you get a palindromic number.
		An antifirst number is a number with more divisors than every number before it.
	mathforum.org /library/drmath/sets/college_number_theory.html (1010 words)

	Java programming: Fun with Fibonacci
		The Fibonacci sequence terms grow exponentially, asymptotically as powers of 1.618033...; that special number is known as the golden ratio, exactly equal to (1+sqrt(5))/2.
		I then extended the Java program to print all terms that are representable in 64-bit integer arithmetic, and to format the output into a neat aligned table.
		A command shell is unexpected to be useful in a programming exercise such as this one, because shells traditionally have not supplied floating-point arithmetic.
	www.math.utah.edu /~beebe/software/java/fibonacci (2998 words)

	The Bible illustrating phi, the golden section, divine proportion and Fibonacci series (Site not responding. Last check: )
		This ratio is also the same as 5 to 3, numbers from the Fibonacci series.
		This beast, regarded by some as the Anti-Christ described by John, is thus related to the number 666, one of the greatest mysteries of the Bible.
		In that sense it is the number of mankind, as the mysterious passage of Revelation perhaps reveals.
	goldennumber.net /classic/bible.htm (676 words)

	JICOS
		The Fibonacci numbers for 1 and 2 are then used to form the 3rd Fibonacci number.
		An illustration of this process for the 4th Fibonacci number is given below as a directed acyclic graph (dag) of tasks.
		To render the task dag as a parallel program in Jicos, we first identify the tasks that we want done in parallel.
	www.cs.ucsb.edu /projects/jicos/tutorial/fibonacci (651 words)

	How to develop Fibonacci Sequence JAVA program
		As an example; the sixth (n=6) Fibonacci number is 8; 0,1,1,2,3,5,8....whereas 0 is the 0th term and 1 is the 1st term.
		I need to deliver a working JAVA program (with a ".java" extention) as well as a class file which can be executed.
		In this program, my class file needs to be executed and the resultss of the program needs to be varified.
	www.webdevelopersjournal.com /Javadiscuss/_javadiscuss/00000105.htm (225 words)

	Shareware software by Leithauser Research
		You can use this program to protect children from harmful information on the Internet, or for security in a business to prevent unauthorized use of the computer outside of business hours.
		Computer Payment Enforcer (cpearc.exe) is a computer program that helps you to collect payments for computers that you have sold on credit or are renting out.
		Computer Use Reporter covertly monitors what programs are used on the computer, what files or Web sites these programs access, when they are accessed, and which user is on the computer at the time.
	leithauserresearch.com (2794 words)

	Fibonacci Number Program Problem - n00b :)
		Now I've made a program to calculate the Fibonacci numbers, but there seems to be some error.
		The last number is 5bytes long so the size of long should be greater than 5 if you will use long.
		Short program in c to calculate first term when sum of n terms and common difference d is given.
	www.astahost.com /info.php/fibonacci-number-program-problem_t10180.html (696 words)

	Fibonacci Numbers
		However if a program takes a lot of memory, you may not be able to run it at all, so this is an important parameter to understand.
		Analysis of recursive program space is more complicated: the space used at any time is the total space used by all recursive calls active at that time.
		According to the number of lines executed, one is twice as fast as the other, but this ratio does not change as a function of n.
	www.ics.uci.edu /~eppstein/161/960109.html (3061 words)

	Wikinfo \| Scheme programming language
		Scheme is a functional programming language and a dialect of Lisp.
		They can be used to add support for new paradigms, like object-oriented programming, logic programming, etc. Scheme provides a hygienic macro system which, while not quite as powerful as Common Lisp's macro system, is much safer and often easier to work with.
		Purely functional programs have no state and don't have side-effects, and are therefore automatically thread-safe and considerably easier to verify than imperative programs.
	www.wikinfo.org /wiki.php?title=Scheme_programming_language (2785 words)

	CSCI 51A / ECE 86 - Lab #6
		Write a program that will allow a user to determine whether a specified integer is a prime number, or is a Fibonacci number.
		The program should prompt the user to select a function, P for prime or F for Fibonacci, and should repeat this prompt until a valid selection is made.
		Testing of a number to see if it is a Fibonacci number must be implemented with a subroutine.
	www.ecst.csuchico.edu /~judyc/0405S-csci51a/labs/lab6-fibonacci.html (533 words)

	Help Please Fibonacci Number Program - GameDev.Net Discussion Forums
		I am programming fibonacci's number program in the c programming language.
		While the iterative identity you are using is kind of characteristic of the Fibonacci sequence, it is far from the quickest way to calculate it.
		However, I was surprised to find that fib(46) is the greatest Fibonacci number that fits in a 32 bit integer.
	www.gamedev.net /community/forums/topic.asp?topic_id=418505 (945 words)

	id:A000045 - OEIS Search Results
		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.
		This is the same as the number of summands in such a determinant in which the main-, sub-, and super-diagonal elements are all nonzero.
		a(n)= the number of different ways to run up a staircase with n steps, taking steps of odd sizes where the order is relevant and there is no other restriction on the number or the size of each step taken.
	www.research.att.com /cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A000045 (2915 words)

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