The ''Fibonacci Quarterly'' is a

scientific journal In academic publishing, a scientific journal is a periodical publication intended to further the progress of science, usually by reporting new research. Content Articles in scientific journals are mostly written by active scientists such as s ...

on mathematical topics related to the

Fibonacci number In mathematics, the Fibonacci numbers, commonly denoted , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from ...

s, published four times per year. It is the primary publication of

The Fibonacci Association The Fibonacci Association is a mathematical organization that specializes in the Fibonacci number sequence and a wide variety of related subjects, generalizations, and applications, including recurrence relations, combinatorial identities, binomia ...

, which has published it since 1963. Its founding editors were

Verner Emil Hoggatt Jr. Verner Emil Hoggatt Jr. (June 26, 1921 – August 11, 1980) was an American mathematician, known mostly for his work in Fibonacci numbers and number theory. Hoggatt received a Ph.D. from Oregon State University in 1955 for his dissertation on ...

and

Alfred Brousseau Brother Alfred Brousseau, F.S.C. (February 17, 1907 – May 31, 1988), was an educator, photographer and mathematician and was known mostly as a founder of the Fibonacci Association and as an educator. Biography Brother Brousseau was born in Nort ...

;Biography of Verner Emil Hoggatt Jr.
by Clark Kimberling the present editor is Professor Curtis Cooper of the Mathematics Department of the

University of Central Missouri The University of Central Missouri (UCM) is a public university in Warrensburg, Missouri. In 2019, enrollment was 11,229 students from 49 states and 59 countries on its 1,561-acre campus. UCM offers 150 programs of study, including 10 pre-profes ...

. The ''Fibonacci Quarterly'' has an editorial board of nineteen members and is overseen by the nine-member board of directors of The Fibonacci Association. The journal includes research articles, expository articles, Elementary Problems and Solutions, Advanced Problems and Solutions, and announcements of interest to members of The Fibonacci Association. Occasionally, the journal publishes special invited articles by distinguished mathematicians. An online Index to The Fibonacci Quarterly covering Volumes 1-55 (1963–2017) includes a Title Index, Author Index, Elementary Problem Index, Advanced Problem Index, Miscellaneous Problem Index, and Quick Reference Keyword Index. The ''Fibonacci Quarterly'' is available online to subscribers; on Dec 31, 2017, online volumes ranged from the current issue back to volume 1 (1963). Many articles in ''The Fibonacci Quarterly'' deal directly with topics that are very closely related to

Fibonacci numbers In mathematics, the Fibonacci numbers, commonly denoted , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from ...

, such as

Lucas numbers The Lucas numbers or Lucas series are an integer sequence named after the mathematician François Édouard Anatole Lucas (1842–1891), who studied both that sequence and the closely related Fibonacci numbers. Lucas numbers and Fibonacci nu ...

, the

golden ratio In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a and b with a > b > 0, where the Greek letter phi ( ...

, Zeckendorf representations, Binet forms,

Fibonacci polynomials In mathematics, the Fibonacci polynomials are a polynomial sequence which can be considered as a generalization of the Fibonacci numbers. The polynomials generated in a similar way from the Lucas numbers are called Lucas polynomials. Definition The ...

, and

Chebyshev polynomials The Chebyshev polynomials are two sequences of polynomials related to the cosine and sine functions, notated as T_n(x) and U_n(x). They can be defined in several equivalent ways, one of which starts with trigonometric functions: The Chebyshe ...

. However, many other topics, especially as related to recurrences, are also well represented. These include

primes A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

pseudoprimes A pseudoprime is a probable prime (an integer that shares a property common to all prime numbers) that is not actually prime. Pseudoprimes are classified according to which property of primes they satisfy. Some sources use the term pseudoprime to ...

, graph colorings,

Euler numbers In mathematics, the Euler numbers are a sequence ''En'' of integers defined by the Taylor series expansion :\frac = \frac = \sum_^\infty \frac \cdot t^n, where \cosh (t) is the hyperbolic cosine function. The Euler numbers are related to a ...

continued fraction In mathematics, a continued fraction is an expression (mathematics), expression obtained through an iterative process of representing a number as the sum of its integer part and the multiplicative inverse, reciprocal of another number, then writ ...

Stirling number In mathematics, Stirling numbers arise in a variety of analytic and combinatorial problems. They are named after James Stirling, who introduced them in a purely algebraic setting in his book ''Methodus differentialis'' (1730). They were rediscov ...

Pythagorean triple A Pythagorean triple consists of three positive integers , , and , such that . Such a triple is commonly written , and a well-known example is . If is a Pythagorean triple, then so is for any positive integer . A primitive Pythagorean triple is ...

Ramsey theory Ramsey theory, named after the British mathematician and philosopher Frank P. Ramsey, is a branch of mathematics that focuses on the appearance of order in a substructure given a structure of a known size. Problems in Ramsey theory typically ask a ...

, Lucas-Bernoulli numbers,

quadratic residues In number theory, an integer ''q'' is called a quadratic residue modulo ''n'' if it is congruent to a perfect square modulo ''n''; i.e., if there exists an integer ''x'' such that: :x^2\equiv q \pmod. Otherwise, ''q'' is called a quadratic no ...

, higher-order recurrence sequences, nonlinear recurrence sequences, combinatorial proofs of number-theoretic identities,

Diophantine equation In mathematics, a Diophantine equation is an equation, typically a polynomial equation in two or more unknowns with integer coefficients, such that the only solutions of interest are the integer ones. A linear Diophantine equation equates to a c ...

s, special matrices and determinants, the

Collatz sequence The Collatz conjecture is one of the most famous unsolved problems in mathematics. The conjecture asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1. It concerns integer sequence, seq ...

, public-key crypto functions,

elliptic curves In mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point . An elliptic curve is defined over a field and describes points in , the Cartesian product of with itself. If the ...

fractal dimension In mathematics, more specifically in fractal geometry, a fractal dimension is a ratio providing a statistical index of complexity comparing how detail in a pattern (strictly speaking, a fractal pattern) changes with the scale at which it is meas ...

, hypergeometric functions, Fibonacci polytopes, geometry,

graph theory In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conne ...

, music, and art.

Notes

References

External links

''The Fibonacci Quarterly''
Homepage

by A. F. Horadam

by Clark Kimberling {{Fibonacci Mathematics journals