The Fibonacci Quarterly is a peer-reviewed academic journal dedicated to the study of the Fibonacci numbers, related recursive sequences, and their applications in mathematics and other fields, published quarterly (ISSN 0015-0517) since its inaugural issue in February 1963.[1][2] It serves as the official publication of the Fibonacci Association, an international organization incorporated that same year to promote research and education on these topics.[1]Founded in 1963 by a group of mathematicians, with Brother Alfred Brousseau and Henry W. Gould among the founding editors, the journal focuses on this specialized area of number theory.[3][4][5]The journal's scope encompasses original research articles, problem sections for high school, undergraduate, and advanced audiences, and outreach pieces aimed at early-career mathematicians, including applications in science such as biology.[1] As of 2025, it is edited by Anitha Srinivasan as Editor-in-Chief, alongside managing editors Gessica Alecci, Steven J. Miller, and Elif Tan, and is published by Taylor & Francis.[1][2] The Fibonacci Association supports the journal through biennial international conferences, fostering a global community of researchers.[1]
History
Founding
The Fibonacci Association was established in December 1962 as a nonprofit 501(c)(3) corporation by Verner E. Hoggatt Jr., Brother Alfred Brousseau, Paul Byrd, I. Dale Ruggles, Stanley L. Basin, and Terrance A. Brennan, with the primary goal of fostering interest in Fibonacci numbers and providing a platform for enthusiasts to exchange ideas on the topic.[6][7] This initiative emerged amid increasing public and academic curiosity about Fibonacci sequences, which had gained attention through recreational mathematics publications and educational discussions in the early 1960s.[7] The founders, a mix of mathematicians and educators, recognized the need for a dedicated organization to centralize research and outreach efforts related to these numbers, which trace back to the 13th-century work of Leonardo of Pisa (Fibonacci).[7]A key foundational effort tied to the association's inception was the computation and proofreading of the first 571 Fibonacci numbers in 1962, culminating in F571, a 119-digit number, for an article published in Recreational Mathematics Magazine that October.[7] This computational milestone not only demonstrated the practical challenges of extending the sequence but also served as early publicity for the forthcoming journal, highlighting the association's commitment to advancing knowledge in number theory.[7] The work underscored the specialized focus on Fibonacci-related mathematics, setting the stage for rigorous scholarly contributions.The Fibonacci Quarterly, the association's official journal, launched its first issue in February 1963 (labeled as Spring 1963), edited by Verner E. Hoggatt Jr. as general editor and Brother Alfred Brousseau as managing editor. Among the founding editors was also Henry W. Gould.[5] Initial operations relied on modest financial support from charter members through subscriptions and donations, supplemented by extensive volunteer labor, as no significant external funding was available at the outset.[7] Subscriptions began with just 59 by late January 1963 but rapidly expanded to 915 by the end of the first year, reflecting the burgeoning enthusiasm for the journal's niche content.[7]
Development and Milestones
Following its founding in 1963, The Fibonacci Quarterly experienced rapid initial growth in readership. By September 1963, the journal had secured 659 subscribers, rising to 915 by the end of its first year of publication.[7] This expansion continued steadily, reflecting growing interest in Fibonacci-related mathematics among academics and enthusiasts.Key recognitions in the late 1960s bolstered the journal's visibility. In March 1969, Martin Gardner's column in Scientific American explicitly mentioned The Fibonacci Quarterly, contributing to a surge in subscriptions.[7] Similarly, an April 1969 article in Time magazine featured interviews with founding editors Verner E. Hoggatt Jr. and Brother Alfred Brousseau, highlighting the journal's role in Fibonacci studies.[7] By 1972, the publication was regularly indexed in Mathematical Reviews and Zentralblatt für Mathematik, affirming its scholarly standing.[7]Operational developments marked the journal's maturation. In 1968, an editorial board was formed to guide content and policy, comprising initial members Brother Alfred Brousseau, Verner E. Hoggatt Jr., G. L. Alexanderson, George Ledin, I. Dale Ruggles, and Marjorie Bicknell-Johnson.[7] Storage needs prompted the relocation of back issues and library materials to Santa Clara University in 1975, encompassing 257 boxes of archives.[7] The Fibonacci Association established a Board of Directors in 1981 to oversee governance.[8]International reach expanded notably by the journal's 25th anniversary in 1987 (Volume 25), with over 200 foreign subscribers from more than 36 countries, including significant numbers from West Germany, Canada, Japan, Australia, the United Kingdom, Greece, and Italy.[7] This milestone issue reflected on the journal's evolution from a modest newsletter to a cornerstone of sequencemathematics.[7]In subsequent decades, structural enhancements improved accessibility. Starting with Volume 44 in 2006, all articles included abstracts to aid researchers in navigating the growing body of work.[9] By 2025, marking over 60 years of uninterrupted quarterly publication, the journal transitioned to Taylor & Francis as its publisher beginning with Volume 63, Number 1 (February 2025), enhancing global distribution and digital integration. As of November 2025, Volume 63, Issue 3 has been published.[9][10]
Editorial Leadership
The Fibonacci Quarterly was founded with Verner E. Hoggatt Jr. serving as its inaugural editor from 1963 to 1980, a tenure of 18 years during which he oversaw the journal's early growth and international outreach efforts.[6] Brother Alfred Brousseau complemented this role as managing editor from 1963 until his retirement in 1975, handling production, subscriptions, and bibliographic compilations that supported the journal's foundational operations.[6]Following these initial leaders, Marjorie Bicknell-Johnson joined as co-editor from 1973 to 1975, while also fulfilling roles as secretary of the Fibonacci Association from 1963 to 2010, treasurer from 1979 to 1998, and informal historian who documented the journal's early history.[6] After Hoggatt's death in 1980, Gerald E. Bergum assumed the editorship from 1980 to 1998, an 18-year period marked by operational stabilization, including the relocation of the journal to South Dakota State University and reorganization of manuscript processing.[11] Curtis N. Cooper then edited the journal from 1998 until 2024, a 26-year span at the University of Central Missouri during which he guided its transition to digital formats and partnerships, such as with Taylor & Francis for electronic access.[6][2]As of 2025, Anitha Srinivasan of Universidad Pontificia Comillas serves as editor-in-chief, succeeding Cooper who holds the title of editor-in-chiefemeritus.[2] The journal's editorial board comprises 19 members, including long-serving contributors such as David M. Bressoud, Henry W. Gould, and Heiko Harborth, and operates under the oversight of the Fibonacci Association's nine-member board of directors.[12][2] The initial editorial board was formed in January 1968 to assist with content review and advisory functions.[7]
Content and Scope
Primary Topics
The Fibonacci Quarterly centers its publications on the Fibonacci sequence, a fundamental integer sequence defined by the recurrence relation F_n = F_{n-1} + F_{n-2} for n \geq 2, with initial conditions F_0 = 0 and F_1 = 1, generating terms such as 0, 1, 1, 2, 3, 5, 8, 13, and so on.[9] This sequence serves as the cornerstone for exploring properties like growth rates and closed-form expressions via Binet's formula. Closely intertwined are the Lucas numbers, another linear recurrence sequence satisfying L_n = L_{n-1} + L_{n-2} for n \geq 2, but with initial values L_0 = 2 and L_1 = 1, yielding 2, 1, 3, 4, 7, 11, 18, .... These numbers share many structural similarities with the Fibonacci sequence, including analogous identities and generating functions.[1] The golden ratio, denoted \phi = \frac{1 + \sqrt{5}}{2} \approx 1.618, emerges prominently as the irrational number to which the ratio F_{n+1}/F_n converges as n increases, underpinning aesthetic and structural analyses in the journal's content.[9]Beyond these core sequences, the journal delves into generalizations, such as the broader class of Lucas sequences, which parametrize families of recurrences including both Fibonacci and Lucas numbers as special cases, often studied for their algebraic properties and periodicity modulo primes.[1] Key related areas encompass Fibonacci primes—prime numbers appearing in the sequence, like 2, 3, 5, 13, and 89—and their distribution, as well as applications in graph theory, exemplified by Fibonacci graphs where vertices or edges follow sequence-based labeling to model connectivity and enumeration problems. Continued fractions derived from Fibonacci ratios provide insights into approximations of irrational numbers, while combinatorial identities, such as those linking Fibonacci numbers to binomial coefficients or tiling problems, highlight enumerative aspects.[9]The scope extends to broader connections within integer sequences and number theory, particularly divisibility properties, where rules like the gcd identity \gcd(F_m, F_n) = F_{\gcd(m,n)} reveal deep structural patterns.[1] Applications in prime number theory explore conjectures on the infinitude of Fibonacci primes, and geometric interpretations leverage the golden ratio for constructions in tilings—such as pentagonal tilings—and phyllotaxis patterns in nature. These themes underscore the sequence's ubiquity in modeling spiral growth and proportional harmony.[9]The evolution of topics in the Fibonacci Quarterly reflects growing mathematical sophistication: the 1960s issues emphasized foundational properties and identities of the sequences, whereas in subsequent decades, coverage expanded to computational algorithms for large-scale calculations and interdisciplinary applications, including biological modeling of population dynamics and artistic designs inspired by golden ratio proportions.[7]
Formats and Features
The Fibonacci Quarterly publishes a diverse array of contributions, including research papers that present original proofs and theorems on Fibonacci numbers and related sequences, expository articles designed to offer accessible explanations for broader mathematical audiences such as university students and teachers, and special invited articles contributed by prominent mathematicians exploring advanced connections in the field.[13][14] These formats emphasize intelligible and stimulating content, with a focus on new results, innovative proofs, and interdisciplinary links, while maintaining rigorous mathematical standards suitable for both specialists and enthusiasts.[14]A distinctive feature is the problems and solutions section, which invites reader-submitted problems ranging from elementary to advanced undergraduate level on Fibonacci-related topics, with proposed solutions published in later issues to encourage collaborative problem-solving and community engagement among researchers, students, and educators.[2][13] Articles in the journal typically range from 5 to 20 pages, adopting a clear and rigorous style that prioritizes logical exposition, complete references, and the judicious use of diagrams or tables, particularly for geometric interpretations of sequences.[9][14]Special features include book reviews of literature on Fibonacci numbers and their applications, as well as sections highlighting practical uses in areas like science and biology, often through invited contributions that bridge pure mathematics with real-world contexts.[2][13] The submission process is peer-reviewed, with manuscripts submitted electronically in double-spaced format via the Taylor & Francis online portal; authors receive acknowledgment upon submission and are encouraged to retain personal copies of their work.[13] These structural elements support the journal's coverage of core topics in number theory, combinatorics, and recurrences.
Publication Information
Publisher and Distribution
The Fibonacci Quarterly was self-published by the Fibonacci Association, a nonprofit organization based in the United States, from its inception in 1963 through Volume 62 in 2024.[9][8] Beginning with Volume 63, Issue 1 in February 2025, the journal transitioned to publication by Taylor & Francis, an international academic publisher, while remaining the official journal of the Fibonacci Association.[9][15]The journal maintains a quarterly publication schedule, releasing four issues annually in February, May, August, and November.[15] It is published in English and bears the print ISSN 0015-0517.Distribution has historically relied on print subscriptions for both individual and institutional subscribers, with early issues mailed via third-class post from St. Mary's College, California, under the auspices of the Fibonacci Association.[16] Subscription management was handled directly by the Fibonacci Association until 2024.[9] By 2025, under Taylor & Francis, distribution shifted to a hybrid model offering print and digital access, with institutional subscriptions managed through the publisher's platform.[15][9]
Accessibility and Archives
The Fibonacci Quarterly provides online access to its full volumes, from Volume 1 (1963) to the present, through subscriber portals on Taylor & Francis Online, following the journal's transition to this publisher in 2025.[15] Free abstracts for articles have been available since Volume 44 (2006) on the journal's heritage website at fq.math.ca.[9]The heritage site at fq.math.ca serves as a primary archive, hosting scanned issues up to Volume 62 (2024), with PDF files accessible for historical volumes.[17] A comprehensive general index covers all materials from Volumes 1–62 (1963–2024), including proceedings of international conferences, and receives ongoing updates to maintain searchability.[18]The journal is indexed in several key databases, including SCImago Journal Rank (SJR) for bibliometric analysis, zbMATH for mathematical literature, and Mathematical Reviews for abstracting and reviewing mathematical publications.[19][20] Additionally, records are available in WorldCat, the global library catalog, and the Library of Congress catalog for institutional access and preservation.While the Fibonacci Quarterly does not offer full open access, subscribers and members of the Fibonacci Association gain access through dedicated portals, and physical back issues have been stored at Santa Clara University since 1975 for archival purposes.[21][7]
Influence and Legacy
Academic Impact
The Fibonacci Quarterly maintains a specialized impact within mathematics, reflected in its 2024 impact factor of 0.4, which underscores its steady, albeit niche, influence in areas like number theory and sequences.[2] Its SCImago Journal Rank (SJR) stands at 0.365 for 2024, positioning it in the Q3 quartile for algebra and number theory, with an overall ranking of 14,726 among mathematics journals.[22] The journal's h-index of 31 indicates that 31 articles have each received at least 31 citations, a moderate figure attributable to its focused scope rather than broad interdisciplinary appeal.[19] Total citations hover around 911 as of recent updates, further highlighting its role as a dedicated venue for targeted research.[23]Since 1996, the journal has been indexed in Scopus, facilitating discoverability and contributing to its cumulative scholarly footprint, with coverage extending through 2024.[19] Notable contributions include seminal papers advancing Fibonacci identities, such as those exploring powers of Fibonacci and Lucas numbers, which have provided foundational tools for deriving new relations in linear recurrences.[24] The journal has also pioneered generalizations to other sequences, exemplified by works extending the Q-matrix framework to broader families of recurrences, enabling applications beyond classical Fibonacci properties.[25] Early investigations into Fibonacci primes, including analyses of prime Fibonacci sequences and their divisibility patterns, have informed ongoing searches for primality in recursive structures.[26]As the primary outlet for Fibonacci-related research, the Fibonacci Quarterly is frequently cited in broader number theory contexts, with its publications referenced over 8,400 times across 4,500 documents in zbMATH.[20] It has influenced computational mathematics by featuring early and advanced calculations of large Fibonacci numbers, including periodicity studies modulo primes that support efficient algorithmic implementations for sequence generation.[27] These efforts have extended to practical domains, such as algorithmic optimizations drawing on sequence generalizations for cryptography and graph-theoretic models involving golden ratio properties.[2]
Associated Events
The Fibonacci Quarterly is closely associated with the biennial International Conference on Fibonacci Numbers and Their Applications, organized by the Fibonacci Association since 1984. These conferences bring together researchers to present advancements in Fibonacci-related mathematics, with proceedings often published in the journal. The 21st conference was held July 8–12, 2024, at Harvey Mudd College in Claremont, California.[28] The 22nd conference is scheduled for July 6–10, 2026, at Galatasaray University in Istanbul, Turkey.[29]