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Journal articles on the topic 'Fibonacci, Leonardo, Fibonacci numbers'

Author: Grafiati

Published: 4 June 2021

Last updated: 12 February 2022

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1

Bonda, Moreno. "Modal Difficulty in Medieval Literature Analysis: the Frame-Notation Correlation in Dante’s Quotations of Fibonacci." Aktuālās problēmas literatūras un kultūras pētniecībā: rakstu krājums, no. 26/2 (March 11, 2021): 106–21. http://dx.doi.org/10.37384/aplkp.2021.26-2.106.

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The investigation of medieval literature poses a number of challenges, even to native speaker researchers. Such difficulties are related to (a) linguistic – syntactical and lexical – obstacles, (b) to the ability to recognise dense networks of interdisciplinary references and, (c) mainly to the cognitive challenges posed by “unfamiliar modes of expression”. The aim of this research is to discuss a methodological approach to deal with these unusual manners of composition, technically known as modal difficulty, in medieval literature. The theoretic setting is represented by Davide Castiglione’s

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2

Howard, Fredric T. "Fibonacci numbers." Mathematical Intelligencer 26, no. 1 (2004): 65. http://dx.doi.org/10.1007/bf02985406.

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3

Han, Jeong, Hee Kim, and Joseph Neggers. "On Fibonacci functions with Fibonacci numbers." Advances in Difference Equations 2012, no. 1 (2012): 126. http://dx.doi.org/10.1186/1687-1847-2012-126.

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4

Laugier, Alexandre, and Manjil P. Saikia. "Some Properties of Fibonacci Numbers, Generalized Fibonacci Numbers and Generalized Fibonacci Polynomial Sequences." Kyungpook mathematical journal 57, no. 1 (2017): 1–84. http://dx.doi.org/10.5666/kmj.2017.57.1.1.

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5

Wituła, Roman, та Damian Słota. "δ-Fibonacci numbers". Applicable Analysis and Discrete Mathematics 3, № 2 (2009): 310–29. http://dx.doi.org/10.2298/aadm0902310w.

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The scope of the paper is the definition and discussion of the polynomial generalizations of the Fibonacci numbers called here ?-Fibonacci numbers. Many special identities and interesting relations for these new numbers are presented. Also, different connections between ?-Fibonacci numbers and Fibonacci and Lucas numbers are proven in this paper.

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6

Safran, Charles. "The Fibonacci Numbers." CHANCE 5, no. 1-2 (1992): 43–46. http://dx.doi.org/10.1080/09332480.1992.11882462.

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7

Gómez Ruiz, Carlos Alexis, and Florian Luca. "Fibonacci factoriangular numbers." Indagationes Mathematicae 28, no. 4 (2017): 796–804. http://dx.doi.org/10.1016/j.indag.2017.05.002.

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8

Ma, Yuankui, and Wenpeng Zhang. "Some Identities Involving Fibonacci Polynomials and Fibonacci Numbers." Mathematics 6, no. 12 (2018): 334. http://dx.doi.org/10.3390/math6120334.

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The aim of this paper is to research the structural properties of the Fibonacci polynomials and Fibonacci numbers and obtain some identities. To achieve this purpose, we first introduce a new second-order nonlinear recursive sequence. Then, we obtain our main results by using this new sequence, the properties of the power series, and the combinatorial methods.

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9

Došlić, Tomišlać. "Fibonacci in Hogwarts?" Mathematical Gazette 87, no. 510 (2003): 432–36. http://dx.doi.org/10.1017/s0025557200173607.

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An elementary algebraic problem attributed to Leonardo of Pisa is analysed and some illogical elements in its formulation and solution are exposed. The natural context in which the problem was formulated is then proposed, and some consequences are discussed.How many times have you heard that somebody is a wizard? And how many times did you take it literally? Most likely, the answer to the second question is ‘never’. And yet, there are reasons to believe that some people among us are real wizards, of the kind described with so much charm in the recently published series of books on Harry Potter

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10

Shannon, Anthony G., Özgür Erdağ, and Ömür Deveci. "On the connections between Pell numbers and Fibonacci p-numbers." Notes on Number Theory and Discrete Mathematics 27, no. 1 (2021): 148–60. http://dx.doi.org/10.7546/nntdm.2021.27.1.148-160.

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In this paper, we define the Fibonacci–Pell p-sequence and then we discuss the connection of the Fibonacci–Pell p-sequence with the Pell and Fibonacci p-sequences. Also, we provide a new Binet formula and a new combinatorial representation of the Fibonacci–Pell p-numbers by the aid of the n-th power of the generating matrix of the Fibonacci–Pell p-sequence. Furthermore, we derive relationships between the Fibonacci–Pell p-numbers and their permanent, determinant and sums of certain matrices.

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11

Yurttas Gunes, Aysun, Sadik Delen, Musa Demirci, Ahmet Sinan Cevik, and Ismail Naci Cangul. "Fibonacci Graphs." Symmetry 12, no. 9 (2020): 1383. http://dx.doi.org/10.3390/sym12091383.

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Apart from its applications in Chemistry, Biology, Physics, Social Sciences, Anthropology, etc., there are close relations between graph theory and other areas of Mathematics. Fibonacci numbers are of utmost interest due to their relation with the golden ratio and also due to many applications in different areas from Biology, Architecture, Anatomy to Finance. In this paper, we define Fibonacci graphs as graphs having degree sequence consisting of n consecutive Fibonacci numbers and use the invariant Ω to obtain some more information on these graphs. We give the necessary and sufficient conditi

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12

Özkan, Engin, Merve Taştan, and Ali Aydoğdu. "2-Fibonacci polynomials in the family of Fibonacci numbers." Notes on Number Theory and Discrete Mathematics 24, no. 3 (2018): 47–55. http://dx.doi.org/10.7546/nntdm.2018.24.3.47-55.

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13

Harne, Sanjay, V. H. Badshah, and Sapna Sethiya. "Determinantal Identities of Fibonacci, Fibonacci Like and Lucas Numbers." Turkish Journal of Analysis and Number Theory 2, no. 4 (2014): 110–12. http://dx.doi.org/10.12691/tjant-2-4-1.

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14

Mamombe, Lovemore. "Generalized a:k:m-Fibonacci Numbers." Asian Research Journal of Mathematics 10, no. 3 (2018): 1–12. http://dx.doi.org/10.9734/arjom/2018/42751.

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15

W., H. C., G. E. Bergum, A. N. Philippou, and A. F. Horadam. "Applications of Fibonacci Numbers." Mathematics of Computation 60, no. 202 (1993): 875. http://dx.doi.org/10.2307/2153146.

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16

Kalman, Dan, and Robert Mena. "The Fibonacci Numbers: Exposed." Mathematics Magazine 76, no. 3 (2003): 167. http://dx.doi.org/10.2307/3219318.

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17

Lewis, Barry. "Fibonacci numbers and trigonometry." Mathematical Gazette 88, no. 512 (2004): 194–204. http://dx.doi.org/10.1017/s002555720017490x.

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This article started life as an investigation into certain aspects of the Fibonacci numbers, ‘morphed’ seamlessly into the structure of some infinite matrices and finally resolved into a general set of results that link structural aspects of Fibonacci numbers with trigonometric and hyperbolic functions. It is a surprising fact, but while I can find evidence that the link between these areas has been noted in the past, I can find no evidence that the link has been systematically developed.

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18

Lewis, Barry. "Trigonometry and Fibonacci numbers." Mathematical Gazette 91, no. 521 (2007): 216–26. http://dx.doi.org/10.1017/s0025557200181550.

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This article sets out to explore some of the connections between two seemingly distinct mathematical objects: trigonometric functions and the integer sequences composed of the Fibonacci and Lucas numbers. It establishes that elements of Fibonacci/Lucas sequences obey identities that are closely related to traditional trigonometric identities. It then exploits this relationship by converting existing trigonometric results into corresponding Fibonacci/Lucas results. Along the way it uses mathematical tools that are not usually associated with either of these objects.

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19

Pirillo, Giuseppe. "Fibonacci numbers and words." Discrete Mathematics 173, no. 1-3 (1997): 197–207. http://dx.doi.org/10.1016/s0012-365x(94)00236-c.

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20

Pethe, S., and A. F. Horadam. "Generalised Gaussian Fibonacci numbers." Bulletin of the Australian Mathematical Society 33, no. 1 (1986): 37–48. http://dx.doi.org/10.1017/s0004972700002847.

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In this paper, generalised Gaussian Fibonacci numbers are defined and, using the recurrence relation satisfied by them, we obtain a number of summation identities involving the products of combinations of Fibonacci, Pell and Chebyshev polynomials.

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21

Kalman, Dan, and Robert Mena. "The Fibonacci Numbers—Exposed." Mathematics Magazine 76, no. 3 (2003): 167–81. http://dx.doi.org/10.1080/0025570x.2003.11953176.

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22

W., H. C., A. N. Philippou, A. F. Horadam, and G. E. Bergum. "Applications of Fibonacci Numbers." Mathematics of Computation 53, no. 187 (1989): 453. http://dx.doi.org/10.2307/2008383.

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23

Stephan Ramon Garcia and Florian Luca. "Quotients of Fibonacci Numbers." American Mathematical Monthly 123, no. 10 (2016): 1039. http://dx.doi.org/10.4169/amer.math.monthly.123.10.1039.

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24

Bravo, Jhon J., and Carlos A. Gómez. "Mersenne k-Fibonacci numbers." Glasnik Matematicki 51, no. 2 (2016): 307–19. http://dx.doi.org/10.3336/gm.51.2.02.

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25

Gray, C. T., A. N. Philippou, A. F. Horadam, and G. E. Bergum. "Applications of Fibonacci Numbers." Statistician 38, no. 4 (1989): 308. http://dx.doi.org/10.2307/2349066.

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26

W., H. C., G. E. Bergum, A. N. Philippou, and A. F. Horadam. "Applications of Fibonacci Numbers." Mathematics of Computation 57, no. 195 (1991): 450. http://dx.doi.org/10.2307/2938693.

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27

Bacani, Jerico B., and Julius Fergy T. Rabago. "On generalized Fibonacci numbers." Applied Mathematical Sciences 9 (2015): 3611–22. http://dx.doi.org/10.12988/ams.2015.5299.

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28

Cull, Paul, and James L. Holloway. "Computing fibonacci numbers quickly." Information Processing Letters 32, no. 3 (1989): 143–49. http://dx.doi.org/10.1016/0020-0190(89)90015-x.

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29

Randić, Milan, Daniel A. Morales, and Oswaldo Araujo. "Higher-order Fibonacci numbers." Journal of Mathematical Chemistry 20, no. 1 (1996): 79–94. http://dx.doi.org/10.1007/bf01165157.

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30

Gültekin, Inci, and Ömür Deveci. "On the arrowhead-Fibonacci numbers." Open Mathematics 14, no. 1 (2016): 1104–13. http://dx.doi.org/10.1515/math-2016-0100.

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AbstractIn this paper, we define the arrowhead-Fibonacci numbers by using the arrowhead matrix of the characteristic polynomial of the k-step Fibonacci sequence and then we give some of their properties. Also, we study the arrowhead-Fibonacci sequence modulo m and we obtain the cyclic groups from the generating matrix of the arrowhead-Fibonacci numbers when read modulo m. Then we derive the relationships between the orders of the cyclic groups obtained and the periods of the arrowhead-Fibonacci sequence modulo m.

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31

Bednarz, Natalia. "On (k,p)-Fibonacci Numbers." Mathematics 9, no. 7 (2021): 727. http://dx.doi.org/10.3390/math9070727.

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In this paper, we introduce and study a new two-parameters generalization of the Fibonacci numbers, which generalizes Fibonacci numbers, Pell numbers, and Narayana numbers, simultaneously. We prove some identities which generalize well-known relations for Fibonacci numbers, Pell numbers and their generalizations. A matrix representation for generalized Fibonacci numbers is given, too.

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32

Rihane, S. E. "On $k$-Fibonacci balancing and $k$-Fibonacci Lucas-balancing numbers." Carpathian Mathematical Publications 13, no. 1 (2021): 259–71. http://dx.doi.org/10.15330/cmp.13.1.259-271.

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The balancing number $n$ and the balancer $r$ are solution of the Diophantine equation $$1+2+\cdots+(n-1) = (n+1)+(n+2)+\cdots+(n+r). $$ It is well known that if $n$ is balancing number, then $8n^2 + 1$ is a perfect square and its positive square root is called a Lucas-balancing number. For an integer $k\geq 2$, let $(F_n^{(k)})_n$ be the $k$-generalized Fibonacci sequence which starts with $0,\ldots,0,1,1$ ($k$ terms) and each term afterwards is the sum of the $k$ preceding terms. The purpose of this paper is to show that 1, 6930 are the only balancing numbers and 1, 3 are the only Lucas-bala

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33

Ramírez, José L. "Some Properties of Convolved k-Fibonacci Numbers." ISRN Combinatorics 2013 (June 12, 2013): 1–5. http://dx.doi.org/10.1155/2013/759641.

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We define the convolved k-Fibonacci numbers as an extension of the classical convolved Fibonacci numbers. Then we give some combinatorial formulas involving the k-Fibonacci and k-Lucas numbers. Moreover we obtain the convolved k-Fibonacci numbers from a family of Hessenberg matrices.

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34

Shannon, Anthony G., Irina Klamka, and Robert van Gend. "Generalized Fibonacci Numbers and Music." JOURNAL OF ADVANCES IN MATHEMATICS 14, no. 1 (2018): 7564–79. http://dx.doi.org/10.24297/jam.v14i1.7323.

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Mathematics and music have well documented historical connections. Just as the ordinary Fibonacci numbers have links with the golden ratio, this paper considers generalized Fibonacci numbers developed from generalizations of the golden ratio. It is well known that the Fibonacci sequence of numbers underlie certain musical intervals and compositions but to what extent are these connections accidental or structural, coincidental or natural and do generalized Fibonacci numbers share any of these connections?

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35

Tasci, Dursun, Mirac Cetin Firengiz, and Naim Tuglu. "Incomplete Bivariate Fibonacci and Lucas -Polynomials." Discrete Dynamics in Nature and Society 2012 (2012): 1–11. http://dx.doi.org/10.1155/2012/840345.

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We define the incomplete bivariate Fibonacci and Lucas polynomials. In the case , , we obtain the incomplete Fibonacci and Lucas numbers. If , , we have the incomplete Pell and Pell-Lucas numbers. On choosing , , we get the incomplete generalized Jacobsthal number and besides for the incomplete generalized Jacobsthal-Lucas numbers. In the case , , , we have the incomplete Fibonacci and Lucas numbers. If , , , , we obtain the Fibonacci and Lucas numbers. Also generating function and properties of the incomplete bivariate Fibonacci and Lucas polynomials are given.

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36

Deveci, Ömür. "On the connections among Fibonacci, Pell, Jacobsthal and Padovan numbers." Notes on Number Theory and Discrete Mathematics 27, no. 2 (2021): 111–28. http://dx.doi.org/10.7546/nntdm.2021.27.2.111-128.

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In this paper, we define the Fibonacci–Jacobsthal, Padovan–Fibonacci, Pell–Fibonacci, Pell–Jacobsthal, Padovan–Pell and Padovan–Jacobsthal sequences which are directly related with the Fibonacci, Jacobsthal, Pell and Padovan numbers and give their structural properties by matrix methods. Then we obtain new relationships between Fibonacci, Jacobsthal, Pell and Padovan numbers.

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37

Raman, Indhumathi. "A Note on Closed-Form Representation of Fibonacci Numbers Using Fibonacci Trees." ISRN Discrete Mathematics 2014 (February 12, 2014): 1–3. http://dx.doi.org/10.1155/2014/132925.

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We give a new representation of the Fibonacci numbers. This is achieved using Fibonacci trees. With the help of this representation, the nth Fibonacci number can be calculated without having any knowledge about the previous Fibonacci numbers.

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38

Bilgici, Göksal, and Ahmet Daşdemir. "Some unrestricted Fibonacci and Lucas hyper-complex numbers." Acta et Commentationes Universitatis Tartuensis de Mathematica 24, no. 1 (2020): 37–48. http://dx.doi.org/10.12697/acutm.2020.24.03.

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A number of studies have investigated the Fibonacci quaternions and octonions that include consecutive terms of the Fibonacci sequence. This paper presents a new generalization of Fibonacci quaternions, octonions and sedenions, where non-consecutive Fibonacci numbers are used. We present the Binet formulas, generating functions and some identities for these new types of hyper-complex numbers.

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39

Yılmaz, Nazmiye, Ali Aydoğdu, and Engin Özkan. "Some properties of k-generalized Fibonacci numbers." Mathematica Montisnigri 50 (2021): 73–79. http://dx.doi.org/10.20948/mathmontis-2021-50-7.

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In the present paper, we propose some properties of the new family 𝑘-generalized Fibonacci numbers which related to generalized Fibonacci numbers. Moreover, we give some identities involving binomial coefficients for 𝑘-generalized Fibonacci numbers.

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40

Adegoke, Kunle. "Fibonacci series from power series." Notes on Number Theory and Discrete Mathematics 27, no. 3 (2021): 44–62. http://dx.doi.org/10.7546/nntdm.2021.27.3.44-62.

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We show how every power series gives rise to a Fibonacci series and a companion series involving Lucas numbers. For illustrative purposes, Fibonacci series arising from trigonometric functions, the gamma function and the digamma function are derived. Infinite series involving Fibonacci and Bernoulli numbers and Fibonacci and Euler numbers are also obtained.

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41

Singh, Bijendra, Kiran Sisodiya, and Farooq Ahmad. "On the Products ofk-Fibonacci Numbers andk-Lucas Numbers." International Journal of Mathematics and Mathematical Sciences 2014 (2014): 1–4. http://dx.doi.org/10.1155/2014/505798.

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In this paper we investigate some products ofk-Fibonacci andk-Lucas numbers. We also present some generalized identities on the products ofk-Fibonacci andk-Lucas numbers to establish connection formulas between them with the help of Binet's formula.

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42

Zhuravleva, Victoria. "Diophantine approximations with Fibonacci numbers." Journal de Théorie des Nombres de Bordeaux 25, no. 2 (2013): 499–520. http://dx.doi.org/10.5802/jtnb.846.

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43

Jamieson, M. J. "Fibonacci Numbers and Cotangent Sequences." American Mathematical Monthly 109, no. 7 (2002): 655. http://dx.doi.org/10.2307/3072430.

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44

Varnadore, James. "Pascal's Triangle and Fibonacci Numbers." Mathematics Teacher 84, no. 4 (1991): 314–19. http://dx.doi.org/10.5951/mt.84.4.0314.

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45

Atkins, John, and Robert Geist. "Fibonacci Numbers and Computer Algorithms." College Mathematics Journal 18, no. 4 (1987): 328. http://dx.doi.org/10.2307/2686807.

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46

Ryder, Jack. "Exploring Fibonacci Numbers Mod M." College Mathematics Journal 27, no. 2 (1996): 122. http://dx.doi.org/10.2307/2687401.

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47

Trzaska, Zdzislaw W. "81.4 On Factorial Fibonacci Numbers." Mathematical Gazette 81, no. 490 (1997): 82. http://dx.doi.org/10.2307/3618775.

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48

Ferraro, Peter J. "Fibonacci Numbers and Powers: 10765." American Mathematical Monthly 108, no. 10 (2001): 978. http://dx.doi.org/10.2307/2695429.

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49

Jamieson, M. J. "Fibonacci Numbers and Cotangent Sequences." American Mathematical Monthly 109, no. 7 (2002): 655–57. http://dx.doi.org/10.1080/00029890.2002.11919896.

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50

Atkins, John, and Robert Geist. "Fibonacci Numbers and Computer Algorithms." College Mathematics Journal 18, no. 4 (1987): 328–36. http://dx.doi.org/10.1080/07468342.1987.11973055.

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