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Dissertations / Theses on the topic 'Fibonacci numbers'

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Published: 4 June 2021
Last updated: 25 July 2025

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1

Fransson, Jonas. "Generalized Fibonacci Series Considered modulo n." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-26844.

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In this thesis we are investigating identities regarding Fibonacci sequences. In particular we are examiningthe so called Pisano period, which is the period for the Fibonacci sequence considered modulo n to repeatitself. The theory shows that it suces to compute Pisano periods for primes. We are also looking atthe same problems for the generalized Pisano period, which can be described as the Pisano period forthe generalized Fibonacci sequence.
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2

Meinke, Ashley Marie. "Fibonacci Numbers and Associated Matrices." Kent State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=kent1310588704.

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3

Edson, Marcia Ruth Zamboni Luca Quardo. "Around the Fibonacci numeration system." [Denton, Tex.] : University of North Texas, 2007. http://digital.library.unt.edu/permalink/meta-dc-3676.

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4

Silva, Bruno Astrolino e. "Números de Fibonacci e números de Lucas." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/55/55136/tde-03032017-143706/.

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Neste trabalho, exploramos os números de Fibonacci e de Lucas. A maioria dos resultados históricos sobre esses números são apresentados e provados. Ao longo do texto, um grande número de identidades a respeito dos números de Fibonacci e de Lucas são mostradas válidas para todos os inteiros. Sequências generalizadas de Fibonacci, a relação entre os números de Fibonacci e de Lucas com as raízes da equação x2 -x -1 = 0 e a conexão entre os números de Fibonacci e de Lucas com uma classe de matrizes em M2(R) são também exploradas.<br>In this work we explore the Fibonacci and Lucas numbers. The majo
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5

Heberle, Curtis. "A Combinatorial Approach to $r$-Fibonacci Numbers." Scholarship @ Claremont, 2012. https://scholarship.claremont.edu/hmc_theses/34.

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In this paper we explore generalized “$r$-Fibonacci Numbers” using a combinatorial “tiling” interpretation. This approach allows us to provide simple, intuitive proofs to several identities involving $r$-Fibonacci Numbers presented by F.T. Howard and Curtis Cooper in the August, 2011, issue of the Fibonacci Quarterly. We also explore a connection between the generalized Fibonacci numbers and a generalized form of binomial coefficients.
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6

Salter, Ena. "Fibonacci vectors." [Tampa, Fla.] : University of South Florida, 2005. http://purl.fcla.edu/fcla/etd/SFE0001244.

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7

Leonesio, Justin Michael. "Fascinating characteristics and applications of the Fibonacci sequence /." Lynchburg, VA : Liberty University, 2007. http://digitalcommons.liberty.edu.

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8

Almeida, Edjane Gomes dos Santos. "Propriedades e generalizações dos números de Fibonacci." Universidade Federal da Paraíba, 2014. http://tede.biblioteca.ufpb.br:8080/handle/tede/7658.

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Submitted by Maria Suzana Diniz (msuzanad@hotmail.com) on 2015-11-30T12:34:27Z No. of bitstreams: 1 arquivototal.pdf: 766531 bytes, checksum: ad20186d0268a15265279ab809f9fd2f (MD5)<br>Approved for entry into archive by Maria Suzana Diniz (msuzanad@hotmail.com) on 2015-11-30T12:38:24Z (GMT) No. of bitstreams: 1 arquivototal.pdf: 766531 bytes, checksum: ad20186d0268a15265279ab809f9fd2f (MD5)<br>Made available in DSpace on 2015-11-30T12:38:24Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 766531 bytes, checksum: ad20186d0268a15265279ab809f9fd2f (MD5) Previous issue date: 2014-08-29<br>Coor
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9

Edson, Marcia Ruth. "Around the Fibonacci Numeration System." Thesis, University of North Texas, 2007. https://digital.library.unt.edu/ark:/67531/metadc3676/.

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Let 1, 2, 3, 5, 8, … denote the Fibonacci sequence beginning with 1 and 2, and then setting each subsequent number to the sum of the two previous ones. Every positive integer n can be expressed as a sum of distinct Fibonacci numbers in one or more ways. Setting R(n) to be the number of ways n can be written as a sum of distinct Fibonacci numbers, we exhibit certain regularity properties of R(n), one of which is connected to the Euler φ-function. In addition, using a theorem of Fine and Wilf, we give a formula for R(n) in terms of binomial coefficients modulo two.
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10

Luwes, N. J. "Fibonacci numbers and the golden rule applied in neural networks." Interim : Interdisciplinary Journal: Vol 9, Issue 1: Central University of Technology Free State Bloemfontein, 2010. http://hdl.handle.net/11462/343.

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Published Article<br>In the 13th century an Italian mathematician Fibonacci, also known as Leonardo da Pisa, identified a sequence of numbers that seemed to be repeating and be residing in nature (http://en.wikipedia.org/wiki/Fibonacci) (Kalman, D. et al. 2003: 167). Later a golden ratio was encountered in nature, art and music. This ratio can be seen in the distances in simple geometric figures. It is linked to the Fibonacci numbers by dividing a bigger Fibonacci value by the one just smaller of it. This ratio seems to be settling down to a particular value of 1.618 (http://en.wikipedia.org/w
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11

MELO, MARIA ISABEL AFONSO. "GOLDEN RATIO AND FIBONACCI NUMBERS: FROM THEORY TO PRACTICE THROUGH PHOTOGRAPHY." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2017. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=33080@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO<br>COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>PROGRAMA DE MESTRADO PROFISSIONAL EM MATEMÁTICA EM REDE NACIONAL<br>Este trabalho teve o intuito de conciliar o ensino de matemática com práticas muito presentes no cotidiano dos alunos nos dias atuais: o uso da tecnologia e a comunicação através da fotografia. Com esse objetivo, foram selecionados conteúdos matemáticos que historicamente estão relacionados com a beleza e harmonia: a razão áurea e a sequência de Fibonacci. Tais enfoques permitem associações diretas em outros ca
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12

Silva, Kênia Cristina Pereira 1984. "Sobre questões de combinatória envolvendo os números de Fibonacci, Pell e Jacobsthal." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307508.

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Orientador: José Plínio de Oliveira Santos<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-26T01:08:23Z (GMT). No. of bitstreams: 1 Silva_KeniaCristinaPereira_D.pdf: 1388554 bytes, checksum: 5bb3b8622c46807f58b3ebf6cb458fca (MD5) Previous issue date: 2014<br>Resumo: Neste trabalho apresentamos novas interpretações combinatórias para sequências que incluem os números de Fibonacci, os números de Pell e os números de Jacobsthal, em termos de partição. Na primeira parte listamos as identi
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13

Spreafico, Elen Viviani Pereira 1986. "Novas identidades envolvendo os números de Fibonacci, Lucas e Jacobsthal via ladrilhamentos." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307509.

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Orientador: José Plínio de Oliveira Santos<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-26T02:14:38Z (GMT). No. of bitstreams: 1 Spreafico_ElenVivianiPereira_D.pdf: 1192138 bytes, checksum: 2b12cd351b94a0f2f7ec24fc172305c9 (MD5) Previous issue date: 2014<br>Resumo: Neste trabalho, colaboramos com provas combinatórias que utilizam a contagem e a q-contagem de elementos em conjuntos de ladrilhamentos com restrições. Na primeira parte do trabalho utilizamos os ladrilhamentos para demo
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14

Stein, Martin [Verfasser]. "Algebraic independence results for reciprocal sums of Fibonacci and Lucas numbers / Martin Stein." Hannover : Technische Informationsbibliothek und Universitätsbibliothek Hannover (TIB), 2012. http://d-nb.info/1021189294/34.

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15

Santos, Fabio Honorato dos. "Funções de Fibonacci: um estudo sobre a razão áurea e a sequência de Fibonacci." Universidade Federal de Alagoas, 2018. http://www.repositorio.ufal.br/handle/riufal/3507.

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Due to the system does not recognize equations and formulas the resumo and abstract can be found in the PDF file.<br>Devido ao sistema não reconhecer equações e fórmulas o resumo e abstract encontra-se no arquivo em PDF.
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16

Макоедов, М. С. "Элементы числовой последовательности". Thesis, Сумский государственный университет, 2014. http://essuir.sumdu.edu.ua/handle/123456789/38792.

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Элементы числовой последовательности – это числа 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597 …, где каждое следующее число равное сумме двух предыдущих чисел. Этот способ был назван именем великого средневекового математика Леонардо Фибоначчи.
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17

Демченко, А. І. "Краса природи очима математики (числа Фібоначчі)". Thesis, Сумський державний університет, 2018. http://essuir.sumdu.edu.ua/handle/123456789/66948.

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Цікаво, що закономірності явищ природи, різноманіття форм живих організмів і рослин нашої планети, що дивують нас своєю красою і гармонією – все це можна пояснити за допомогою математики (числами Фібоначчі). У послідовності Фібоначчі кожне наступне число дорівнює сумі двох попередніх.
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18

Šiurys, Jonas. "Linear recurrence sequences of composite numbers." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2013. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2013~D_20131015_155936-95267.

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The main objects studied in this thesis are linear recurrence sequences of composite numbers. We have studied the second order (binary) linear recurrence, tribonacci – like and higher order sequences. Many examples have been given.<br>Disertacijoje nagrinėjamos tiesinės rekurenčiosios sekos. Ieškoma tokių pradinių narių, kurie generuotų rekurenčiąsias sekas sudarytas iš sudėtinių skaičių. Pilnai išnagrinėtos antros eilės tiesinės rekurenčiosos ir tribonačio tipo sekos, patiekiami pavyzdžiai. Gauti rezultatai ir k-bonačio tipo sekoms.
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19

Taran, A. "Number Phi." Thesis, Сумський державний університет, 2014. http://essuir.sumdu.edu.ua/handle/123456789/35106.

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Fibonacci is one of the most famous names in mathematics. This would come as a surprise to Leonardo Pisano, the mathematician we now know by that name. And he might have been equally surprised that he has been immortalised in the famous sequence – 0, 1, 1, 2, 3, 5, 8, 13, ... – rather than for what is considered his far greater mathematical achievement – helping to popularise our modern number system in the Latin-speaking world. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/35106
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20

Amaca, Edgar Gilbuena. "On rational functions with Golden Ratio as fixed point /." Online version of thesis, 2008. http://hdl.handle.net/1850/6212.

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21

Dias, Alberto Faustino 1972. "A sequência de Fibonacci e o número de ouro : modelos variacionais." [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306455.

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Orientador: Rodney Carlos Bassanezi<br>Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-27T16:18:31Z (GMT). No. of bitstreams: 1 Dias_AlbertoFaustino_M.pdf: 1122688 bytes, checksum: a62e35c5bae8f636d723761c61dcfcd7 (MD5) Previous issue date: 2015<br>Resumo: Apresentamos neste trabalho, uma relação existente entre a despretensiosa Sequência de Fibonacci e o Número de Ouro, conhecido também como Razão Áurea ou Número Áureo. Neste mesmo contexto, tratamos de um modelo varia
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22

Santos, Alberto Tadeu Acaiaba dos. "Das "trevas" à luz de Fibonacci: uma visão histórica." Pontifícia Universidade Católica de São Paulo, 2009. https://tede2.pucsp.br/handle/handle/13439.

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Made available in DSpace on 2016-04-28T14:16:42Z (GMT). No. of bitstreams: 1 Alberto Tadeu Acaiaba dos Santos.pdf: 1898301 bytes, checksum: dff408eb33e28cabba94fce850811da9 (MD5) Previous issue date: 2009-10-15<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>The contribution of Leonardo de Pisa for the commercial mathematics of XIII century, from the publication of the Líber Abacci and the spreading of the hindu arabian numbers in the Europe in substitution to the Roman numbers, thus facilitating the commercial transactions between the peoples after the opening of the por
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23

Ferreira, Ronaebson de Carvalho. "Números Mórficos." Universidade Federal da Paraíba, 2015. http://tede.biblioteca.ufpb.br:8080/handle/tede/8040.

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Submitted by Maike Costa (maiksebas@gmail.com) on 2016-03-28T11:10:07Z No. of bitstreams: 1 arquivototal.pdf: 800250 bytes, checksum: 42e76ab05ea580b4fd24a3312b9b4212 (MD5)<br>Made available in DSpace on 2016-03-28T11:10:07Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 800250 bytes, checksum: 42e76ab05ea580b4fd24a3312b9b4212 (MD5) Previous issue date: 2015-04-30<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES<br>Morphic numbers are numbers related to the form and, somehow, they establish a conception of beauty, aesthetics and harmony. These numbers have important
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24

Silva, Júnior Normando. "Aplicações para o princípio de indução matemática." Universidade Federal de Goiás, 2014. http://repositorio.bc.ufg.br/tede/handle/tede/7508.

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Submitted by JÚLIO HEBER SILVA (julioheber@yahoo.com.br) on 2017-06-23T18:24:17Z No. of bitstreams: 2 Dissertação - Normando Silva Junior - 2014.pdf: 1908561 bytes, checksum: 892d0c609dce5de60fb3458349a15243 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<br>Approved for entry into archive by Cláudia Bueno (claudiamoura18@gmail.com) on 2017-07-07T20:23:37Z (GMT) No. of bitstreams: 2 Dissertação - Normando Silva Junior - 2014.pdf: 1908561 bytes, checksum: 892d0c609dce5de60fb3458349a15243 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<br
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Hanley, Jodi Ann. "Egyptian fractions." CSUSB ScholarWorks, 2002. https://scholarworks.lib.csusb.edu/etd-project/2323.

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Egyptian fractions are what we know as unit fractions that are of the form 1/n - with the exception, by the Egyptians, of 2/3. Egyptian fractions have actually played an important part in mathematics history with its primary roots in number theory. This paper will trace the history of Egyptian fractions by starting at the time of the Egyptians, working our way to Fibonacci, a geologist named Farey, continued fractions, Diophantine equations, and unsolved problems in number theory.
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26

Svanström, Fredrik. "Properties of a generalized Arnold’s discrete cat map." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-35209.

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After reviewing some properties of the two dimensional hyperbolic toral automorphism called Arnold's discrete cat map, including its generalizations with matrices having positive unit determinant, this thesis contains a definition of a novel cat map where the elements of the matrix are found in the sequence of Pell numbers. This mapping is therefore denoted as Pell's cat map. The main result of this thesis is a theorem determining the upper bound for the minimal period of Pell's cat map. From numerical results four conjectures regarding properties of Pell's cat map are also stated. A brief exp
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27

Даценко, Д. С. "Числа Фібоначчі". Thesis, Сумський державний університет, 2015. http://essuir.sumdu.edu.ua/handle/123456789/43364.

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Багато різних процесів природи підкоряються однаковим закономірностям. Одні з них задає числовий ряд Фібоначчі, який ще в XIII ст. помітив італійський математик Леонардо Пізанський (більш відомий як Фібоначчі).
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28

Jacques, Rodrigo da Costa. "O número de ouro no Ensino Fundamental." reponame:Repositório Institucional da UFABC, 2016.

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Orientador: Prof. Dr. Jeferson Cassiano<br>Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Mestrado Profissional em Matemática em Rede Nacional, 2016.<br>Neste trabalho de dissertação, apresentamos uma linha de pesquisa envolvendo a incomensurabilidade com um estudo de caso do número de ouro; sua definição, suas aplicações, sua relação com o pentagrama e com a sequência de Fibonacci e também suas curiosidades que o relacionamos com a arte e a natureza. O objetivo é mostrar como este tema pode vir a ser abordado entre os alunos do Ensino Fundamental e Medio de
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29

Šiurys, Jonas. "Tiesinės rekurenčiosios sekos sudarytos iš sudėtinių skaičių." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2013. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2013~D_20131015_155954-89079.

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Disertacijoje nagrinėjamos tiesinės rekurenčiosios sekos. Ieškoma tokių pradinių narių, kurie generuotų rekurenčiąsias sekas sudarytas iš sudėtinių skaičių. Pilnai išnagrinėtos antros eilės tiesinės rekurenčiosos ir tribonačio tipo sekos, patiekiami pavyzdžiai. Gauti rezultatai ir k-bonačio tipo sekoms.<br>The main objects studied in this thesis are linear recurrence sequences of composite numbers. We have studied the second order (binary) linear recurrence, tribonacci – like and higher order sequences. Many examples have been given.
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30

Sodré, Leandro de Oliveira. "O número 142857 e o número de ouro: curiosidades, propriedades matemáticas e propostas de atividades didáticas." Universidade Federal de Juiz de Fora (UFJF), 2013. https://repositorio.ufjf.br/jspui/handle/ufjf/2364.

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Submitted by isabela.moljf@hotmail.com (isabela.moljf@hotmail.com) on 2016-08-18T13:58:42Z No. of bitstreams: 1 leandrodeoliveirasodre.pdf: 681870 bytes, checksum: 2aa85f9c6534a3e3fbb9b9999b6dc538 (MD5)<br>Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-08-19T11:52:31Z (GMT) No. of bitstreams: 1 leandrodeoliveirasodre.pdf: 681870 bytes, checksum: 2aa85f9c6534a3e3fbb9b9999b6dc538 (MD5)<br>Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-08-19T11:52:50Z (GMT) No. of bitstreams: 1 leandrodeoliveirasodre.pdf:
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Wan, Jessica J. "Violet Archer’s “The Twenty-Third Psalm” (1952): An Analytical Study of Text and Music Relations through Fibonacci Numbers, Melodic Contour, Motives, and Piano Accompaniment." Thèse, Université d'Ottawa / University of Ottawa, 2012. http://hdl.handle.net/10393/23346.

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This study explores text and music relations in Canadian composer Violet Archer’s “The Twenty-Third Psalm” by analysing the text of Psalm 23, Fibonacci numbers, melodic contours, motives, and the role of the accompaniment. The text focuses on David’s faith in God and his acceptance of God as his shepherd on earth. The four other approaches allow us to examine the work on three different structural levels: background through Fibonacci numbers, middleground through melodic contour analysis, and foreground through motivic analysis and the role of the accompaniment. The measure numbers that align
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32

Палажченко, В. В., та Л. Л. Щецова. "Числа Фібоначчі". Thesis, Сумський державний університет, 2017. http://essuir.sumdu.edu.ua/handle/123456789/66976.

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В елементарній математиці існує багато завдань, часто важких і цікавих, які не пов'язані з якимось ім'ям, а скоріше носять характер свого роду "математичного фольклору" .У кожному такому завданні ми маємо справу з маленькими математичними теоріями. Такою теорією є і теорія чисел Фібоначчі, що виросли зі знаменитої "задачі про кроликів", з якою ми зіштовхуємося в цій роботі. Числа Фібоначчі до сих пір залишаються однією з найбільш захоплюючих глав елементарної математики. Завдання, пов'язані з числами Фібоначчі наводяться в багатьох популярних виданнях з математики, розглядаються на заня
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Кудояр, И. А. "Замечательные числа. Числа Фибоначчи". Thesis, Сумский государственный университет, 2015. http://essuir.sumdu.edu.ua/handle/123456789/43356.

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В данной работе рассмотрено, какие свойства имеют числа Фибоначчи. Интересный факт состоит в том, что если взять два соседних числа из этой последовательности и найти их сумму, то получим значение числа следующего в этой последовательности.
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Castelo, Branco Audino 1961. "A má temática da dislexia : aspectos da utilização da arte e da tecnologia na aprendizagem da matemática por alunos portadores de dislexia." [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306036.

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Orientador: Maria Aparecida Diniz Ehrhardt<br>Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-26T19:41:27Z (GMT). No. of bitstreams: 1 CasteloBranco_Audino_M.pdf: 12945958 bytes, checksum: 5e68ba53d0cb9f79c140abfa9532c05b (MD5) Previous issue date: 2015<br>Resumo: Essa pesquisa tem como objetivo explorar a aprendizagem de certos tópicos da Matemática por parte de alunos disléxicos e a contribuição que a Arte e a tecnologia podem dar, servindo como instrumentos facilitad
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Hong, Haojie. "Grands diviseurs premiers de suites récurrentes linéaires." Electronic Thesis or Diss., Bordeaux, 2024. http://www.theses.fr/2024BORD0107.

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Cette thèse porte sur les minorations des plus grands diviseurs premiers de suites récurrentes linéaires. Tout d’abord, nous obtenons une version uniforme et explicite du résultat séminal de Stewart sur les diviseurs premiers des suites de Lucas. Nous montrons que les constantes du théorème de Stewart ne dépendent que du corps quadratique correspondant à la suite de Lucas, mais pas d’autres paramètres. Nous étudions ensuite les diviseurs premiers des ordres de courbes elliptiques sur des corps finis. En fixant une courbe elliptique sur un corps fini Fq avec q puissance d’un nombre premier, la
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Miotto, Eder. "A análise combinatória e seu ensino." Universidade Tecnológica Federal do Paraná, 2014. http://repositorio.utfpr.edu.br/jspui/handle/1/1013.

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CAPES<br>O presente trabalho tem dois objetivos: o primeiro está relacionado ao ensino da análise combinatória nas séries do ensino fundamental 2 e ensino médio. O segundo objetivo e buscar aprofundar meus conhecimentos relacionados aos conceitos combinatoriais. Com relação ao primeiro objetivo, o ensino da análise combinatória, na minha trajetória como docente, tem sido uma das tarefas mais árduas que o professor de matemática da educação básica enfrenta. Diante disso, surgem algumas perguntas. Por que um assunto totalmente aplicável ao cotidiano tem gerado tanta dificuldade de compreensão? U
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Reiland, Elizabeth. "Combinatorial Interpretations of Fibonomial Identities." Scholarship @ Claremont, 2011. http://scholarship.claremont.edu/hmc_theses/10.

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The Fibonomial numbers are defined by \[ \begin{bmatrix}n \\ k \end{bmatrix} = \frac{\prod_{i=n-k+1} ^{n} F_i}{\prod_{j=1}^{k} F_j} \] where $F_i$ is the $i$th Fibonacci number, defined by the recurrence $F_n=F_{n-1}+F_{n-2}$ with initial conditions $F_0=0,F_1=1$. In the past year, Sagan and Savage have derived a combinatorial interpretation for these Fibonomial numbers, an interpretation that relies upon tilings of a partition and its complement in a given grid.In this thesis, I investigate previously proven theorems for the Fibonomial numbers and attempt to reinterpret and reprove them in
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Peters, Martine Francis. "NUMBER SYSTEM: VARIATIONS IN WEAVING." Kent State University / OhioLINK, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=kent1281547154.

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McDonnell, Francis James. "Inequalities with small coefficients and the reformulation of integer programmes." Thesis, Loughborough University, 1998. https://dspace.lboro.ac.uk/2134/28223.

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Sentone, Francielle Gonçalves. "Paradoxos geométricos em sala de aula." Universidade Tecnológica Federal do Paraná, 2017. http://repositorio.utfpr.edu.br/jspui/handle/1/2701.

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CAPES<br>Apresentamos neste trabalho alguns paradoxos lógico-matemáticos, como o paradoxo de Galileu, e também alguns paradoxos geométricos, como os paradoxos de Curry, de Hooper e de Banach-Tarski. Empregamos os paradoxos de Curry e de Hooper para motivar o estudo de conceitos de Geometria e de Teoria dos Números, tais como área, semelhança de triângulos, o Teorema de Pitágoras, razões trigonométricas no triângulo retângulo, o coeficiente angular da reta e a sequência de Fibonacci, e organizamos atividades lúdicas para a sala de aula no Ensino Fundamental e no Ensino Médio.<br>We present in t
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Smith, Andrew Martin. "Remnants." Bowling Green, Ohio : Bowling Green State University, 2009. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=bgsu1237661688.

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Thesis (M.M.)--Bowling Green State University, 2009.<br>Document formatted into pages; contains 1 score (vi, 29 p.) For clarinet, bassoon, and chamber orchestra (two trumpets, two horns, tenor trombone, bass trombone, percussion, piano, harp, and strings (six first violins, six second violins, four violas, four cellos, and two basses) Includes bibliographical references.
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Silva, Renato Rodrigues. "Razão áurea: como motivação ao estudo de conteúdos matemáticos." Universidade Federal de Goiás, 2014. http://repositorio.bc.ufg.br/tede/handle/tede/4027.

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Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2015-01-30T10:55:39Z No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação - Renato Rodrigues Silva -2014.pdf: 4704384 bytes, checksum: 1dafae2c957953e4722a13b5af371ec4 (MD5)<br>Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-01-30T13:24:27Z (GMT) No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação - Renato Rodrigues Silva -2014.pdf: 4704384 bytes, checksum: 1dafae2c957953e4722a13b5af371ec4 (MD
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Іванчук, Олексій Васильович, Алексей Васильевич Иванчук, and Oleksii Vasylovych Ivanchuk. "Self-controlled binomial counters." Thesis, Сумський державний університет, 2013. http://essuir.sumdu.edu.ua/handle/123456789/33535.

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Counters take a special place among digital circuits used for data processing. Nowadays we more and more often face the task of improving their supervisory capacity. However, controlling their errors is a rather complex task, which requires the development of an additional control device added to the counter, the operation of which it is also necessary to check. Moreover, in this case the counter becomes an inhomogeneous structure, which is not easy to design and adjust while its reliability may even decrease. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/
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Борисенко, Александр Андреевич, Олександр Андрійович Борисенко, Oleksandr Andriiovych Borysenko та ін. "Преобразование фибоначчи-восьмеричных чисел в двоичные". Thesis, Сумский государственный университет, 2017. http://essuir.sumdu.edu.ua/handle/123456789/65303.

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В настоящее время широко используется различные системы счисления для обработки и передачи информации. При этом, обмен информацией между цифровыми устройствами является одной из важнейших задач систем обработки информации. При этом каждое переданное сообщение должно обладать достаточным уровнем достоверности. Для этого применяют помехоустойчивые коды, которое наряду с кодами с искусственной избыточностью, используют естественную избыточность. К таким кодам относятся коды Фибоначчи.
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SERN, CHEW JOHN, and 周昌勝. "On Anti-Fibonacci Numbers." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/pns2rw.

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Rockwell, Daniel Luke. "A reinterpretation, and new demonstrations of, the Borel Normal Number Theorem." Thesis, 2011. http://hdl.handle.net/1957/23486.

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The notion of a normal number and the Normal Number Theorem date back over 100 years. Émile Borel first stated his Normal Number Theorem in 1909. Despite their seemingly basic nature, normal numbers are still engaging many mathematicians to this day. In this paper, we provide a reinterpretation of the concept of a normal number. This leads to a new proof of Borel's classic Normal Number Theorem, and also a construction of a set that contains all absolutely normal numbers. We are also able to use the reinterpretation to apply the same definition for a normal number to any point in a symbolic d
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Li, Zong-Han, and 李宗翰. "Introduction to Fibonacci Numbers and the Golden Ratio." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/mx4h5v.

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碩士<br>逢甲大學<br>應用數學系<br>107<br>We all know that the Fibonacci numbers are a famous sequence. But do you really know how it came from? Can you identify some of its interesting properties? Do you know its relationship with the so-called Golden ratio? This paper introduces the origin of the Fibonacci numbers, and derives the general formula of the Fibonacci numbers through several methods. Then we use the general formula to verify some of the important properties, including and the relationship between the Fibonacci numbers and the gold ratio. To demonstrate the power of the applications of Fibon
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Nag, Kappagantu Prudhavi. "Sum of Product of Reciprocals of Fibonacci Numbers." Thesis, 2015. http://ethesis.nitrkl.ac.in/7297/1/Sum_Nag_2015.pdf.

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Fibonacci numbers are the number sequences which follow the linear mathematical recurrence𝐹0 = 0, 𝐹1 = 1 and 𝐹𝑛 = 𝐹𝑛−1 + 𝐹𝑛−2 𝑛 ≥ 2. In this work, we study certain sum formulas involving products of reciprocals of Fibonacci numbers. Sum formulas with alternating signs are also studied
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Scheibelhut, Kira. "Polynomials that are Integer-Valued on the Fibonacci Numbers." 2013. http://hdl.handle.net/10222/35316.

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An integer-valued polynomial is a polynomial with rational coefficients that takes an integer value when evaluated at an integer. The binomial polynomials form a regular basis for the Z-module of all integer-valued polynomials. Using the idea of a p-ordering and a p-sequence, Bhargava describes a similar characterization for polynomials that are integer-valued on some subset of the integers. This thesis focuses on characterizing the polynomials that are integer-valued on the Fibonacci numbers. For a certain class of primes p, we give a formula for the p-sequence of the Fibonacci numbers and an
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Mandal, B. P. "On sums and reciprocal sum of generalized fibonacci numbers." Thesis, 2014. http://ethesis.nitrkl.ac.in/6242/1/E-9.pdf.

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The purpose of this report is to analyze the properties of Fibonacci numbers modulo a Lucas numbers. Any Fibonacci number, except the first two, is the sum of the two immediately preceding Fibonacci numbers and closely related to Fibonacci numbers are Lucas number. Fibonacci numbers are used in the application of computer algorithms. They can be used to compress audio files and generate code. The most recently Fibonacci number have been used to symbolize mathematical relationship in the Davinci code as well as in the TV shows fringe, criminal minds. In this report, some generalized identities
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