To see the other types of publications on this topic, follow the link: Numbers and Geometry.
Dissertations / Theses on the topic 'Numbers and Geometry'
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the top 50 dissertations / theses for your research on the topic 'Numbers and Geometry.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Browse dissertations / theses on a wide variety of disciplines and organise your bibliography correctly.
1
Rivard-Cooke, Martin. "Parametric Geometry of Numbers." Thesis, Université d'Ottawa / University of Ottawa, 2019. http://hdl.handle.net/10393/38871.
Full textAbstract:
This thesis is primarily concerned in studying the relationship between different exponents of Diophantine approximation, which are quantities arising naturally in the study of rational approximation to a fixed n-tuple of real irrational numbers.
As Khinchin observed, these exponents are not independent of each other, spurring interest in the study of the spectrum of a given family of exponents, which is the set of all possible values that can be taken by said family of exponents.
Introduced in 2009-2013 by Schmidt and Summerer and completed by Roy in 2015, the parametric geometry of numbers provides strong tools with regards to the study of exponents of Diophantine approximation and their associated spectra by the introduction of combinatorial objects called n-systems. Roy proved the very surprising result that the study of spectra of exponents is equivalent to the study of certain quantities attached to n-systems. Thus, the study of rational approximation can be replaced by the study of n-systems when attempting to determine such spectra.
Recently, Roy proved two new results for the case n=3, the first being that spectra are semi-algebraic sets, and the second being that spectra are stable under the minimum with respect to the product ordering. In this thesis, it is shown that both of these results do not hold in general for n>3, and examples are given.
This thesis also provides non-trivial examples for n=4 where the spectra is stable under the minimum.
An alternate and much simpler proof of a recent result of Marnat-Moshchevitin proving an important conjecture of Schmidt-Summerer is also given, relying only on the parametric geometry of numbers instead. Further, a conjecture which generalizes this result is also established, and some partial results are given towards its validity. Among these results, the simplest, but non-trivial, new case is also proven to be true.
In a different vein, this thesis considers certain generalizations theta(q) of the classical theta q-series. We show under conditions on the coefficients of the series that theta(q) is neither rational nor quadratic irrational for each integer q>1.
2
Landstedt, Erik. "Parametric Geometry of Numbers and Exponents of Diophantine Approximation." Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-388506.
Full text
3
Holmin, Samuel. "Geometry of numbers, class group statistics and free path lengths." Doctoral thesis, KTH, Matematik (Avd.), 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-177888.
Full textAbstract:
This thesis contains four papers, where the first two are in the area of geometry of numbers, the third is about class group statistics and the fourth is about free path lengths. A general theme throughout the thesis is lattice points and convex bodies. In Paper A we give an asymptotic expression for the number of integer matrices with primitive row vectors and a given nonzero determinant, such that the Euclidean matrix norm is less than a given large number. We also investigate the density of matrices with primitive rows in the space of matrices with a given determinant, and determine its asymptotics for large determinants. In Paper B we prove a sharp bound for the remainder term of the number of lattice points inside a ball, when averaging over a compact set of (not necessarily unimodular) lattices, in dimensions two and three. We also prove that such a bound cannot hold if one averages over the space of all lattices. In Paper C, we give a conjectural asymptotic formula for the number of imaginary quadratic fields with class number h, for any odd h, and a conjectural asymptotic formula for the number of imaginary quadratic fields with class group isomorphic to G, for any finite abelian p-group G where p is an odd prime. In support of our conjectures we have computed these quantities, assuming the generalized Riemann hypothesis and with the aid of a supercomputer, for all odd h up to a million and all abelian p-groups of order up to a million, thus producing a large list of “missing class groups.” The numerical evidence matches quite well with our conjectures. In Paper D, we consider the distribution of free path lengths, or the distance between consecutive bounces of random particles in a rectangular box. If each particle travels a distance R, then, as R → ∞ the free path lengths coincides with the distribution of the length of the intersection of a random line with the box (for a natural ensemble of random lines) and we determine the mean value of the path lengths. Moreover, we give an explicit formula for the probability density function in dimension two and three. In dimension two we also consider a closely related model where each particle is allowed to bounce N times, as N → ∞, and give an explicit formula for its probability density function.QC 20151204
4
Thiel, Carsten [Verfasser], and Martin [Akademischer Betreuer] Henk. "Adelic convex geometry of numbers / Carsten Thiel. Betreuer: Martin Henk." Magdeburg : Universitätsbibliothek, 2014. http://d-nb.info/1054638128/34.
Full text
5
Pham, Van Anh. "Loop Numbers of Knots and Links." TopSCHOLAR®, 2017. http://digitalcommons.wku.edu/theses/1952.
Full textAbstract:
This thesis introduces a new quantity called loop number, and shows the conditions in which loop numbers become knot invariants. For a given knot diagram D, one can traverse the knot diagram and count the number of loops created by the traversal. The number of loops recorded depends on the starting point in the diagram D and on the traversal direction. Looking at the minimum or maximum number of loops over all starting points and directions, one can define two positive integers as loop numbers of the diagram D. In this thesis, the conditions under which these loop numbers become knot invariants are identified. In particular, the thesis answers the question when these numbers are invariant under flypes in the diagram D.
6
Hahn, Marvin Anas Verfasser], and Hannah [Akademischer Betreuer] [Markwig. "Combinatorics and degenerations in algebraic geometry : Hurwitz numbers, Mustafin varieties and tropical geometry / Marvin Anas Hahn ; Betreuer: Hannah Markwig." Tübingen : Universitätsbibliothek Tübingen, 2018. http://d-nb.info/1199355968/34.
Full text
7
Conley, Randolph M. "A survey of the Minkowski?(x) function." Morgantown, W. Va. : [West Virginia University Libraries], 2003. http://etd.wvu.edu/templates/showETD.cfm?recnum=3055.
Full text
8
Mohammed, Dilbak. "Generalised Frobenius numbers : geometry of upper bounds, Frobenius graphs and exact formulas for arithmetic sequences." Thesis, Cardiff University, 2015. http://orca.cf.ac.uk/98161/.
Full textAbstract:
Given a positive integer vector ${\ve a}=(a_{1},a_{2}\dots,a_k)^t$ with \bea 1< a_{1}<\cdots
9
Shaughnessy, John F. "Finding Zeros of Rational Quadratic Forms." Scholarship @ Claremont, 2014. http://scholarship.claremont.edu/cmc_theses/849.
Full textAbstract:
In this thesis, we introduce the notion of quadratic forms and provide motivation for their study. We begin by discussing Diophantine equations, the field of p-adic numbers, and the Hasse-Minkowski Theorem that allows us to use p-adic analysis determine whether a quadratic form has a rational root. We then discuss search bounds and state Cassels' Theorem for small-height zeros of rational quadratic forms. We end with a proof of Cassels' Theorem and suggestions for further reading.
10
Johnson, Jamie. "Continued Radicals." TopSCHOLAR®, 2005. http://digitalcommons.wku.edu/theses/240.
Full textAbstract:
If a1, a2, . . . , an are nonnegative real numbers and fj(x) = paj + x, then f1o f2o· · · fn(0) is a nested radical with terms a1, . . . , an. If it exists, the limit as n ! 1 of such an expression is a continued radical. We consider the set of real numbers S(M) representable as an infinite nested radical whose terms a1, a2, . . . are all from a finite set M. We give conditions on the set M for S(M) to be (a) an interval, and (b) homeomorphic to the Cantor set.
11
Albuquerque, JoÃo Victor Maximiano. "Finitude do grupo das classes de um corpo de nÃmeros via empacotamentos reticulados." Universidade Federal do CearÃ, 2013. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=11247.
Full textAbstract:
Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgicoEste trabalho à baseado no artigo Finiteness of the class group of a number field via lattice packings. Daremos aqui uma prova alternativa da finitude do grupo das classes de um corpo de nÃmeros de grau n. Ela à baseada apenas no fato de que a densidade de centro de um empacotamento reticulado n-dimensional à limitado fora do infinito.
This work is based on the article Finiteness of the class group of a number field via lattice packings. An alternative proof of the finiteness of the class group of a number field of the degree n is presented. It is based solely on the fact that the center density of an n-dimensional lattice packing is bounded away from infinity.
12
Sengupta, Indranath. "Betti Numbers, Grobner Basis And Syzygies For Certain Affine Monomial Curves." Thesis, Indian Institute of Science, 2000. http://hdl.handle.net/2005/271.
Full textAbstract:
Let e > 3 and mo,... ,me_i be positive integers with gcd(m0,... ,me_i) = 1, which form an almost arithmetic sequence, i.e., some e - 1 of these form an arithmetic progression. We further assume that m0,... ,mc_1 generate F := Σ e-1 I=0 Nmi minimally. Note that any three integers and also any arithmetic progression form an almost arithmetic sequence.
We assume that 0 < m0 < • • • < me-2 form an arithmetic progression and n := mc-i is arbitrary Put p := e - 2. Let K be a field and XQ) ... ,Xj>, Y,T be indeterminates. Let p denote the kernel of the if-algebra homomorphism η: K[XQ, ..., XV) Y) -* K^T], defined by r){Xi) = Tm\.. .η{Xp) = Tmp, η](Y) = Tn. Then, p is the defining ideal for the affine monomial curve C in A^, defined parametrically by Xo = Trr^)...)Xv = T^}Y = T*. Furthermore, p is a homogeneous ideal with respect to the gradation on K[X0)... ,XP,F], given by wt(Z0) = mo, • • •, wt(Xp) = mp, wt(Y) = n. Let 4 := K[XQ> ...,XP) Y)/p denote the coordinate ring of C.
With the assumption ch(K) = 0, in Chapter 1 we have derived an explicit formula for μ(DerK(A)), the minimal number of generators for the A-module DerK(A), the derivation module of A. Furthermore, since type(A) = μ(DerK(A)) — 1 and the last Betti number of A is equal to type(A), we therefore obtain an explicit formula for the last Betti number of A as well
A minimal set of binomial generatorsG for the ideal p had been explicitly constructed by PatiL In Chapter 2, we show that the set G is a Grobner basis with respect to grevlex monomial ordering on K[X0)..., Xp, Y]. As an application of this observation, in Chapter 3 we obtain an explicit minimal free resolution for affine monomial curves in A4K defined by four coprime positive integers mo,.. m3, which form a minimal arithmetic progression.
(Please refer the pdf file forformulas)
13
Lima, Claudio Woerle [UNESP]. "Representações dos números racionais e a medição de segmentos: possibilidades com tecnologias informáticas." Universidade Estadual Paulista (UNESP), 2010. http://hdl.handle.net/11449/91103.
Full textAbstract:
Made available in DSpace on 2014-06-11T19:24:54Z (GMT). No. of bitstreams: 0
Previous issue date: 2010-04-01Bitstream added on 2014-06-13T20:13:19Z : No. of bitstreams: 1
lima_cw_me_rcla.pdf: 3093037 bytes, checksum: 82ceff562d5a32cc23b45ec23e51ab60 (MD5)See-Sp
Essa pesquisa investiga as contribuições que a exploração dos números racionais como medidas de segmentos, em um programa de geometria dinâmica, podem trazer ao entendimento de frações, decimais e da reta numérica entre outras representações dos racionais. A pesquisa se fundamenta em evidências históricas e resultados de pesquisas que mostram a importância do significado de medida para o entendimento dos números. Através das tecnologias informáticas viu-se uma alternativa para a exploração da medida de segmentos. Essa pesquisa é baseada no processo de medição de segmentos, em teorias sobre visualização, experimentação e representações múltiplas. Também se inspira em preceitos construcionistas. Essa investigação qualitativa se baseou na metodologia de experimentos de ensino, em que foram formados dois grupos com alunos de 6ª série / 7º ano do ensino fundamental de uma escola pública estadual do interior de São Paulo. Esses grupos participaram de encontros em que foram desenvolvidas atividades que envolviam: divisão de segmentos; frações como medidas de segmentos; operações de adição e subtração de frações utilizando os segmentos; processo de medição para criação dos números decimais; relações entre decimais e frações; adição e subtração dos números decimais; adição e subtração de frações e decimais. As atividades realizadas se basearam nos recursos de visualização e experimentação proporcionadas pelo software de geometria dinâmica Régua e Compasso. O trabalho evidenciou a importância da aprendizagem das representações múltiplas dos números racionais e como as tecnologias informáticas (computadores, software de geometria e calculadoras) podem atuar nessa aprendizagem. A pesquisa também evidência que a utilização de recursos tecnológicos pode modificar a matemática da sala de aula, proporcionando aos estudantes...
This research investigates the contributions that the exploration of rational numbers as measure of segments, using geometry dynamic software, can introduce into the understanding of fractions, decimal numbers and the number line, amongst other rational number representations. The research is motivated by both historical evidence and evidence from the research literature showing the importance of the measure meaning to the understanding of rational numbers. Digital technologies offer an alternative method for the exploration of segments measure, as yet underexplored in the field of mathematics education. This research is based on an approach to numbers as measurements of segments, which draws from theories emphasizing the role of visualization, experimentation and multiple representations in mathematics learning. It is also inspired by a constructionist perspective. The qualitative investigation made use of the teaching experiment methodology, in that two groups were formed with students of 6th grade / 7th year within an elementary school of a public school in the state of São Paulo. These groups took part in research sessions where they developed activities that involve: division of segments; fractions as measure of segments; operations of addition and subtraction of fraction using segments; measurement for decimal numbers creation; relations between decimal numbers and fractions; addition and subtraction of decimal numbers; addition and subtraction of fractions and decimal numbers. The activities exploited the resources visualization and experimentation proportioned by the dynamic geometry software “Compass and Rule”. Analyses of the data collected pointed to the importance of the understanding of multiple representations for rational numbers and to the role that digital technologies (computers, geometry software and calculators) can play in this learning. This research, also, ... (Complete abstract click electronic access below)
14
Koc, Betul. "From Numbers To Digits: On The Changing Role Of Mathematics In Architecture." Master's thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/3/12609645/index.pdf.
Full textAbstract:
This study is a critical reconsideration of architecture&rsquos affiliation with mathematics and geometry both as practical instrument and theoretical reference. The thesis claims that mathematics and its methodological structure provided architects with an ultimate foundation and a strong reference outside architecture itself ever since the initial formations of architectural discourse. However, the definitive assumptions and epistemological consequences of this grounding in mathematical clarity, methodological certainty and instrumental precision gain a new insight with the introduction of digital technologies. Since digital technologies offer a new formation for this affiliation either with their claim of a better geometric representation or mathematical controllability of physical reality (space), the specific focus on these newly emerging technologies will be developed within a theoretical frame presenting the significant points of mathematics in architecture.
15
Oliveira, Stanley Borges de. "Números complexos e geometria." Universidade Estadual da Paraíba, 2014. http://tede.bc.uepb.edu.br/tede/jspui/handle/tede/2340.
Full textAbstract:
Submitted by Jean Medeiros (jeanletras@uepb.edu.br) on 2016-03-08T12:13:27Z
No. of bitstreams: 2
license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)
PDF - Stanley Borges de Oliveira.pdf: 3340773 bytes, checksum: de816c79a26915787dd60d54ce472134 (MD5)Approved for entry into archive by Secta BC (secta.csu.bc@uepb.edu.br) on 2016-06-13T20:37:16Z (GMT) No. of bitstreams: 2 PDF - Stanley Borges de Oliveira.pdf: 3340773 bytes, checksum: de816c79a26915787dd60d54ce472134 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)
Made available in DSpace on 2016-07-21T20:49:44Z (GMT). No. of bitstreams: 2 PDF - Stanley Borges de Oliveira.pdf: 3340773 bytes, checksum: de816c79a26915787dd60d54ce472134 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2014-07-25
In the presentdissertation we study complex numbers with a special attention to the geometric aspect. Many geometric problems can be answered using the algebraic notation of complex numbers with their rich geometric interpretations with relative ease. The geometric aspects of the complex numbers are often not taught in high school, not even the trigonometric form (or polar form). Therefore, students do not apply the knowledge of complex numbers to solve geometric problems. In this paper we will approach the complex numbers applied to solve both geometric as algebraic problems, making relate geometric concepts with algebraic concepts of complex numbers, and launched as a proposal to develop the ability of students to relate mathematical content offering opportunity of even better fix the concepts of complex numbers.
No presente trabalho de conclusão de curso trataremos sobre os números complexos com uma atenção especial ao seu aspecto geométrico. Alguns problemas geométricos podem ser solucionados usando a notação algébrica dos números complexos com ajuda das suas ricas interpretações geométricas com certa facilidade. O aspecto geométrico dos números complexos muitas vezes não é ensinado no ensino médio, nem sequer a forma trigonométrica (ou polar). Por essa razão, os alunos não aplicam os conhecimentos de números complexos para resolver problemas geométricos. Em muitos casos, essa abordagem vem a facilitar a resolução das soluções. Neste trabalho faremos uma abordagem dos números complexos aplicados para resolver problemas, ora geométricos, ora algébricos, fazendo relacionar os conceitos geométricos com os conceitos algébricos dos números complexos e vice versa, e lançamos como proposta para desenvolver a habilidade dos alunos em relacionar os conteúdos matemáticos oferecendo oportunidade dos mesmo fixarem melhor conceitos dos números complexos.
16
Collazo, Antonio. "The Mathematical Landscape." Scholarship @ Claremont, 2011. http://scholarship.claremont.edu/cmc_theses/116.
Full textAbstract:
The intent of this paper is to present the reader will enough information to spark a curiosity in to the subject. By no means is the following a complete formulation of any of the topics covered. I want to give the reader a tour of the mathematical landscape. There are plenty of further details to explore in each section, I have just touched the tip the iceberg. The work is basically in four sections: Numbers, Geometry, Functions, Sets and Logic, which are the basic building blocks of Math. The first sections are a exposition into the mathematical objects and their algebras. The last section dives into the foundation of math, sets and logic, and develops the ``language'' of Math. My hope is that after this, the reader will have the necessary (maybe not sufficient) information needed to talk the language of Math.
17
Feitosa, Laércio Francisco. "Aplicações dos números complexos na geometria." Universidade Federal da Paraíba, 2013. http://tede.biblioteca.ufpb.br:8080/handle/tede/7381.
Full textAbstract:
Made available in DSpace on 2015-05-15T11:46:06Z (GMT). No. of bitstreams: 0
Previous issue date: 2013-04-12Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
The teaching of Complex Numbers is based almost exclusively on an algebraic approach, although the geometric approach of complex numbers is contemplated in the study of its polar form (or trigonometric). The purpose of this paper is to present some significant applications of complex numbers in plane geometry, making thus a contrast to this view strictly algebraic and formal, that has traditionally characterized the teaching of these numbers. We'll cover some classical theorems of geometry and some geometric problems, evaluating the efficiency of complex numbers as a tool to demonstrate the theorems and results relevant to the resolution of such problems. Some of the theorems selected in our study were: Napoleon's Theorem, the Circle of Nine Points and Simson Line.
O ensino dos números complexos baseia-se quase que exclusivamente em uma abordagem algébrica. Embora, a abordagem geométrica dos números complexos estejá contemplada no estudo da sua forma polar (ou trigonométrica).O propósito deste trabalho é apresentar algumas aplicações significativas dos números complexos na geometria plana, fazendo assim uma contraposição a essa visão estritamente algébrica e formal que tradicionalmente caracteriza o ensino dos números complexos. Com esse objetivo, vamos abordar alguns teoremas clássicos da geometria e alguns problemas geométricos, avaliando a eficiência dos números complexos como ferramenta para demonstrar os teoremas e os resultados pertinentes a resolução de tais problemas. Alguns dos teoremas selecionados foram : o Teorema de Napoleão, o Círculo dos Nove Pontos e a Reta de Simson.
18
Caldeira, Cláudia Rosana da Costa. "Números complexos : uma proposta geométrica." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2013. http://hdl.handle.net/10183/77729.
Full textAbstract:
Esta dissertação apresenta os resultados da aplicação de uma sequência didática que teve como objetivo o desenvolvimento de atividades que priorizassem a abordagem geométrica no ensino dos Números Complexos. A pesquisa foi realizada ao longo de nove encontros semanais no Instituto Federal Sul-rio-grandense, em Pelotas (RS), em uma turma de primeiro ano do Ensino Médio Técnico de Eletrônica, na modalidade subsequente. Inicialmente, fizemos a revisão da temática valendo-nos da análise dos Parâmetros Curriculares Nacionais, de diversos livros didáticos e também de pesquisas sobre o tema. Para a aplicação das atividades em sala de aula, consideramos a associação de pares ordenados e pontos do plano e também a associação da soma e da subtração dos pares ordenados com a soma e subtração de vetores. Definimos a unidade imaginária i como o ponto (0,1) e, posteriormente, trabalhamos as operações na forma algébrica. O referencial teórico que deu suporte a este trabalho baseou-se na Teoria de Registros de Representação Semióticas, de Raymond Duval, a qual trata dos aspectos cognitivos relacionados à aquisição de conhecimentos matemáticos. A coleta de dados foi feita por meio de anotações feitas pela professora pesquisadora, pela filmagem dos encontros e pelo material produzido pelos alunos durante as aulas. Após o término dos nove encontros, os alunos realizaram uma avaliação escrita na qual constatamos que os resultados obtidos mostraram-se satisfatórios. Também verificamos o empenho dos alunos durante a resolução das diferentes tarefas que deram suporte a esta pesquisa.This master’s degree thesis shows the results from the application of a didactic sequence, which focused on the development of activities regarding Complex Numbers. The research was carried out during nine weekly meetings at the Instituto Federal Sul-rio-grandense in Pelotas/RS, in a 1st year class from the Secondary Technical School in Electronics. Initially, a review of the theme was carried out using the analysis of the National Curriculum Parameters for secondary schools not only from various course books but also from studies regarding the topic. In order to use the activities in the classroom, the association of ordered pairs and their respective points plan were considered as well as the association of the sum and subtraction of the ordered pairs with the sum and subtraction of vectors. The imaginary unit i was defined as point (0,1) and after this, the operations in algebraic form were dealt with. This work was based on Raymond Duval’s Semiotic Representation Register Theory, which deals with the cognitive aspects related to the acquisition of mathematical knowledge. The data collection was carried out using the notes made by the researcher, by filming the meetings and using the material produced by the students during the classes. After the 9 (nine) meetings, students carried out a written assessment in which the obtained results were considered satisfactory. The effort made by the students was also verified during the performance of different tasks, which supported this research.
19
Bougard, Nicolas. "Regular graphs and convex polyhedra with prescribed numbers of orbits." Doctoral thesis, Universite Libre de Bruxelles, 2007. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210688.
Full textAbstract:
Etant donné trois entiers k, s et a, nous prouvons dans le premier chapitre qu'il existe un graphe k-régulier fini (resp. un graphe k-régulier connexe fini) dont le groupe d'automorphismes a exactement s orbites sur l'ensemble des sommets et a orbites sur l'ensemble des arêtes si et seulement si(s,a)=(1,0) si k=0,
(s,a)=(1,1) si k=1,
s=a>0 si k=2,
0< s <= 2a <= 2ks si k>2.
(resp.
(s,a)=(1,0) si k=0,
(s,a)=(1,1) si k=1 ou 2,
s-1<=a<=(k-1)s+1 et s,a>0 si k>2.)
Nous étudions les polyèdres convexes de R³ dans le second chapitre. Pour tout polyèdre convexe P, nous notons Isom(P) l'ensemble des isométries de R³ laissant P invariant. Si G est un sous-groupe de Isom(P), le f_G-vecteur de P est le triple d'entiers (s,a,f) tel que G ait exactement s orbites sur l'ensemble sommets de P, a orbites sur l'ensemble des arêtes de P et f orbites sur l'ensemble des faces de P. Remarquons que (s,a,f) est le f_{id}-vecteur (appelé f-vecteur dans la littérature) d'un polyèdre si ce dernier possède exactement s sommets, a arêtes et f faces. Nous généralisons un théorème de Steinitz décrivant tous les f-vecteurs possibles. Pour tout groupe fini G d'isométries de R³, nous déterminons l'ensemble des triples (s,a,f) pour lesquels il existe un polyèdre convexe ayant (s,a,f) comme f_G-vecteur. Ces résultats nous permettent de caractériser les triples (s,a,f) pour lesquels il existe un polyèdre convexe tel que Isom(P) a s orbites sur l'ensemble des sommets, a orbites sur l'ensemble des arêtes et f orbites sur l'ensemble des faces.
La structure d'incidence I(P) associée à un polyèdre P consiste en la donnée de l'ensemble des sommets de P, l'ensemble des arêtes de P, l'ensemble des faces de P et de l'inclusion entre ces différents éléments (la notion de distance ne se trouve pas dans I(P)). Nous déterminons également l'ensemble des triples d'entiers (s,a,f) pour lesquels il existe une structure d'incidence I(P) associée à un polyèdre P dont le groupe d'automorphismes a exactement s orbites de sommets, a orbites d'arêtes et f orbites de sommets.
Doctorat en sciences, Spécialisation mathématiques
info:eu-repo/semantics/nonPublished
20
Naves, Lígia Rodrigues Bernabé 1982. "A densidade de empacotamentos esfericos em reticulados." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306625.
Full textAbstract:
Orientadores: Sueli Irene Rodrigues Costa, Patricia Helena Araujo da Silva NogueiraDissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
Made available in DSpace on 2018-08-15T04:07:16Z (GMT). No. of bitstreams: 1 Naves_LigiaRodriguesBernabe_M.pdf: 1248780 bytes, checksum: a87e22d1d349ffc57557fdb83454f7d3 (MD5) Previous issue date: 2009
Resumo: Neste trabalho, estudamos a teoria de reticulados com foco na densidade de empacotamento, a qual possui várias aplicações e possibilita estabelecer interessantes conexões entre tópicos de álgebra linear, cálculo de várias variáveis e geometria discreta. No primeiro capítulo, introduzimos conceitos fundamentais sobre reticulados. No segundo capítulo, abordamos a densidade de empacotamentos esféricos e analisamos a importância e a dificuldade de se conhecer os empacotamentos mais densos. Discutimos também exemplos de reticulados com densidade máxima em suas dimensões. No terceiro capítulo, detalhamos a demonstração do teorema de Minkowski - Hlawka, que fornece um limitante inferior para a densidade de empacotamentos reticulados. Apresentamos também o problema dos fat struts, que tem origem em teoria de comunicação e que se relaciona com a busca de reticulados-projeção de densidade máxima
Abstract: This dissertation addresses the lattice theory with focus on packing density, which has many applications and allows to establish interesting connections between topics of linear algebra, calculus of several variables and discrete geometry. The first chapter is an introduction to the main concepts and properties of lattices. In the second chapter we discuss the sphere packing density problem, its importance and the difficulty in finding denser packings. Examples of lattices with maximum density are analyzed for lower dimensions. In the third chapter we detail the proof of the theorem of Min-kowski - Hlawka which provides a lower bound for lattice packing density of lattices in any dimension. We also present the problem of the fat struts which comes from communication theory and is related to the search for denser projection lattices
Mestrado
Geometria Topologia
Mestre em Matemática
21
Kloster, Gilmar. "NÚMEROS COMPLEXOS E GEOMETRIA PLANA." UNIVERSIDADE ESTADUAL DE PONTA GROSSA, 2014. http://tede2.uepg.br/jspui/handle/prefix/1525.
Full textAbstract:
Made available in DSpace on 2017-07-21T20:56:32Z (GMT). No. of bitstreams: 1
Gilmar KLoster.pdf: 2898946 bytes, checksum: a6884d601b79157da063128a79a81ae6 (MD5)
Previous issue date: 2014-08-04Complex numbers have applications both in mathematics and in other areas of knowledge. But in high school, at which time the student begins the study of this set of numbers, they are taught with emphasis on algebraic manipulations, leaving only the geometric applications reduced the representation of points in the complex plane. In many cases, even this geometric application is addressed. This work aims to address the set of complex numbers using the geometry, enhancing the visualization of some results in GeoGebra, to provide more meaningful to the student learning.
Os números complexos possuem aplicações tanto na matemática como em outras áreas do conhecimento. Porém no ensino médio, momento em que o aluno inicia o estudo deste conjunto numérico, eles são ensinados dando ênfase as manipulações algébricas, deixando as aplicações geométricas reduzidas apenas a representação de pontos no plano complexo. Em muitos casos, nem mesmo esta aplicação geométrica é abordada. Este trabalho tem por objetivo abordar o Conjunto dos Números complexos utilizando a geometria, valorizando a visualização de alguns resultados no GeoGebra, para proporcionar à aprendizagem mais significativa ao aluno.
22
Lima, Claudio Woerle. "Representações dos números racionais e a medição de segmentos : possibilidades com tecnologias informáticas /." Rio Claro : [s.n.], 2010. http://hdl.handle.net/11449/91103.
Full textAbstract:
Orientador: Marcus Vinicius MaltempiBanca: Marcelo de Carvalho Borba
Banca: Siobhan Victoria Healy
Resumo: Essa pesquisa investiga as contribuições que a exploração dos números racionais como medidas de segmentos, em um programa de geometria dinâmica, podem trazer ao entendimento de frações, decimais e da reta numérica entre outras representações dos racionais. A pesquisa se fundamenta em evidências históricas e resultados de pesquisas que mostram a importância do significado de medida para o entendimento dos números. Através das tecnologias informáticas viu-se uma alternativa para a exploração da medida de segmentos. Essa pesquisa é baseada no processo de medição de segmentos, em teorias sobre visualização, experimentação e representações múltiplas. Também se inspira em preceitos construcionistas. Essa investigação qualitativa se baseou na metodologia de experimentos de ensino, em que foram formados dois grupos com alunos de 6ª série / 7º ano do ensino fundamental de uma escola pública estadual do interior de São Paulo. Esses grupos participaram de encontros em que foram desenvolvidas atividades que envolviam: divisão de segmentos; frações como medidas de segmentos; operações de adição e subtração de frações utilizando os segmentos; processo de medição para criação dos números decimais; relações entre decimais e frações; adição e subtração dos números decimais; adição e subtração de frações e decimais. As atividades realizadas se basearam nos recursos de visualização e experimentação proporcionadas pelo software de geometria dinâmica "Régua e Compasso". O trabalho evidenciou a importância da aprendizagem das representações múltiplas dos números racionais e como as tecnologias informáticas (computadores, software de geometria e calculadoras) podem atuar nessa aprendizagem. A pesquisa também evidência que a utilização de recursos tecnológicos pode modificar a matemática da sala de aula, proporcionando aos estudantes ... (Resumo completo, clicar acesso eletrônico abaixo)
Abstract: This research investigates the contributions that the exploration of rational numbers as measure of segments, using geometry dynamic software, can introduce into the understanding of fractions, decimal numbers and the number line, amongst other rational number representations. The research is motivated by both historical evidence and evidence from the research literature showing the importance of the measure meaning to the understanding of rational numbers. Digital technologies offer an alternative method for the exploration of segments measure, as yet underexplored in the field of mathematics education. This research is based on an approach to numbers as measurements of segments, which draws from theories emphasizing the role of visualization, experimentation and multiple representations in mathematics learning. It is also inspired by a constructionist perspective. The qualitative investigation made use of the teaching experiment methodology, in that two groups were formed with students of 6th grade / 7th year within an elementary school of a public school in the state of São Paulo. These groups took part in research sessions where they developed activities that involve: division of segments; fractions as measure of segments; operations of addition and subtraction of fraction using segments; measurement for decimal numbers creation; relations between decimal numbers and fractions; addition and subtraction of decimal numbers; addition and subtraction of fractions and decimal numbers. The activities exploited the resources visualization and experimentation proportioned by the dynamic geometry software "Compass and Rule". Analyses of the data collected pointed to the importance of the understanding of multiple representations for rational numbers and to the role that digital technologies (computers, geometry software and calculators) can play in this learning. This research, also, ... (Complete abstract click electronic access below)
Mestre
23
Figueiredo, Marcelo Cunha. "Fundamentos da geometria euclidiana para o ensino dos números reais." Universidade Federal de Juiz de Fora, 2014. https://repositorio.ufjf.br/jspui/handle/ufjf/824.
Full textAbstract:
Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-02-22T15:29:17Z
No. of bitstreams: 1
marcelocunhafigueiredo.pdf: 1448320 bytes, checksum: d5d065ce34898025ffe848fe7561fe67 (MD5)Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-02-26T14:09:07Z (GMT) No. of bitstreams: 1 marcelocunhafigueiredo.pdf: 1448320 bytes, checksum: d5d065ce34898025ffe848fe7561fe67 (MD5)
Made available in DSpace on 2016-02-26T14:09:07Z (GMT). No. of bitstreams: 1 marcelocunhafigueiredo.pdf: 1448320 bytes, checksum: d5d065ce34898025ffe848fe7561fe67 (MD5) Previous issue date: 2014-02-27
CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
O presente trabalho tem por finalidade mostrar uma metodologia de ensino dos números reais com base em fundamentos da Geometria Euclidiana. A régua e o compasso serão instrumentos de grande importância na construção dos conjuntos numéricos. Partindo das imagens geométricas dos números naturais e das operações entre seus elementos, iremos, gradativamente, construindo o conjunto dos números inteiros e dos racionais. Provaremos a existência de números que não são racionais e uma característica desses números que os livros didáticos, em sua maioria, não abordam: a questão da densidade dos conjuntos dos números racionais e irracionais no conjunto dos reais. A geometria euclidiana como suporte nos números reais facilita o entendimento do aluno e traz dinâmica nas operações entre esses números. Apresentamos também uma possibilidade de continuação da proposta de trabalho.
This paper aims to show a teaching methodology of real numbers on the grounds of Euclidean geometry. The ruler and compass are instruments of great importance in the construction of numerical sets. Based on the geometric images of the natural numbers and operations between its elements, we will gradually building the set of integers and rational numbers. We prove the existence of numbers that are not rational and a propertie of those numbers that textbooks mostly do not address: the question of density of the sets of rational and irrational in the set of real numbers. Euclidean geometry as real numbers in support facilitates student understanding and produces dynamic operations between these numbers. We also present a possible continuation of the proposed work.
24
Xue, Fei [Verfasser], Martin [Akademischer Betreuer] Henk, Martin [Gutachter] Henk, Cifre María A. [Gutachter] Hernández, and Iskander [Gutachter] Aliev. "Convex geometry of numbers: covering, successive minima and Banach-Mazur distance / Fei Xue ; Gutachter: Martin Henk, María A. Hernández Cifre, Iskander Aliev ; Betreuer: Martin Henk." Berlin : Technische Universität Berlin, 2019. http://d-nb.info/1196688648/34.
Full text
25
Santos, Júlio César Amaral dos. "Números complexos aplicados à geometria." Universidade Federal de Juiz de Fora, 2014. https://repositorio.ufjf.br/jspui/handle/ufjf/788.
Full textAbstract:
Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-02-18T13:57:06Z
No. of bitstreams: 1
juliocesaramaraldossantos.pdf: 681712 bytes, checksum: a8cc889d8be4662ca3c5217acb432f41 (MD5)Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-02-26T13:31:01Z (GMT) No. of bitstreams: 1 juliocesaramaraldossantos.pdf: 681712 bytes, checksum: a8cc889d8be4662ca3c5217acb432f41 (MD5)
Made available in DSpace on 2016-02-26T13:31:01Z (GMT). No. of bitstreams: 1 juliocesaramaraldossantos.pdf: 681712 bytes, checksum: a8cc889d8be4662ca3c5217acb432f41 (MD5) Previous issue date: 2014-08-09
Esse trabalho tem como propósito mostrar algumas aplicações básicas dos números complexos na geometria euclidiana plana. Aqui procuramos ilustrar como é possível trabalhar com os números complexos na sua forma geométrica e também vetorial, com o intuito de apresentar uma forma mais concreta de ensino desse conteúdo dentro da educação básica. A versatilidade e aplicabilidade dos números complexos são apresentadas de uma forma acessível tanto a professores quanto à alunos. A maioria das demonstrações geométricas sugeridas são simples e podem ser facilmente trabalhadas com alunos da educação básica, visto que os conceitos geométricos abordados se resumem ao conteúdo apresentado nas escolas durante o ensino fundamental. Buscamos em diversas situações estabelecer comparações entre o algébrico e o geométrico, com o intuito de que os alunos entendessem que essas duas áreas, ao contrário do que a maioria deles imagina, possuem diversas relações e podem ser facilmente trabalhadas juntas.
This work aims to show some basic applications of complex numbers in plane Euclidean geometry. Here we seek to illustrate how you can work with complex numbers on geometric and also vector form, in order to present a more concrete way of teaching that content in the basic education. The versatility and applicability of complex numbers are presented in an accessible way to both teachers and students. Most of the geometrical demonstrations suggested are simple and can be easily worked with elementary education students, since geometrical concepts discussed are summarized to the content presented in schools during elementary school. We seek to establish, in several situations, comparisons between the algebraic and geometric, with the intention that students understand that these two areas, unlike most of them think, have different relations and can be easily studied together.
26
Hedmark, Dustin g. "The Partition Lattice in Many Guises." UKnowledge, 2017. http://uknowledge.uky.edu/math_etds/48.
Full textAbstract:
This dissertation is divided into four chapters. In Chapter 2 the equivariant homology groups of upper order ideals in the partition lattice are computed. The homology groups of these filters are written in terms of border strip Specht modules as well as in terms of links in an associated complex in the lattice of compositions. The classification is used to reproduce topological calculations of many well-studied subcomplexes of the partition lattice, including the d-divisible partition lattice and the Frobenius complex. In Chapter 3 the box polynomial B_{m,n}(x) is defined in terms of all integer partitions that fit in an m by n box. The real roots of the box polynomial are completely characterized, and an asymptotically tight bound on the norms of the complex roots is also given. An equivalent definition of the box polynomial is given via applications of the finite difference operator Delta to the monomial x^{m+n}. The box polynomials are also used to find identities counting set partitions with all even or odd blocks, respectively. Chapter 4 extends results from Chapter 3 to give combinatorial proofs for the ordinary generating function for set partitions with all even or all odd block sizes, respectively. This is achieved by looking at a multivariable generating function analog of the Stirling numbers of the second kind using restricted growth words. Chapter 5 introduces a colored variant of the ordered partition lattice, denoted Q_n^{\alpha}, as well an associated complex known as the alpha-colored permutahedron, whose face poset is Q_n^\alpha. Connections between the Eulerian polynomials and Stirling numbers of the second kind are developed via the fibers of a map from Q_n^{\alpha} to the symmetric group on n-elements
27
Segarra, Escandón Jaime Rodrigo. "Pre-service teachers' mathematics teaching beliefs and mathematical content knowledge." Doctoral thesis, Universitat Rovira i Virgili, 2021. http://hdl.handle.net/10803/671686.
Full textAbstract:
L’estudi del coneixement matemàtic i les creences de l’eficàcia de l’ensenyament de les matemàtiques en la formació inicial dels futurs mestres és fonamental, ja que influencia el rendiment acadèmic dels seus estudiants. L’objectiu d’aquesta tesi és estudiar tant el coneixement matemàtic inicial dels futurs mestres com també les seves creences sobre l’eficàcia matemàtica i la seva actitud envers les matemàtiques. Per a complir amb l’objectiu, es realitzen vàries investigacions. Primer, s’estudien els coneixements inicials de nombres i geometria dels estudiants del primer curs del Grau d’Educació Primària a la Universitat Rovira i Virgili (URV). En segon lloc, s’estudien les creences de l’eficàcia de l’ensenyament de les matemàtiques dels futurs mestres durant el grau. En tercer lloc, en aquesta Tesi es compara l’autoeficàcia i l’expectativa de resultats de l’ensenyament de les matemàtiques de futurs mestres, mestres novells i mestres experimentats. En quart lloc, s’estudia la relació entre les creences de l’ensenyament de les matemàtiques, l’actitud envers les matemàtiques i el rendiment acadèmic dels futurs mestres. En cinquè lloc, s’estudia la influència dels factors experiència docent, nivell d’educació i nivell d’ensenyament sobre les creences de l’eficàcia de l’ensenyament de les matemàtiques en mestres en actiu. Finalment, es compara l’autoeficàcia de l’ensenyament de les matemàtiques entre els estudiants del quart any del grau de mestres a la Universitat del Azuay i a la URV. Els resultats d’aquesta Tesi ofereixen informació potencialment important sobre el coneixement matemàtic, les creences, l’autoeficàcia de l’ensenyament de les matemàtiques i l’actitud envers les matemàtiques dels futurs mestres i dels mestres en actiu. Aquests resultats poden ajudar a desenvolupar polítiques adients a l’hora de dissenyar plans d’estudis i també assessorar als professors dels graus de mestre en les institucions d’educació superior.El estudio del conocimiento matemático y las creencias de la eficacia de la enseñanza de las matemáticas en la formación inicial de los futuros maestros es fundamental, ya que influye en el rendimiento académico de los estudiantes. El objetivo de esta tesis es estudiar tanto el conocimiento matemático inicial de los futuros maestros como sus creencias sobre la eficacia matemática y su actitud hacia las matemáticas. Para cumplir con el objetivo se realiza varias investigaciones. Primero, se estudia los conocimientos iniciales de números y geometría de los estudiantes de primer año del Grado de Educación Primaria en la Universidad Rovira y Virgili (URV). En segundo lugar, se estudia las creencias de la eficacia de la enseñanza de las matemáticas de los futuros maestros a lo largo del grado. Tercero, esta Tesis compara la autoeficacia y la expectativa de resultados de la enseñanza de las matemáticas de futuros maestros, maestros novatos y maestros experimentados. Cuarto, se estudia la relación entre las creencias de la enseñanza de las matemáticas, la actitud hacia las matemáticas y su rendimiento académico. Quinto, se estudia la influencia de los factores experiencia docente, nivel de educación y nivel de enseñanza, sobre las creencias de la eficacia de la enseñanza de las matemáticas en maestros en servicio. Finalmente, se compara la autoeficacia de la enseñanza de las matemáticas entre los estudiantes de cuarto año del grado de maestro en la Universidad del Azuay y en la URV. Los resultados de esta Tesis ofrecen información potencialmente importante sobre el conocimiento matemático, las creencias, la autoeficacia de la enseñanza de las matemáticas y la actitud hacia las matemáticas de los futuros maestros y maestros en servicio. Estos resultados pueden ayudar a desarrollar políticas adecuadas para diseñar planes de estudios y también asesorar a los profesores de los grados de maestro en las instituciones de educación superior.
The study of mathematical content knowledge and teachers’ mathematics teaching beliefs of the pre-service teachers is fundamental, since it influences the academic performance of students. The objective of this Thesis is to study the initial mathematical knowledge of pre-service teachers and also their teachers’ mathematics teaching beliefs and their attitude towards mathematics. To meet the objective, various investigations are carried out. First, the initial knowledge of numbers and geometry of first-year students of the primary education degree at the Rovira and Virgili University (URV) is studied. Second, pre-service teachers’ mathematics teaching beliefs are studied throughout the grade. Third, this Thesis compares the self-efficacy and the expectation of results of the teaching of mathematics of pre-service teachers, novice in-service teachers and experienced in-service teachers. Fourth, the relationship between the teachers’ mathematics teaching beliefs, the attitude towards mathematics and their academic performance is studied. Fifth, the influence of the factors teaching level factor and level of training on the teachers’ mathematics teaching beliefs of in-service teachers is studied. Finally, the self-efficacy of mathematics teaching of fourth-year students at the Azuay University and at the URV is compared. The results of this Thesis offer potentially important information on the mathematical knowledge, beliefs, self-efficacy of mathematics teaching and the attitude towards mathematics of pre-service teachers and in-service teachers. These results can help develop policies for curriculum developers and teaching professors at institutes of higher education.
28
Silva, Hércules do Nascimento. "Poliedros Regulares no Ensino Médio." Universidade Federal da Paraíba, 2014. http://tede.biblioteca.ufpb.br:8080/handle/tede/8042.
Full textAbstract:
Submitted by Maike Costa (maiksebas@gmail.com) on 2016-03-28T12:29:14Z
No. of bitstreams: 1
arquivototal.pdf: 800250 bytes, checksum: 42e76ab05ea580b4fd24a3312b9b4212 (MD5)Made available in DSpace on 2016-03-28T12:29:14Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 800250 bytes, checksum: 42e76ab05ea580b4fd24a3312b9b4212 (MD5) Previous issue date: 2014-08-29
In this work we present a study of the regular polyhedra, comparing and discussing the concepts and de nitions given in the study of regular polyhedra in textbooks most widely used in Brazilian high schools. We prove the theorem of Euler, we calculate surface areas and volumes of regular polyhedra. Finally, we present some mathematical software that can be used by students and mathematics teachers in the spatial geometry classes as auxiliary material in the teaching and learning of this subject in the classroom.
Neste trabalho apresentamos um estudo sobre os poliedros regulares, comparando e discutindo os conceitos e as de nições que são dadas no estudo dos poliedros regulares nos livros didáticos mais utilizados nas escolas brasileiras de Ensino Médio. Provamos o teorema de Euler, calculamos áreas de superfícies e os volumes dos poliedros regulares. Por m, apresentamos alguns softwares matemáticos que podem ser utilizados pelos alunos e professores de Matemática nas aulas de geometria espacial como material auxiliar no processo de ensino e aprendizagem deste tema em sala de aula.
29
Silva, Emerson José da. "As construções geométricas via geometria dinâmica do software régua e compasso." Universidade Federal de Goiás, 2014. http://repositorio.bc.ufg.br/tede/handle/tede/3982.
Full textAbstract:
Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2015-01-27T14:46:39Z
No. of bitstreams: 2
license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)
Dissertação - Emerson José da Silva - 2014.pdf: 7690015 bytes, checksum: 913769b0dd5913e4688da0ec1491b760 (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-01-28T12:58:40Z (GMT) No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação - Emerson José da Silva - 2014.pdf: 7690015 bytes, checksum: 913769b0dd5913e4688da0ec1491b760 (MD5)
Made available in DSpace on 2015-01-28T12:58:40Z (GMT). No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação - Emerson José da Silva - 2014.pdf: 7690015 bytes, checksum: 913769b0dd5913e4688da0ec1491b760 (MD5) Previous issue date: 2014-08-21
In this work we revisit the subject Geometric Constructions into ruler and compass, using the dynamic geometry software 'Ruler and Compass' as an auxiliary tool in the teaching and learning of geometry, building examples and suggestions for activities with the software. Brought to the fore the possibility of building into ruler and compass, solutions to several problems that can be presented as algebraic expressions. Yet addressed the possibility of constructing a number, using only ruler and compass and discuss the famous and historical problems of geometrical construction: doubling the cube, squaring the circle and the trisection of the angle. We add appendices which present other possible constructions and also bring suggestions for activities with ruler and compass software. Keywords
Neste trabalho revisitamos o assunto Construções Geométricas via régua e compasso, utilizando o software de Geometria Dinâmica ‘Régua e Compasso’ como uma ferramenta auxiliar no ensino e aprendizagem de Geometria, construindo exemplos e sugestões de atividades com o software. Trouxemos à tona a possibilidade da construção, via régua e compasso, de soluções para vários problemas que podem ser apresentados por expressões algébricas. Abordamos ainda a possibilidade da construção de um número, utilizando-se apenas a régua e o compasso e discutimos os célebres e históricos problemas de construção geométrica: duplicação do cubo, quadratura do círculo e trissecção do ângulo. Acrescemos ainda apêndices onde apresentamos outros tipos de construções possíveis e também trazemos sugestões de atividades com o software ‘Régua e Compasso’.
30
Poëls, Anthony. "Applications de la géométrie paramétrique des nombres à l'approximation diophantienne." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLS115/document.
Full textAbstract:
Pour un réel ξ qui n’est pas algébrique de degré ≤ 2, on peut définir plusieurs exposants diophantiens qui mesurent la qualité d’approximation du vecteur (1, ξ, ξ² ) par des sous-espaces de ℝ³ définis sur ℚ de dimension donnée. Cette thèse s’inscrit dans l’étude de ces exposants diophantiens et des questions relatives à la détermination de leur spectre. En utilisant notamment les outils modernes de la géométrie paramétrique des nombres, nous construisons une nouvelle famille de réels – appelés nombres de type sturmien – et nous déterminons presque complètement le 3-système qui leur est associé. Comme conséquence, nous en déduisons la valeur de leurs exposants diophantiens et certaines informations sur les spectres. Nous considérons également le problème plus général de l’allure d’un 3-système associé à un vecteur de la forme (1, ξ, ξ ²), en formulant entre autres certaines contraintes qui n’existent pas pour un vecteur (1, ξ, η) quelconque, et en explicitant les liens qu’il entretient avec la suite des points minimaux associée à ξ. Sous certaines conditions de récurrence sur la suite des points minimaux nous montrons que nous retrouvons les 3-systèmes associés aux nombres de type sturmienGiven a real number ξ which is not algebraic of degree ≤ 2 one may defineseveral diophantine exponents which measure how “well” the vector (1, ξ, ξ ²) can be approximated by subspaces of fixed dimension defined over ℚ. This thesis is part of the study of these diophantine exponents and their spectra. Using the parametric geometry of numbers, we construct a new family of numbers – called numbers of sturmian type – and we provide an almost complete description of the associated 3-system. As a consequence, we determine the value of the classical exponents for numbers of sturmian type, and we obtain new information on their joint spectra. We also take into consideration a more general problem consisting in describing a 3-system associated with a vector (1, ξ, ξ²). For instance we formulate special constraints which do not exist for a general vector (1, ξ, η) and we also clarify connections between a 3-system which represents ξ and the sequence of minimal points associated to ξ. Under a specific recurrence relation hypothesis on the sequence of minimal points, we show that the previous 3-system has the shape of a 3-system associated to a number of sturmian type
31
Justino, Gildeci José. "A característica de Euler." Universidade Federal da Paraíba, 2013. http://tede.biblioteca.ufpb.br:8080/handle/tede/7471.
Full textAbstract:
Submitted by Clebson Anjos (clebson.leandro54@gmail.com) on 2015-05-18T18:12:57Z
No. of bitstreams: 1
arquivototal.pdf: 13930019 bytes, checksum: d5e52fb67904848f89fafaf5ec93c06d (MD5)Approved for entry into archive by Clebson Anjos (clebson.leandro54@gmail.com) on 2015-05-18T18:15:19Z (GMT) No. of bitstreams: 1 arquivototal.pdf: 13930019 bytes, checksum: d5e52fb67904848f89fafaf5ec93c06d (MD5)
Made available in DSpace on 2015-05-18T18:15:19Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 13930019 bytes, checksum: d5e52fb67904848f89fafaf5ec93c06d (MD5) Previous issue date: 2013-09-24
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
This dissertation is focused on the Euler's theorem for polyhedra homeomorphic to the sphere. Present statements made by Cauchy, Poincaré and Legendre. As a consequence we show that there are only ve regular convex polyhedra, called polyhedra Plato.
Esta dissertação tem como tema central o Teorema de Euler para poliedros homeomorfos à esfera. Apresentamos demonstrações feitas por Cauchy, Poincaré e Legendre. Como consequência mostramos a existência de apenas cinco poliedros convexos regulares, os chamados poliedros de Platão.
32
Marnat, Antoine. "Sur le spectre des exposants d'approximation diophantienne classiques et pondérés." Thesis, Strasbourg, 2015. http://www.theses.fr/2015STRAD042/document.
Full textAbstract:
Pour un n-uplet de nombres réels, vu comme un point de l'espace projectif, on définit pour chaqueindice d entre 0 et n-1 deux exposants d'approximation diophantienne (un ordinaire et un uniforme)qui mesurent l'approximabilité de celui-ci par des sous-espaces rationnels de dimension d dansl'espace projectif. Il se trouve que ces 2n exposants ne sont pas indépendants les uns des autres.Cette thèse s'inscrit dans l'étude du spectre de tout ou partie de ces exposants, qui a fait l'objet denombreux travaux récents. On utilise notamment les outils récents de la géométrie paramétriquedes nombres pour étudier le spectre des exposants uniforme, et on traite un cas pondéré endimension 2Given a n-tuple of real numbers, seen as a point in the projective space, one can define for eachindex d between 0 and n-1 two exponents of diophantine approximation (an ordinary and auniform) which measure the approximability of this n-tuple by rational subspaces of dimension d inthe projective space. These 2n exponents are not independant. This thesis is part of the study fromthe spectrum of all or part of these exponents, which have been much studied recently. We userecent tools coming from the parametric geometry of numbers to study the spectrum of the uniformexponents, and deal with a twisted case in dimension two
33
Sezgin, S. "The unrestricted blocking number in convex geometry." Thesis, University College London (University of London), 2010. http://discovery.ucl.ac.uk/19509/.
Full textAbstract:
Let K be a convex body in \mathbb{R}^n. We say that a set of translates \left \{ K + \underline{u}_i \right \}_{i=1}^{p} block K if any other translate of K which touches K, overlaps one of K + \underline{u}_i, i = 1, . . . , p. The smallest number of non-overlapping translates (i.e. whose interiors are disjoint) of K, all of which touch K at its boundary and which block any other translate of K from touching K is called the Blocking Number of K and denote it by B(K). This thesis explores the properties of the blocking number in general but the main purpose is to study the unrestricted blocking number B_\alpha(K), i.e., when K is blocked by translates of \alpha K, where \alpha is a fixed positive number and when the restrictions that the translates are non-overlapping or touch K are removed. We call this number the Unrestricted Blocking Number and denote it by B_\alpha(K). The original motivation for blocking number is the following famous problem: Can a rigid material sphere be brought into contact with 13 other such spheres of the same size? This problem was posed by Kepler in 1611. Although this problem was raised by Kepler, it is named after Newton since Newton and Gregory had a dispute over the solution which was eventually settled in Newton’s favour. It is called the Newton Number, N(K) of K and is defined to be the maximum number of non-overlapping translates of K which can touch K at its boundary. The well-known dispute between Sir Isaac Newton and David Gregory concerning this problem, which Newton conjectured to be 12, and Gregory thought to be 13, was ended 180 years later. In 1874, the problem was solved by Hoppe in favour of Newton, i.e., N(\beta^3) = 12. In his proof, the arrangement of 12 unit balls is not unique. This is thought to explain why the problem took 180 years to solve although it is a very natural and a very simple sounding problem. As a generalization of the Newton Number to other convex bodies the blocking number was introduced by C. Zong in 1993. “Another characteristic of mathematical thought is that it can have no success where it cannot generalize.” C. S. Pierce As quoted above, in mathematics generalizations play a very important part. In this thesis we generalize the blocking number to the Unrestricted Blocking Number. Furthermore; we also define the Blocking Number with negative copies and denote it by B_(K). The blocking number not only gives rise to a wide variety of generalizations but also it has interesting observations in nature. For instance, there is a direct relation to the distribution of holes on the surface of pollen grains with the unrestricted blocking number.
34
Carroll, Kathleen Mary. "Determining the number of loops of regular polygons /." Norton, Mass. : Wheaton College, 2010. http://hdl.handle.net/10090/15512.
Full text
35
Gonçalves, Junior Eduardo Manuel. "Aspectos computacionais na geometria da espiral de Teodoro." Universidade Federal da Paraíba, 2015. http://tede.biblioteca.ufpb.br:8080/handle/tede/7647.
Full textAbstract:
Submitted by Maria Suzana Diniz (msuzanad@hotmail.com) on 2015-11-25T14:11:47Z
No. of bitstreams: 1
arquivototal.pdf: 21722062 bytes, checksum: bb67c86f0d2ae8a89632226cb61b3636 (MD5)Made available in DSpace on 2015-11-25T14:11:47Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 21722062 bytes, checksum: bb67c86f0d2ae8a89632226cb61b3636 (MD5) Previous issue date: 2015-02-24
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
The present work is a study of Teodoro spiral, for the geometric aspects of the curve. At rst, the construction of Teodoro spiral in two and three dimensions is made. And through the softwares, GeoGebra and wxMaxima were developed respectively, the geometric constructions and the necessary calculations. With the possession of the spiral of concatenation, observe the pattern of behavior of growth and position, the collared peccary in the n - th triangle. Going through measurements of Teodoro spiral with other spirals such as the Archimedean, we come to denote behavior patterns in expanding spiral. The following is an arithmetic study on the spiral obtained by the length of the branches of the same, both perfect and imperfect hits with square also spaced apart relationship between them allows us to observe numbers as the . The distribution of prime numbers is seen as the nal part of this study, where you see speculatively allowing the formation of new curves on the spiral, as parabolas.
O presente trabalho faz um estudo da espiral de Teodoro, no tocante aos aspectos geométricos da curva. De início, é feita a construção da espiral de Teodoro em duas e três dimensões. E por meio dos softwares, GeoGebra e wxMaxima, foram desenvolvidas respectivamente, as construções geométricas e os cálculos necessários. Com a posse da concatenação da espiral, observa-se o comportamento do padrão de crescimento e posição, do cateto no enésimo triângulo. Passando por aferições da espiral de Teodoro com outras espirais, como por exemplo a arquimediana, chega-se a denotar padrões de comportamento na expansão da espiral. A seguir, é mostrado um estudo aritmético na espiral, obtido através do comprimento dos ramos da mesma, que tanto atinge quadrados perfeitos e imperfeitos como também a relação de afastamento entre eles nos permite observar números como o . A distribuição dos números primos é vista como parte fi nal desse estudo, onde se vê de forma especulativa, possibilitando a formação de novas curvas sobre a espiral, como parábolas.
36
Svensson, Cecilia. "Taluppfattningens betydelse för elevers matematiska utveckling : En kvantitativ studie i åk 2 av sambandet mellan elevers taluppfattning och deras kunskapsnivå inom aritmetik respektive geometri." Thesis, Karlstads universitet, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-68945.
Full textAbstract:
Sammanfattning Syftet med denna studie är att undersöka betydelsen av elevers taluppfattning för deras kunskap i geometri och aritmetik. Analyserna baseras på jämförelser av resultat dels från tester i den ordinarie undervisningen inom de två matematikgrenarna aritmetik och geometri och dels resultat från ett test, för bestämning av elevernas taluppfattning, som tagits fram inom denna studie. Undersökningsmetoden som användes för att mäta taluppfattningen var kvantitativa intervjuer, där 30 elever i åk 2 deltog. Intervjuerna var utformade som ett matematiskt samtal utifrån en för årsklassen anpassad intervjuguide, där eleverna samlade poäng genom att lösa uppgifter på olika svårighetsnivåer. Resultaten sammanställdes därefter till ett helhetsresultat. Resultaten från de tre testerna analyserades med statistiska verktyg så som punktdiagram och bestämning av korrelationskoefficienter. En positiv korrelation kan påvisas för sambandet mellan det resultat eleverna uppnår på taluppfattningstestet och deras resultat på både aritmetik och geometri. Korrelationen i denna studie är starkare för sambandet taluppfattning/geometri, korrelationsfaktor 0,73, än för sambandet taluppfattning/aritmetik, korrelationsfaktor 0,50. Genom den positiva korrelation som påvisas stödjer resultaten uppfattningen att taluppfattningen har stor betydelse för elevernas matematiska utveckling. Denna studie visade att detta samband inte enbart gäller aritmetikens räknelära utan även gäller för geometrin.Abstracts The aim of this study is to investigate the importance of students’ number sense on their geometry and arithmetic skills. The analyzes are based on comparisons of results, from tests in the regular teaching within the two mathematical branches, arithmetic and geometry, and the results from a test, for determining the students’ number sense, that was developed within this study. The survey method used to measure number sense skills were quantitative interviews, where 30 students in grade 2 participated. The interviews were designed as a math conversation based on an interview guide adapted for the age group concerned. The students gathered points by solving tasks at different levels of difficulty. The results were then compiled into an overall result. The results of the three tests were analyzed using statistical tools such as, point diagrams and determination of correlation coefficients. A positive correlation was demonstrated for the correlation between the result the students achieved in the test of number sense and their results in the tests in both arithmetic and geometry. The correlation in this study is stronger for the relationship number sense / geometry, correlation factor 0.73, than for the number sense / arithmetic, correlation factor 0.50. Through the positive correlation that is shown, the findings support the perception that number sense is of major importance to the students’ mathematical development, and this study showed that this relationship is valid not only in the pure counting skills, as arithmetic, but also for skills in geometry.
37
La, Haye Reuben N. "Quantitative Combinatorial Geometry with Applications to Number Theory and Optimization." Thesis, University of California, Davis, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10165904.
Full textAbstract:
This dissertation contains a variety of results in quantitative combinatorial geometry, as well as applications to optimization and number theory.
We use Ehrhart theory, the study of the number of lattice points in polytopes, to prove a Rainbow Ramsey analogue of Richard Rado's 1933 result in Ramsey Theory. There were some conjectures as to what this analogue would be; they are disproven by our result. We also prove a few corollaries.
A portion of this dissertation contains new quantitative variants of classical convexity theorems: whereas the classical theorems have hypotheses and conclusions requiring certain sets to be nonempty, their quantitative variants require that the sets have a certain "size" (volume, diameter, etc). The three classical theorems we quantize are Carathéodory's Theorem, Helly's Theorem, and Tverberg's Theorem. The Helly portion contains new non-quantitative results as well. The Tverberg portion proves that any Helly-type theorem implies a corresponding Tverberg-type theorem.
A maximal 1-lattice polytope is a lattice polytope containing exactly one interior lattice point whose facets each contain at least one interior lattice point. In this dissertation, we bound the size of all maximal 1-lattice pyramids and prisms. These bounds may be used with a brute-force algorithm to quickly enumerate all maximal 1-lattice pyramids and prisms up to equivalence.
S-optimization, a generalization of continuous, integer, and mixed-integer optimization in which variables take values from a set S, is introduced and studied in the last part of this dissertation. We generalize two traditional optimization algorithms to S-optimization: the chance-constrained algorithm of Calafiore and Campi, and the sampling algorithm of Clarkson. Interestingly, the complexities of the generalized algorithms are dependent upon the same Helly numbers studied elsewhere in this dissertation.
38
Cavazza, Niccolò <1983>. "Estimating persistent Betti numbers for discrete shape analysis." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2011. http://amsdottorato.unibo.it/3468/.
Full textAbstract:
Persistent Topology is an innovative way of matching topology and geometry, and it proves to be an effective mathematical tool in shape analysis. In order to express its full potential for applications, it has to interface with the typical environment of Computer Science: It must be possible to deal with a finite sampling of the object of interest, and with combinatorial representations of it.
Following that idea, the main result claims that it is possible to construct a relation between the persistent Betti numbers (PBNs; also called rank invariant) of a compact, Riemannian submanifold X of R^m and the ones of an approximation U of X itself, where U is generated by a ball covering centered in the points of the sampling. Moreover we can state a further result in which, this time, we relate X with a finite simplicial complex S generated, thanks to a particular construction, by the sampling points. To be more precise, strict inequalities hold only in "blind strips'', i.e narrow areas around the discontinuity sets of the PBNs of U (or S). Out of the blind strips, the values of the PBNs of the original object, of the ball covering of it, and of the simplicial complex coincide, respectively.
39
Prickett, Martin. "Saturation of Mordell-Weil groups of elliptic curves over number fields." Thesis, University of Nottingham, 2004. http://eprints.nottingham.ac.uk/10052/.
Full textAbstract:
Given a subgroup B of a finitely-generated abelian group A, the saturation B of B is defined to be the largest subgroup of A containing B with finite index. In this thesis we consider a crucial step in the determination of the Mordell-Weil group of an elliptic curve, E(K). Methods such as Descent may produce subgroups H of E(K) with [H:H] > 1. We have determined an algorithm for calculating H given H, and hence for completing the process of finding the Mordell-Weil group. Our method has been implemented in MAGMA with two versions of the programs; one for general number fields K and the other for Q. It builds upon previous work by S. Siksek. Our problem splits into two. First we can use geometry of numbers arguments to establish an upper bound N for the index [H:H]. Second for each remaining prime p < N we seek to prove either that H is p-saturated, i.e. p|[H:H], or to enlarge H by index p. To solve the first problem, 1. We have devised and implemented an algorithm that searches for points on E(K) up to a specified naive height bound. 2. We have devised and implemented an algorithm that calculates the subgroup Egr(K) of points with good reduction at specified valuations. 3. We have implemented joint work with S. Siksek and J. Cremona to calculate an upper bound on the difference of the canonical and naive height of points on an elliptic curve. 4. We have helped to devise and have implemented joint work with S. Siksek and J. Cremona to calculate a lower bound on the canonical heights of non-torsion points on E(K) with K a totally real field. To solve the second problem, 1. As in earlier work by Siksek, we use homomorphisms to prove p-saturation for primes p. We however use the Tate-Lichtenbaum pairing, and we show that, using this pairing, our method will always prove H is p-saturated if that is the case. 2. We show that Siksek's original method will fail for some curves.
40
Pariente, Cesar Alberto Bravo. "Um método probabilístico em combinatória." Universidade de São Paulo, 1996. http://www.teses.usp.br/teses/disponiveis/45/45132/tde-07052010-163719/.
Full textAbstract:
O presente trabalho é um esforço de apresentar, organizado em forma de survey, um conjunto de resultados que ilustram a aplicação de um certo método probabilístico. Embora não apresentemos resultados novos na área, acreditamos que a apresentação sistemática destes resultados pode servir para a compreensão de uma ferramenta útil para quem usa dos métodos probabilísticos na sua pesquisa em combinatória. Os resultados de que falaremos tem aparecido na última década na literatura especializada e foram usados na investigação de problemas que resitiram a outras aproximações mais clássicas. Em vez de teorizar sobre o método a apresentar, nós adotaremos a estratégia de apresentar três problemas, usando-os como exemplos práticos da aplicação do método em questão. Surpeendentemente, apesar da dificuldade que apresentaram para ser resolvidos, estes problemas compartilham a caraterística de poder ser formulados muito intuitivamente, como veremos no Capítulo 1. Devemos advertir que embora os problemas que conduzem nossa exposição pertençam a áreas tão diferentes quanto teoria de números, geometria e combinatória, nosso intuito é fazer énfase no que de comum tem as suas soluções e não das posteriores implicações que estes problemas tenham nas suas respectivas áreas. Ocasionalmente comentaremos sim, outras possíveis aplicações das ferramentas usadas para solucionar estes problemas de motivação. Os problemas de que trataremos tem-se caracterizado por aguardar várias décadas em espera de solução: O primeiro, da teoria de números, surgiu na pesquisa de séries de Fourier que Sidon realizava a princípios de século e foi proposto por ele a Erdös em 1932. Embora tenham havido, desde 1950, diversos avanços na pesquisa deste problema, o resultado de que falaremos data de 1981. Já o segundo problema, da geometria, é uma conjectura formulada em 1951 por Heilbronn e refutada finalmente em 1982. O último problema, de combinatória, é uma conjectura de Erdös e Hanani de 1963, que foi tratada em diversos casos particulares até ser finalmente resolvida em toda sua generalidade em 1985.The following work is an effort to present, in survey form, a collection of results that illustrate the application of a certain probabilistic method in combinatorics. We do not present new results in the area; however, we do believe that the systematic presentation of these results can help those who use probabilistic methods comprenhend this useful technique. The results we refer to have appeared over the last decade in the research literature and were used in the investigation of problems which have resisted other, more classical, approaches. Instead of theorizing about the method, we adopted the strategy of presenting three problems, using them as practical examples of the application of the method in question. Surpisingly, despite the difficulty of solutions to these problems, they share the characteristic of being able to be formulated very intuitively, as we will see in Chapter One. We should warn the reader that despite the fact that the problems which drive our discussion belong to such different fields as number theory, geometry and combinatorics, our goal is to place emphasis on what their solutions have in common and not on the subsequent implications that these problems have in their respective fields. Occasionally, we will comment on other potential applications of the tools utilized to solve these problems. The problems which we are discussing can be characterized by the decades-long wait for their solution: the first, from number theory, arose from the research in Fourier series conducted by Sidon at the beginning of the century and was proposed by him to Erdös in 1932. Since 1950, there have been diverse advances in the understanding of this problem, but the result we talk of comes from 1981. The second problem, from geometry, is a conjecture formulated in 1951 by Heilbronn and finally refuted in 1982. The last problem, from combinatorics, is a conjecture formulated by Erdös and Hanani in 1963 that was treated in several particular cases but was only solved in its entirety in 1985.
41
Nichols, Margaret E. "Intersection Number of Plane Curves." Oberlin College Honors Theses / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1385137385.
Full text
42
González, Alonso Víctor. "Hodge numbers of irregular varieties and fibrations." Doctoral thesis, Universitat Politècnica de Catalunya, 2013. http://hdl.handle.net/10803/129172.
Full textAbstract:
In this thesis we study the geography of irregular complex projective (or compact Kähler) varieties, paying special attention to the existence of fibrations.
The thesis is divided into two parts. In the first one we consider irregular varieties of arbitrary dimension, looking for bounds for the Hodge numbers in the absence of fibrations. In first place, by truncating the BGG complex of the variety (an object recently introduced by Lazarsfeld and Popa), we get lower bounds on the partial Euler characteristics. In order to improve these first results, we define the higher-rank derivative complexes (generalizing the derivative complex introduced by Green and Lazarsfeld). We study their exactness by means of the Eagon-Northcott complexes, and we obtain some inequalities between the Hodge numbers of varieties admitting some kind of subspaces of 1-forms (¿non-degenerate subspaces¿). In the case of subvarieties of Abelian varieties, the existence of non-degenerate subspaces of any dimension allows us to obtain better inequalities than in the general case.
In the case of h^(2,0), a different method gives a much better result. In fact, the bound is much stronger, and the only hypothesis needed is the non-existence of higher irrational pencils (a priori, less restrictive than the existence of non-degenerate subspaces). To close, using the Grassmannian BGG complex (a generalization of the BGG complex that aggregates all the higher-rank derivative complexes) and computing the Chern classes of its last cokernel, we recover the same bound for h^(2,0) using the general results mentioned in the previous paragraph.
In the second part, the scope is restricted to surfaces fibred over a curve. We look for upper bounds for the relative irregularity in terms of properties of the general fibre, in the spirit of the inequality obtained by Xiao for non-isotrivial fibrations over a rational curve. Xiao conjectured the same inequality to hold for fibrations over any base, but Pirola found a counterexample. After that, a corrected conjecture was proposed. The result obtained in this thesis is a bound depending on the genus and the Clifford index of a general fibre, which coincides with the corrected conjecture in the case of maximal Clifford index.
We have used several techniques in our proof. On the one hand, the ¿adjoint images¿ play a crucial role. The adjoint images were introduced by Collino and Pirola to study infinitesimal deformations of smooth curves, and generalized later by Pirola and Zucconi to higher-dimensional varieties. In this thesis we construct the ¿global adjoint map¿, which allows to find subspaces with vanishing adjoint image assuming that the kernel of the infinitesimal deformation has dimension (at least) half the genus of the cruve. More generally, the global adjoint map can also be defined for infinitesimal deformations of irregular varieties of any dimension, and allows to find numerical conditions that guarantee the existence of subspaces with vanishing adjoint.
On the other hand, we have extended to arbitrary (one-dimensional) families of curves some well-stablished concepts of infinitesimal deformations, related with the bicanonical embedding of the curve. As the global adjoint map, some of these constructions can also be extended to families of irregular varieties of arbitrary dimension.
Finally, all these previous constructions lead to a structural result for fibrations supported on a relatively rigid divisor. With this result we can treat some cases of the conjecture of Xiao. The remaining cases are solved using an inequality for the rank of an infinitesimal deformation in terms of a supporting divisor (its degree and the dimension of its complete linear series). This inequality, which we reprove, is originally due to Ginensky.
43
Rassart, Étienne 1975. "Geometric approaches to computing Kostka numbers and Littlewood-Richardson coefficients." Thesis, Massachusetts Institute of Technology, 2004. http://hdl.handle.net/1721.1/16632.
Full textAbstract:
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.Includes bibliographical references (p. 119-125).
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Using tools from combinatorics, convex geometry and symplectic geometry, we study the behavior of the Kostka numbers and Littlewood-Richardson coefficients (the type A weight multiplicities and Clebsch-Gordan coefficients). We sh w that both are given by piecewise polynomial functions in the entries of the partitions and compositions parametrizing them, and that the domains of polynomiality form a complex of cones. Interesting factorization patterns are found in the polyomials giving the Kostka numbers. The case of A3 is studied more carefully and involves computer proofs. We relate the description of the domains of polynomiality for the weight multiplicity function to that of the domains for the Duistermaat-Heckman measure from symplectic geometry (a continuous analogue of the weight multiplicity function). As an easy consequence of this work, one obtains simple proofs of the fact the Kostka numbers, and Littlewood-Richardson numbers are given by polynomial functions in the nonnegative integer variable N. Both these results were known previously but have non-elementary proofs involving fermionic formulas for Kostka-Foulkes polynomials and semi-invariants of quivers. Also investigated is a new q-analogue of the Kostant partition function, which is shown to be given by polynomial functions over the relative interiors of the cells of a complex of cones.
(cont.) It arises in the work of Guillemin, Sternberg and Weitsman on quantization with respect to the signature Dirac operator, where they give a formula for the multiplicities of weights in representations associated to twisted signatures of coadjoint orbits which is very similar to the Kostant multiplicity formula, but involves the q = 2 specialization of this q-analogue. We give an algebraic proof of this results, find an analogue of the Steinberg formula for these representations and, in type A, find a branching rule which we can iterate to obtain an analogue of Gelfand-Tsetlin theory.
by Etienne Rassart.
Ph.D.
44
Epstein, Peter Carleton University Dissertation Computer Science. "Generating geometric objects at random." Ottawa, 1992.
Find full text
45
Gusakova, Anna [Verfasser]. "Application of Probability Methods in Number Theory and Integral Geometry / Anna Gusakova." Bielefeld : Universitätsbibliothek Bielefeld, 2018. http://d-nb.info/1174670371/34.
Full text
46
Bury, Mark Eric. "Influence of Reynolds number and blade geometry on low pressure turbine performance." Thesis, Massachusetts Institute of Technology, 1997. http://hdl.handle.net/1721.1/50310.
Full text
47
Passuello, Alberto. "Semidefinite programming in combinatorial optimization with applications to coding theory and geometry." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2013. http://tel.archives-ouvertes.fr/tel-00948055.
Full textAbstract:
We apply the semidefinite programming method to obtain a new upper bound on the cardinality of codes made of subspaces of a linear vector space over a finite field. Such codes are of interest in network coding.Next, with the same method, we prove an upper bound on the cardinality of sets avoiding one distance in the Johnson space, which is essentially Schrijver semidefinite program. This bound is used to improve existing results on the measurable chromatic number of the Euclidean space.We build a new hierarchy of semidefinite programs whose optimal values give upper bounds on the independence number of a graph. This hierarchy is based on matrices arising from simplicial complexes. We show some properties that our hierarchy shares with other classical ones. As an example, we show its application to the problem of determining the independence number of Paley graphs.
48
Vonk, Jan Bert. "The Atkin operator on spaces of overconvergent modular forms and arithmetic applications." Thesis, University of Oxford, 2015. http://ora.ox.ac.uk/objects/uuid:081e4e46-80c1-41e7-9154-3181ccb36313.
Full textAbstract:
We investigate the action of the Atkin operator on spaces of overconvergent p-adic modular forms. Our contributions are both computational and geometric. We present several algorithms to compute the spectrum of the Atkin operator, as well as its p-adic variation as a function of the weight. As an application, we explicitly construct Heegner-type points on elliptic curves. We then make a geometric study of the Atkin operator, and prove a potential semi-stability theorem for correspondences. We explicitly determine the stable models of various Hecke operators on quaternionic Shimura curves, and make a purely geometric study of canonical subgroups.
49
Sentone, Francielle Gonçalves. "Paradoxos geométricos em sala de aula." Universidade Tecnológica Federal do Paraná, 2017. http://repositorio.utfpr.edu.br/jspui/handle/1/2701.
Full textAbstract:
CAPESApresentamos 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.
We present in this work some logical-mathematical paradoxes, as Galileo's paradox, and also some geometric paradoxes, such as Curry's paradox, Hooper's paradox and the Banach-Tarski paradox. We employ the Curry and Hooper paradoxes to motivate the study of concepts of Geometry and Number Theory, such as area, triangle similarity, Pythagorean Theorem, trigonometric ratios in the right triangle, angular coefficient of the line, and Fibonacci sequence, and we organize recreation activities for the classroom in Elementary and High School.
50
Usatine, Jeremy. "Arithmetical Graphs, Riemann-Roch Structure for Lattices, and the Frobenius Number Problem." Scholarship @ Claremont, 2014. http://scholarship.claremont.edu/hmc_theses/57.
Full textAbstract:
If R is a list of positive integers with greatest common denominator equal to 1, calculating the Frobenius number of R is in general NP-hard. Dino Lorenzini defines the arithmetical graph, which naturally arises in arithmetic geometry, and a notion of genus, the g-number, that in specific cases coincides with the Frobenius number of R. A result of Dino Lorenzini's gives a method for quickly calculating upper bounds for the g-number of arithmetical graphs. We discuss the arithmetic geometry related to arithmetical graphs and present an example of an arithmetical graph that arises in this context. We also discuss the construction for Lorenzini's Riemann-Roch structure and how it relates to the Riemann-Roch theorem for finite graphs shown by Matthew Baker and Serguei Norine.
We then focus on the connection between the Frobenius number and arithmetical graphs. Using the Laplacian of an arithmetical graph and a formulation of chip-firing on the vertices of an arithmetical graph, we show results that can be used to find arithmetical graphs whose g-numbers correspond to the Frobenius number of R. We describe how this can be used to quickly calculate upper bounds for the Frobenius number of R.