Made available in DSpace on 2018-06-27T19:13:27Z (GMT). No. of bitstreams: 2 Liane Maria.pdf: 4194151 bytes, checksum: 21c58fa7edeca8800066e4f46c6c57b3 (MD5) Liane Maria.pdf.jpg: 3619 bytes, checksum: fcc760f954148dd19c699c2b8ef9afd5 (MD5) Previous issue date: 2008-06-16 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This paper has the purpose of bringing up the results of a qualitative character research, concerning the contributions and limitations of the employment of the Geoboard didactic resource in the learning of some geometrical concepts by students of the Elementary School. Thus, an experiment was accomplished with twelve students from the seventh grade of the Military School of Santa Maria (CMSM) Elementary School. For this, the report of an experiment was realized in the classroom, consisted of six sections, in which activities related to concepts and properties of triangles and quadrilaterals were developed, using the Geoboard didactic resource. During the application of each of the stages, notes were taken down by the teacher-researcher through reference cards, where the development of activities, the speeches,the actions and the students comments were registered. Besides that, students written reports, about each of the activities developed, were handed in to the teacher-researcher at the end of each stage. After the development of the sections, a questionnaire with semi-structured questions was applied, answered by each of the participants of the research. From the analysis of content of the answers from the questionnaire applied and through the notes of the teacherresearcher, it is possible to infer that the usage of the Geoboard didactic resource is a positive and effective factor for the learning of concepts and properties of triangles and quadrilaterals. It is prominent that not all the concepts related to triangles and quadrilaterals, that consist of the seventh grade program, were approached with the usage of the Geoboard, for a restriction of this resource in the construction of a few geometrical elements is perceived. / Este trabalho tem como objetivo apresentar os resultados de uma pesquisa, de cunho qualitativo, sobre as contribuições e limitações do emprego do recurso didático Geoplano na aprendizagem de alguns conceitos geométricos por alunos do Ensino Fundamental. Realizouse, assim, uma experimentação com doze alunos da 7ª série do Ensino Fundamental do Colégio Militar de Santa Maria (CMSM). Para isto, foi feito o relato de uma experiência, em sala de aula, compreendida por seis seções, nas quais foram desenvolvidas atividades relacionadas a conceitos e propriedades de triângulos e quadriláteros, utilizando o recurso didático Geoplano. Durante a aplicação de cada uma das seções, foram realizadas anotações pela professora-pesquisadora, em fichas, onde eram registrados o desenvolvimento das atividades, as falas, as ações e os comentários dos alunos. Além disso, relatos escritos dos alunos, sobre cada uma das atividades desenvolvidas, eram entregues à professorapesquisadora no final de cada seção. Após o desenvolvimento das seções, foi aplicado um questionário com perguntas semi- estruturadas, respondido por cada um dos participantes da pesquisa. A partir da análise de conteúdo das respostas do questionário aplicado e das anotações da professora-pesquisadora, é possível inferir que o uso do recurso didático Geoplano é um fator positivo e eficaz para a aprendizagem de conceitos e propriedades de triângulos e quadriláteros. Salienta-se que nem todos os conceitos relacionados a triângulos e quadriláteros, que constam no programa de 7ª série, foram abordados com o uso do Geoplano, pois se percebe uma limitação deste recurso na construção de alguns elementos geométricos.

Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2015-10-21T13:07:28Z No. of bitstreams: 2 Dissertação - Dayanne Ferreira Costa - 2015.pdf: 11787247 bytes, checksum: 1174be0a78b838318c0d73a300725777 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-10-22T13:05:45Z (GMT) No. of bitstreams: 2 Dissertação - Dayanne Ferreira Costa - 2015.pdf: 11787247 bytes, checksum: 1174be0a78b838318c0d73a300725777 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2015-10-22T13:05:45Z (GMT). No. of bitstreams: 2 Dissertação - Dayanne Ferreira Costa - 2015.pdf: 11787247 bytes, checksum: 1174be0a78b838318c0d73a300725777 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2015-03-20 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work aims to recognize methods and methodologies that seek remedy some di culties in the teaching and learning process in the geometry branch. These methods were applied to a class 7 year of a school on the outskirts of Federal District in 2014, and has the theme "Playful Activities for Teaching Geometry. "With this theme, a brief historical overview was presented on geometry. It then sets a study of this branch of mathematics, speci cally content and properties of triangles. Subsequently described the application site this work and the methodologies used were; concrete material and writing mathematics. Finally, the application is analyzed these methods and methodologies in room school as well as the results achieved. It is concluded that with the methodologies adopted the results were satisfactory, as the students were involved signi cantly. / Este trabalho tem como objetivo reconhecer métodos e metodologias que buscam sanar algumas di culdades no processo de ensino aprendizagem no ramo da geometria. Esses métodos foram aplicados numa turma de 7 ano de uma escola na periferia do Distrito Federal no ano de 2014, e têm como tema "Atividades Lúdicas para o Ensino de Geometria". Com esse tema, foi apresentada uma breve contextualização histórica sobre geometria. Em seguida, expõe um estudo sobre esse ramo da matemática, especi camente o conteúdo de triângulos e suas propriedades. Posteriormente, foi descrito o local da aplicação deste trabalho e as metodologias adotadas que foram: material concreto e redação matemática. Por último, analisa-se a aplicação desses métodos e metodologias em sala de aula, além dos resultados alcançados. Conclui-se que com as metodologias adotadas os resultados foram satisfatórios, pois os alunos envolveram-se de forma signi cativa.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O principal objetivo deste trabalho foi estudar, em triângulos construídos sobre uma superfície esféerica, versões para resultados conhecidos da geometria euclidiana plana e da trigonometria nos triângulos planos. Inicialmente apresentam-se os conceitos fundamentais da geometria esférica e alguns elementos de trigonometria triangular esférica. Para isso, iniciou-se com uma breve revisão de alguns desses resultados e também com algumas definições da geometria plana necessárias para a construção de resultados da geometria esférica. Feito isso, foram construídas, em um triângulo esférico, versões para a lei dos senos, a lei dos cossenos e outros resultados da trigonometria triangular plana. Também foi visto o Teorema de Girard, onde pode-se estudar a área de um triângulo construído sobre a superfície de uma esfera de raio R e a soma de seus ângulos internos, que ao contrário do que ocorre nos triângulos planos inscritos em um círculo de raio r, não é constante. Foi apresentado um contraexemplo, neste ambiente, em que o famoso teorema de Pitagoras não vale. Ao longo do texto são apresentados alguns exemplos com a utilização das relações trigonométricas estudadas, bem como alguns conceitos elementares de coordenadas geograficas e aplicações práaticas da trigonometria esférica na aviação e na geografia. Finalmente, observa-se que esse trabalho utiliza fortemente a matemática do Ensino Básico, facilitando assim a compreensão e o acesso de alunos e professores do Ensino Médio, bem como profissionais que fazem uso da matematica. / The main objective of this work was to study in triangles constructed on a spherical surface, versions of known results of the plane euclidean geometry and trigonometry in plans triangles. Initially it presents the fundamental concepts of spherical geometry and some elements of spherical triangular trigonometry. For this, begins with a brief review of some of these results and also with some denitions of plane geometry required for the construction of spherical geometry results. That done, are build, in a spherical triangle, versions for the law of sines, law of cosines and other results of the plane triangular trigonometry. Was also seen is the theorem of Girard, where can study the area of a triangle built on the surface of a sphere of radius R and the sum of its internal angles, which is not constant unlike what occurs in triangles plans built on disc of radius r. The Pythagorean theorem is not true in this environment and a counter-example will be presented. Throughout the text will be presented some examples with the use of trigonometric relations, as well as some elementary concepts of geographical coordinates and practical applications of spherical trigonometry in aviation and geography. Finally it is observed that this work strongly uses the mathematics of basic education, facilitating the understanding of the said theory, of students and teachers of basic education, as well as of the professionals who use math.

O ensino de Matemática é, de modo geral, orientado pelos processos contidos nos livros didáticos. Sendo assim, a organização dos conceitos matemáticos nesses livros deveria ser capaz de permitir ao leitor interpretar a Matemática em sua essência, admitindo o estabelecimento de relações entre os conteúdos. No entanto, o que geralmente se observa nos materiais é um aglomerado de definições e conceitos desconexos que conduzem o leitor a dificuldades de aprendizado na área. Por essa razão, a presente dissertação teve o objetivo principal de localizar, além de caracterizar, os pontos notáveis do triângulo: o centróide ou baricentro (G), o ortocentro (H), o circuncentro (O), o centro (N) da circunferência de nove pontos, os três ex-centros das circunferências ex-inscritas, as projeções ortogonais dos vértices sobre os lados opostos e os pontos de tangência da circunferência inscrita e ex-inscrita. Quatro abordagens são apresentadas em busca de tal objetivo: a-) apresentar a geometria do triângulo segundo técnicas de percepção visual; b-) caracterizar alguns pontos notáveis do triângulo, como pontos de máximo ou de mínimo de funções com as demonstrações utilizando desigualdade de Cauchy-Schwarz e entre média aritmética e geométrica; c-) utilizar um sistema cartesiano adequado para o cálculo das abscissas e ordenadas do centróide (G), do ortocentro (H) e do circuncentro (O) de um triângulo; d-) utilizar os números complexos para a completa localização de todos os pontos notáveis do triângulo além de apresentar a equação da reta de Euler, o incentro (I) e os três excentros IA, IB e IC localizados em fórmulas simples. A dissertação finaliza com o Teorema de Feuerbach, apresentado com uma prova elementar, mostrando que a circunferência de nove pontos e a circunferência inscrita são tangentes internamente e que a circunferência dos nove pontos é tangente exteriormente a cada uma das três ex circunferências e o Teorema de Napoleão, no qual os baricentros de triângulos equiláteros, construídos a partir dos lados de um triângulo qualquer, formam um outro triângulo equilátero. Comparando as várias abordagens da dissertação, a conclusão é a de que a compreensão dos números complexos paradoxalmente simplifica a resolução de problemas de geometria plana e a solução de equações polinomiais. Assim, acredita-se que uma maior exploração desse conteúdo no ensino da Matemática poderia tornar o aprendizado mais atraente e simplificado / The teaching of Mathematics is generally guided by the procedures contained in the textbooks. Thus, the organization of the mathematical concepts in these books should be able to allow the reader to interpret the Mathematics in its essence, admitting the establishment of relationships between the contents. However, what is observed in the materials is a conglomeration of disparate definitions and concepts that lead the reader to learning difficulties in the area. For this reason, this work aimed to locate and characterize the notable points of the triangle: the centroid or barycenter (G), the orthocenter (H), the circumcenter (O), the center (N) of circumference of nine points, three former centers of the ex-inscribed circles, orthogonal projections of the vertices on the opposite sides and the points of tangency of the inscribed and the ex-inscribed circumference. Four approaches are presented to achieve these goals: a-) to introduce the geometry of the triangle using visual perception techniques, b-) to characterize some notable points of the triangle, as points of maximum or minimum of functions with the demonstrations using the Cauchy-Schwarz inequality and between the arithmetic and geometric mean;-c) to use a suitable Cartesian system for calculating the abscissas and ordinates of the centroid (G), of orthocenter (H) and of the circumcenter (O) of a triangle;-d) to use complex numbers for the complete location of all notable points of the triangle, beyond depicting the Euler equation of the line, the incenter (I) and the three former centers IA, IB and IC located in simple formulas. The work is concluded with the Feuerbach\'s Theorem, presented with an elementary proof, showing that the nine-point circle and the incircle is tangent internally and that the circumference of the nine points is externally tangent to each of the three ex-inscribed circles and the Napoleons Theorem, in which the barycenters of equilateral triangles, constructed from the sides of any triangle, form another equilateral triangle. Comparing the approaches detached hitherto, the conclusion is that the understanding of complex numbers paradoxically simplifies troubleshooting of plane geometry and the solution of polynomial equations. Thus, it is believed that further exploration of this content in mathematics education could make learning more attractive and simplified

The classical (proper) graph colouring problem asks for a colouring of the vertices of a graph with the minimum number of colours such that no two vertices with the same colour are adjacent. Equivalently the colouring is required to be such that the graph induced by the vertices coloured the same colour has the maximum degree equal to zero. The graph parameter associated with the minimum possible number of colours of a graph is called chromatic number of that graph. One generalization of this classical problem is to relax the requirement that the maximum degree of the graph induced by the vertices coloured the same colour be zero, and instead allow it to be some integer d. For d = 0, we are back at the classical proper colouring. For other values of d we say that the colouring has defect d. Another generalization of the classical graph colouring, is list colouring and its associated parameters: choosability and choice number. The main result of this thesis is to show that every graph G of Euler genus μ is ⌈2 + √(3μ + 3)⌉–choosable with defect 1 (equivalently, with clustering 2). Thus allowing any defect, even 1, reduces the choice number of surface embeddable graphs below the chromatic number of the surface. For example, the chromatic number of the family of toroidal graphs is known to be 7. The bound above implies that toroidal graphs are 5-choosable with defect 1. This strengthens the result of Cowen, Goddard and Jesurum (1997) who showed that toroidal graphs are 5-colourable with defect 1. In a graph embedded in a surface, two faces that share an edge are called adjacent. We improve the above bound for graphs that have embeddings without adjacent triangles. In particular, we show that every non-planar graph G that can be embedded in a surface of Euler genus μ without adjacent triangles, is ⌈(5+ √(24μ + 1)) /3⌉–choosable with defect 1. This result generalizes the result of Xu and Zhang (2007) to all the surfaces. They proved that toroidal graphs that have embeddings on the torus without two adjacent triangles are 4-choosable with defect 1.

No description available.

In this work I explore the geometry found both in the narrative structures and the internal shapes proposed in Jorge Luis Borges’ short stories and seek to arrive at new interpretations of those works by mapping out—in graphical form—the shapes found therein. I move from basic two-dimensional shapes (lines, triangles, quadrilaterals) to those involving the element of temporality and atemporality (circles, interruptive loops, chiasmus) to shapes dealing with repetition—both geometric and temporal—and eternity (labyrinths, fractals, and Alephs). In each case and for each short story analyzed, either an existent interpretation is favored or a new interpretation is set forth.

Examensarbetet har skett inom mastersprogrammet Maskinkonstruktion på KTH. Arbetet gjorde tillsammans med Epiroc genom Svea Teknik AB. I dagens gruvarbete använder nästan alla borr- och sprängteknik, men det finns stora problem med detta. Epiroc har börjat utveckla så kallade Mobile Miners, som är konstruerade för att bryta malm utan borr- och sprängteknik. Maskinen ska ha möjlighet att göra alla processer i samma maskin istället för borr- och sprängtekniken, där maskiner byts beroende på process. Den nya tekniken använder sig av ett skärhjul för att utvinna malm. En av maskinerna Epiroc har konstruerat är Mobile Miner 40 V. Maskinen har två moduler, drivmodulen, där alla typ av drivning som hydraulpumpar är placerade och avverkningsmodulen, där skärhjulet sitter. Från tidigare versioner av Mobile Miner har det upptäckts, att det blir väldigt stora vibrationer i operatörshytten, som sitter på drivmodulen. För den nya 40 V skall kopplingen mellan modulerna kunna kopplas isär vid avverking. Dagens koncept är likt en dragkrok, som tillåter rotation i tre frihetsgrader, vilket är något som nu anses vara en risk på grund av sämre stabilitet. De tre olika leden är gir-, roll-, och tipp-led och det är roll-led som inte är önskat då 40 V är väldigt hög relativt sin bredd, vilket ger en ökad risk för tippning. Syftet med detta examensarbete var att utveckla nya stabilare koncept. Utifrån detta gjordes en parameteranalys för att definiera vad en stabilare koppling är. Nya koncept generades och dessa evaluerades med hjälp av en Pughs matris. Två koncept valdes att vidareutvecklas utifrån de givna kraven. Koncept A har låsning i tipp-led med hjälp av en krokkonstruktion, där rotationsaxlarna är separerade samtidigt som koncept B har låsningen i gir-led med hjälp av två hydrauliska cylindrar där rotationsaxlarna skär varandra likt en kardanknut. Med två frihetsgrader utsätts kopplingen för högre laster. Dimensioneringen skedde utifrån det värsta lastfallet, vilket är när avverkningsmodul kör över ett gupp och tvingar med drivmodulen. De två nya koncepten blev stabilare enligt parameteranalysen, men är något större än dagens koncept. / This Master Thesis has been done within the Master's program in Machine Design at KTH. The work was carried out together with Epiroc through Svea Teknik AB.  Today almost all mining uses drill and blast techniques, but there are major problems with this. Epiroc has started to design a so-called Mobile Miners, which are designed to excavate ore without drill and blast technology. The machine should be able to do all processes in the same operation instead of the drill and blast technology where different machines are used depending on the process. The new process uses only a cutting wheel to excavate ore. One of the machines Epiroc has designed is the Mobile Miner 40 V. The machine has two modules, the power module where all types of power supply, such as hydraulic, pumps are located and then the mining module where the cutting wheel is located. From other Mobile Miner it has been discovered that there will be very large amount of vibrations in the operator cabin, which is located on the power module, so for the new 40 V the idea is that the coupling between the modules can be disconnected while operating. The current concept is similar to a towbar that allows rotation in three degrees of freedom, which is something that was later considered a risk. The three different axes are yaw, roll, and pitch axis and it is roll axis which is not desired since 40 V is very high relative to its width, which gives a risk of tipping. The purpose of this Master Thesis were to develop a more stable concept. Based on this, a parameter analysis was made to define what a more stable coupling is. New concepts were generated and then evaluated using a Pugh's matrix. Two concepts were chosen to be further developed based on the given requirements.  Concept A has the locking procedure in pitch axis with the aid of a hook construction where the rotation axes are separated meanwhile in concept B has the locking procedure in the yaw axis with the help of two hydraulic cylinders where the rotation axes intersect each other like a universal joint. With two degrees of freedom, higher forces are transmitted. The dimensioning was based on the worst load case, which is when the mining module runs over a bump and carry the power module. The two new concepts became more stable according to the parameter analysis, but are somewhat bigger than the current concept.

The Age of Innocence is an opera based on the 1920 novel by Edith Wharton. Set in New York high society of the 1870's, it tells the story of Newland Archer, a young lawyer, his fiancée May Welland, and her cousin, the Countess Ellen Olenska, who has returned to her native New York in an aura of scandal, having left her husband, the dissolute Polish Count Olenski, in Europe. Although Archer and Ellen fall in love, he nevertheless follows the expectations of his family and marries the lovely but conventional May. For her part, while she sees a life with Archer as an escape from her loneliness, Ellen cannot allow herself to betray her cousin, insisting that she and Archer can love each other only if they remain apart. This love triangle is unique because of the social pressures placed upon Archer: he is a product of New York society, which has taught him to believe in the factitious idea of female innocence, as personified by May. Though he questions this and other conventions of his society, he is unable to bring himself to abandon the safety of these social norms that govern every aspect of proper behavior in New York. It is Archer's love for Ellen that prompts him to challenge these standards, pointing out New York's hypocrisy in welcoming May's cousin back to America while at the same time treating her as a pariah for abandoning her husband in Europe. None of their objections to Ellen is explicitly stated, however, for this is a world which has a morbid fear of "the unpleasant"--that is, anything that would disturb the calm surface of society's politesse and social grace. It comes as no surprise, then, that Archer's desire for Ellen (especially after he marries May), becomes a potential social nightmare for his family and all of New York, as they ruthlessly plot to drive the two apart, and send Ellen back to Europe. The main challenge in creating an opera out of this story, in addition to streamlining a lengthy and complex plot, was to delineate both in the libretto and the music the realms of the said and unsaid--that is, what the characters say in public, and what they say to themselves or to others that represents their innermost feelings. In the libretto, this was achieved by drawing upon Wharton's dialogue and narration in the novel in order to create these private and public utterances, in the form of recitatives, arias, duets, or ensemble pieces. The language of the libretto has been fashioned to serve these different musical forms, with dialogue from the novel employed in moments of recitative; and freely-metered verse, with a modest use of rhyme, for the "numbers" of the opera. The music, meanwhile, employs a system of codes to define the realms of the said and unsaid--motives, sonorities and key relationships that bring into focus the interactions of the characters, especially Archer, Ellen and May as their drama plays out under the ever-watchful eyes of New York society. The music has also been rendered to bring out the stresses and meter of the text, and heighten the import of the words as sung by a particular character. I have attempted in my opera to bring to life the timeless themes of Wharton's novel: unfulfilled love, the individual versus society, the potential corrupting influence of desire, and the moral choices that human beings face as they wrestle with these common issues. Opera, through the language of music, is one of the few art forms capable of fully realizing these themes in a dramatic context--in this sense, it is just as relevant to our time as it was to Wharton's, and therefore remains a viable medium for the twenty-first-century composer. / Music Composition / Accompanied by one .pdf file.

Le concept d'auto-stabilisation a été introduit par Dijkstra en 1973. Un système distribué est auto-stabilisant s'il peut démarrer de n'importe quelle configuration initiale et retrouver une configuration légitime en un temps fini par lui-même et sans aucune intervention extérieure. La convergence est également garantie lorsque le système est affecté par des fautes transitoires, ce qui en fait une approche élégante, non masquante, pour la tolérance aux pannes. L'auto-stabilisation a été étudiée dans divers domaines des systèmes distribués tels que les problèmes de synchronisation de l'horloge, de la communication et les protocoles de routage. Vu l'importance des paramètres de graphes notamment pour l'organisation et l'optimisation des communications dans les réseaux et les systèmes distribués, plusieurs algorithmes auto-stabilisants pour des paramètres de graphe ont été proposés dans la littérature, tels que les algorithmes autostabilisants permettant de trouver les ensembles dominants minimaux, coloration des graphes, couplage maximal et arbres de recouvrement. Dans cette perspective, nous proposons, dans cette thèse, des algorithmes distribués et autostabilisants pour certains problèmes de graphes bien connus, en particulier pour les décompositions de graphes et les ensembles dominants qui n'ont pas encore été abordés avec le concept de l'autostabilisation. Les quatre problèmes majeurs considérés dans cette thèse sont: partitionnement en triangles, décomposition en p-étoiles, Monitoring des arêtes, fort ensemble dominant et indépendant. Ainsi, le point commun entre ces problèmes, est qu'ils sont tous considérés comme des variantes des problèmes de domination et de couplage dans les graphes et leur traitement se fait d'une manière auto-stabilisante / The concept of self-stabilization was first introduced by Dijkstra in 1973. A distributed system is self-stabilizing if it can start from any possible configuration and converges to a desired configuration in finite time by itself without using any external intervention. Convergence is also guaranteed when the system is affected by transient faults. This makes self-stabilization an effective approach for non-masking fault-tolerance. The self-stabilization was studied in various fields in distributed systems such as the problems of clock synchronization, communication and routing protocols. Given the importance of graph parameters, especially for organization and communication of networks and distributed systems, several self-stabilizing algorithms for classic graph parameters have been developed in this direction, such as self-stabilizing algorithms for finding minimal dominating sets, coloring, maximal matching, spanning tree and so on. Thence, we propose in this thesis, distributed and self-stabilizing algorithms to some wellknown graphs problems, particularly for graph decompositions and dominating sets problems that have not yet been addressed in a view of self-stabilization. The four major problems considered in this thesis are: the partitioning into triangles, p-star decomposition, edge monitoring set and independent strong dominating set problems. The common point between these four problems is that they are considered as variants of dominating set and matching problems and all propositions deal with the self-stabilization paradigm