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Dissertations / Theses on the topic 'Geometrical Construction'
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Gover, Ashwin Roderick. "A geometrical construction of conformally invariant differential operators." Thesis, University of Oxford, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.329953.
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McClain, Nichola Sue. "A study in geometric construction." CSUSB ScholarWorks, 1998. https://scholarworks.lib.csusb.edu/etd-project/1811.
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Sabir, Tanveer, and Aamir Muneer. "Geometrical Constructions : Trisecting the Angle, Doubling the Cube, Squaring the Circle and Construction of n-gons." Thesis, Växjö University, School of Mathematics and Systems Engineering, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-5401.
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Kalden, Tenzin. "Geometrical Construction of MUBS and SIC-POVMS for Spin-1 Systems." Digital WPI, 2016. https://digitalcommons.wpi.edu/etd-theses/1235.
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The objective of this thesis is to use the Majorana description of a spin-1 system to give a geometrical construction of a maximal set of Mutually Unbiased Bases (MUBs) and Symmetric Informationally Complete Positive Operator Valued Measures (SIC-POVMs) for this system. In the Majorana Approach, an arbitrary pure state of a spin-1 system is represented by a pair of points on the Reimann sphere, or a pair of unit vectors (known as Majorana vectors or M-vectors). Spin-1 states can be of three types: those whose vectors are parallel, those whose vectors are antiparallel and those whose vectors make an arbitrary angle. The types of bases possible for a spin-1 system are thus geometrically much more varied than for a spin-half system or qubit, which is the standard unit of information storage in most quantum protocols. Our derivation of the MUBs and SIC-POVMs proceeds from a recently derived expression for the squared overlap of two spin-1 states in terms of their M-vectors and the minimal additional set of assumptions that are needed. These assumptions include time-reversal invariance in the case of the MUBs and the requirement of three-fold symmetry in the case of the SIC-POVMs. The applications of these results to problems in quantum information are mentioned.
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Van, Brunt Bruce. "Functional differential equations and lens design in geometrical optics." Thesis, University of Oxford, 1989. http://ora.ox.ac.uk/objects/uuid:d56090fc-b360-492b-9bd9-c6f36c30db86.
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The subject of this thesis is lens design using a system of functional differential equations arising from Fermat's Principle in geometrical optics. The emphasis is primarily on existence, uniqueness, and analyticity, properties of solutions to these equations, but some asymptotic methods are developed for special cases. Three specific lens problems are considered in detail: the first is an axial lens having two pairs of foci on the optical axis, the second is an axial lens which focuses light at two different frequencies to two distinct points, the third is a lens symmetric about an axis having foci not on said axis.
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Aparicio, German Walter Jr. "Holzbau : timber construction and material information exchanges for the design of complex geometrical structures." Thesis, Massachusetts Institute of Technology, 2010. http://hdl.handle.net/1721.1/59105.
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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Architecture, 2010.Page 77 blank. Cataloged from PDF version of thesis.
Includes bibliographical references (p. 74).
In a universe made of bits where everything is continuously computing and nature itself is processing information everyday, what is it that our materials compute? Specifically, what are the bits of information registered within timber? More importantly, in this universe made of bits how do we design using this information and how do we imagine new buildings? This thesis explores the use of wood as a natural material in the design and construction of complex geometrical timber structures by capturing the natural curvature found in timber into digital data and building a framework for surface timber mapping as a design method. Key results include a detailed framework for translation, method for timber mapping and a prototype utilizing this method. Future steps include growth of timber structures and the use of living material in combination with typical timber construction methods for the design and construction of future buildings.
by German Walter Aparicio Jr.
S.M.
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Campos, Filipe Alexandre Duarte González Migães de. "A sustentabilidade geométrica da construção em Terra Crua: Geometrical sustainability of raw earth construction." Master's thesis, Universidade de Évora, 2004. http://hdl.handle.net/10174/15799.
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A construção em terra é um processo milenar, e a sua transmissão enquanto tal tem sido feita entre gerações, de país para filhos, e quase sempre de forma operativa. A utilização da terra pauta-se por uma qualidade que consiste na sua reciclabilidade. Esta característica assume especial importância quando se aborda cada vez mais a sustentabilidade ou desenvolvimento sustentável. A reciclabilidade da terra como material construtivo, enquanto processo natural ou artificial, dificulta o seu estudo uma vez que os testemunhos mais antigos não podem ser avaliados devido à sua perda total. Pretende este trabalho criar uma ferramenta aglutinadora de processos construtivos, classificação da terra enquanto material de construção e por ultimo, ferramenta analítica das geometrias utilizáveis na construção com esse material, atendendo às suas propriedades. Trata-se de uma análise comparativa dos processos construtivos em terra crua, suas geometrias e estereotomias, dentro do conceito de obra global, analisando-a no todo e na parte. Esse trabalho redefine o processo de classificação das técnicas construtivas em terra crua em função dos processos auxiliares de construção, e não pelo estado físico do material utilizado ou mesmo pela família de sistema construtivo. ***/Abstract - The construction with earth is a millenary building process and its transmission as such has been passed down from generation into generation i.e. from parents to children and almost always by operative process. The utilization of earth is regulated by its recyclable quality. This characteristic gains special importance when again and again sustainability or sustainable development is approached. The recyclability of earth as a building material, considered as a natural process, makes its study difficult once the more ancient testimonials cannot be evaluated due to their total loss. This work aims at creating an agglutinating tool of constructing processes, classification of earth as a construction material and ultimately an analytical tool of the usable geometries in construction with this material, having in mind its properties. This is a comparative analysis of the constructive processes with crude earth, its geometries and stereotomies, within the concept of global work, analyzing it as a whole or in parts. This work redefines the process of classification of the techniques of construction with earth in function of the auxiliary processes of construction and not by the physical state of the material being used or even by the family of the constructive system. ***/Resumen - La construcción en tierra es un proceso melenar y la suya transmisión en cuanto tal ha sido hecha desde generaciones pasando de padres a hijos y casi siempre de forma operativa. La utilización de la tierra se regula por una cualidad que es la suya reciclabilidad. Esta característica toma una importancia especial cuando, más y más, se aborda la sustentabilidad ó el desarrollo sustentable. La reciclabilidad de la tierra como material de construcción, en cuanto proceso natural ó artificial, se vuelve difícil una vez que los testimonios más antiguos no pueden ser avaluados debido a su pierda total. Con esta obra se pretende criar una herramienta aglutinadora de los procesos de construcción y de clasificación de la tierra en cuanto material de construcción y por último, una herramienta analítica de las geometrías utilizables en la construcción con este material, considerando sus propiedades. Tratase de un análisis comparativo de los procesos de construcción con tierra cruda, sus geometrías y estereotomías, dentro de lo concepto de obra global, analizándola en el todo y en la parte. Esta obra redefine el proceso de clasificación de las técnicas con tierra cruda en función de los procesos auxiliares de construcción y no por el estado físico del material utilizado o mismo por la familia del sistema de construcción.
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Svensson, Frida. "Can you describe your home? : A study about students understanding about concepts within construction." Thesis, Linnéuniversitetet, Institutionen för matematikdidaktik (MD), 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-36357.
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The purpose with this research paper is to examine the students’ shown knowledge in geometry, with a focus on construction and its concepts, and the educational value and teaching the students got in this area. The students’ homes are used as a starting-point. The students shall, from a self-made drawing of their home and a photograph of it, describe what their home looks like. In this paper, the mathematical concepts the students used will be analyzed and compared with the education they received. The analytical framework is based on Van Hieles levels of knowledge and Blooms Taxonomy. The study was done at a Secondary School in Kenya. Four students were selected and interviewed. The lesson observations were made with the purpose to get an understanding for how the education for these students look like and to get examples on how the teaching is conducted for these students. Finally, interviews with the teachers were carried out. The students show a good knowledge in the national exams. However, the study shows that when the students are supposed to use this particular knowledge outside of the classroom, the students experience difficulties. Mostly, the students encounter problems when they are supposed to estimate measurements. Furthermore, they lack the ability to compare scales. The research also shows that the education for these students is monotone and much time during the lessons is spend either with a teacher lecturing in front of the board or students working with examples in the textbook. According to the Variation Theory, the knowledge of the students should deepen if the objects of learning are varying. This variation is not something the students receive in the present situation.Syftet är att undersöka några gymnasieelevers visade kunskaper i geometri med fokus på konstruktion och begreppsanvändning samt den undervisning som erbjuds eleverna inom området. Elevernas hem används som utgångspunkt. Eleverna ska utifrån en teckning, som de själva ritat, och ett fotografi beskriva hemmet. De matematiska begrepp som eleverna använder analyseras. Analysverktyget bygger på van Hieles kvalitativa kunskapsnivåer och Blooms Taxonomi. Undersökningen genomfördes på en gymnasieskola i Kenya. Fyra utvalda elever intervjuades. Lektionsobservationer genomfördes i syfte att få förståelse för hur elevernas undervisningssituation ser ut och få exempel på hur undervisningen bedrivs. Slutligen intervjuades två av elevernas lärare. Eleverna har goda kunskaper på nationella prov men undersökningen visar att när dessa kunskaper skall överföras till något utanför lektionssalen stöter eleverna på problem. De har svårt att uppskatta längdenheter och svårt att jämföra skala. Det kommer också fram att deras undervisning är ganska monoton. Mycket tid läggs till att läraren undervisar eleverna framme vid tavlan eller att eleverna jobbar med uppgifter i sin övningsbok. Enligt variationsteorin, som beskrivs i arbetet, skulle elevernas kunskaper ges möjlighet att fördjupas om de geometriska objekt som skall förstås varieras. Denna variation erbjuds inte eleverna i nuläget.
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Jayaram, Uma. "Extracting dimensional geometric parameters from B-spline surface models." Diss., Virginia Tech, 1991. http://hdl.handle.net/10919/37877.
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In an integrated design environment, the common thread between the different design stages is usually the geometric model of the part. However, the requirements for the geometric definition of the design is usually different for each stage. The transformation of data between these different stages is essential for the success of the integrated design environment. For example, conceptual design systems usually deal with geometric dimensional parameters (e.g. length, radius, etc.) whereas preliminary design systems frequently require the geometry definition to be in the form of surface models.
This dissertation presents the necessity and scope of creating and implementing methodologies to obtain dimensional geometric parameters from the surface description of an object. Since the study of geometric modeling and parametric surfaces is a new field, few classical methods are applicable. Methods and algorithms for the extraction of various geometry parameters are created. A few methods to pre-process and manipulate these surfaces before the parameter extraction methods can be applied are outlined.
One of the most important applications of parameter extraction is in the field of aircraft design. There are two important aspects of geometry data conversion in the design cycle. The first is the conversion from conceptual CAD models to CFD compatible models. The second is the conversion from surface representations of CFD models to obtain component parameters (e.g. wing span, fuselage fineness ratio, moments of inertia, etc.). The methods created in this dissertation are used to extract geometric parameters of importance in aircraft design. This enables the design cycle to be complete and promotes integrated design.
These methods have been implemented in the aircraft design software, ACSYNT. Examples of the conversion of data from B-spline surface models to dimensional geometric parameters using these methods are included.
The emphasis of this dissertation is on non-uniform B-spline surfaces. Methods for obtaining geometric parameters from aircraft models described by characteristic points are also considered briefly.Ph. D.
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Dalstam, Anna. "Better fashion for a better future : Exploring geometrical pattern-making in relation to trend based ready-to-wear garments, with a focus on no fabric waste." Thesis, Högskolan i Borås, Akademin för textil, teknik och ekonomi, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:hb:diva-25178.
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This study examines how to make trend fashion based ready-to-wear apparels with no fabric waste in the cutting phase through geometric pattern-making. To work with sustainability through geometrical pattern-making in construction, within the context of commercial fashion. The fashion industry is one of the world's top polluters. Several million tonnes of textile ends up in landfills all over the world every year, landfills are overwhelmed and that has a great impact on the environment. The purpose of this study is to investigate how the method of geometric pattern making can have a commercial value in sustainability. How it can bring benefits within fashion design to become more sustainable, and thus help tackle issues in relation to fabric waste in garment production. Significantly, the project discusses if there can be a way of making commercial clothes more sustainable through geometric pattern-making so no fabric is wasted when it is being cut. The work proposes potential solutions and expressions through this chosen methodology.
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Pauley, Blaga Slavcheva. "Constructible circles on the unit sphere." CSUSB ScholarWorks, 2000. https://scholarworks.lib.csusb.edu/etd-project/1675.
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In this paper we show how to give an intrinsic definition of a constructible circle on the sphere. The classical definition of constructible circle in the plane, using straight edge and compass is there by translated in ters of so called Lenart tools. The process by which we achieve our goal involves concepts from the algebra of Hermitian matrices, complex variables, and Sterographic projection. However, the discussion is entirely elementary throughout and hopefully can serve as a guide for teachers in advanced geometry.
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Mandil, Guillaume. "Modèle de représentation géométrique intégrant les états physiques du produit." Phd thesis, Ecole Centrale Paris, 2011. http://tel.archives-ouvertes.fr/tel-00714559.
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Cette thèse introduit le concept de comportement géométrique d'un assemblage mécanique. Cette notion permet de rendre compte du caractère assemblable ou mobile d'un mécanisme sous la forme d'un système de relations algébriques entre les paramètres géométriques permettant de le décrire. Dans un premier temps, cette thèse montre l'intérêt de ce concept pour traiter des problèmes faisant intervenir plusieurs effets physiques et plusieurs scénarios d'utilisation. Ce chapitre est appliqué à l'étude de l'assemblabilité d'un treillis pyramidal de conception à 4 barres décrit par un modèle géométrique non cartésien issu de la littérature. Dans un second temps, après avoir constaté le manque de modèles adaptés permettant de représenter des mécanismes mobiles, ce travail en propose un non cartésien. Il détaille aussi une méthode de mise en équation afin de traduire la mobilité d'un mécanisme. Une application de ce modèle et de la méthode est également faite. Elle permet de résoudre localement le problème de la mobilité d'un mécanisme de Bennett. Enfin, la dernière partie de ce travail expose une solution pour associer et comparer deux objets décrits par des représentations non cartésiennes. Cette technique est utile pour comparer deux états physiques du même objet utilisé dans différents scénarios pour assurer le suivi d'une exigence géométrique. Elle peut également être utilisée pour associer des objets réels et des objets idéalisés pour traiter des problèmes de tolérancement
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Silva, Silvio Marcelino da. "Construções geométricas planas e espaciais no ensino da geometria." Universidade Estadual Paulista (UNESP), 2018. http://hdl.handle.net/11449/154808.
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Este trabalho foi formulado, visando diminuir as dificuldades apresentadas na aprendizagem da geometria, e também, proporcionar aos professores da área mais um recurso didático para trabalhar este assunto que é de total relevância no ensino da Matemática. Vivemos em um mundo real e não abstrata. Além de demonstrações virtuais das figuras planas e espaciais, podemos muitas vezes, construí-las e torná-las reais manualmente, e assim, colaborar com o desenvolvimento das habilidades de construção dos educandos, além do que a aprendizagem se torna mais prazerosa e mais prática. Nosso objetivo geral é reafirmar que a geometria está presente em toda parte, que tudo o que nos cerca tem formas geométricas, tanto na natureza quanto nas coisas produzidas pelo homem no decorrer da evolução da espécie humana. E nosso objetivo específico tem como estrutura os seguintes pensamentos: facilitar uma maior compreensão da geometria plana e espacial para os alunos do Ensino Fundamental e Médio, através de construções geométricas; desenvolver um estudo mais aprofundado sobre esta temática, visando colaborar com o trabalho do professor que atua no ensino de geometria; oferecer um recurso didático adicional para facilitar a exposição do conteúdo de geometria.
This work was formulated aiming to reduce the difficulties presented in the learning of geometry, and also to provide to the teachers of this field an extra didactic resource to work on this subject which is of total relevance in the teaching of Mathematics. We live in a real world, not in a virtual one. In addition to virtual demonstrations of flat and spatial figures, we can often construct them and make them real by hand, and thus collaborate with the development of the students' construction skills, and the learning becomes more pleasurable and more practical. Our general objective is to reaffirm that geometry is present everywhere, and everything around us has geometric forms, both in nature and in things produced by man in the course of the evolution of the human species. And our specific objectives are structured as follows: facilitate a better understanding of flat and spatial geometry for elementary, middle and high school students through geometric constructions; develop a more detailed study on this subject, aiming to collaborate with teachers who work in the teaching of geometry, and offer an additional didactic resource to facilitate the exposure of the geometry contents
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Belkacem, Sihem. "Recherche de forme par relaxation dynamique des structures reticulees spatiales autocontraintes." Toulouse 3, 1987. http://www.theses.fr/1987TOU30146.
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Benkert, Marc. "Construction and Analysis of Geometric Networks." [S.l. : s.n.], 2007. http://digbib.ubka.uni-karlsruhe.de/volltexte/1000007167.
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CRISSAFF, LHAYLLA DOS SANTOS. "AN ALGEBRAIC CONSTRUCTION OF GEOMETRIC CODES." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2005. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=7082@1.
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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIORComeçamos estudando uma classe particular de códigos lineares, os chamados códigos de Goppa que são obtidos calculando o valor de certas funções em pontos de Kn, onde K é um corpo finito. Apresentamos uma generalização desta construção e definimos códigos de avaliação sobre K- ágebras satisfazendo certas propriedades. Para estes códigos, descrevemos um algoritmo de decodificação e mostramos que se considerarmos os códigos de Goppa em um ponto como exemplo desta nova construção, o algoritmo corrige mais erros do que o algoritmo clássico para os códigos de Goppa.
We begin studying a certain type of linear code the so-called Goppa codes. These codes are constructed by taking the evaluation of certain functions at points in Kn, where K is a finite field. As a generalization of this construction, we introduce the so-called evaluation codes defined over K-algebras satisfying some properties. For these codes, we describe a decoding algorithm and we show that if we consider classical one-point Goppa codes as an example of the new construction, this algorithm correct more errors that the classical algorithm for Goppa codes.
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Gusmai, Rafael Martins. "Um estudo sobre três problemas clássicos da geometria euclidiana." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/55/55136/tde-29112016-141932/.
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Este trabalho aborda os três problemas clássicos de geometria da Grécia antiga trazendo as principais histórias e conceitos necessários para compreensão dos mesmos. Construções geométricas com régua não graduada e compasso, números construtivos, corpos, números complexos e polinômios são alguns dos assuntos que antecedem o tratamento dos problemas. As construções são exibidas usando as relações existentes nas operações aritméticas, dá opções de como se representar geometricamente as quatro operações básicas e a extração de raízes quadradas, mostrando que todo problema modelado nessas condições pode ser solucionado através dos instrumentos euclidianos. Essa exibição vem ao encontro dos números construtivos, trazendo à tona quais os principais pensamentos sobre construções com régua e compasso, deixando claro a definição de construções geométricas para os gregos. São apresentados também propriedades da álgebra abstrata envolvendo conjuntos numéricos que possuem características de corpo, dentre eles os números complexos. Além disso, tratamos dos polinômios, os quais são fundamentais nas demonstração das impossibilidades clássicas. Por fim, esta pesquisa deixará claro a integração de todos os conteúdos citados acima e de que forma toda teoria pode ser organizada na realização das demonstrações da impossibilidade da duplicação do cubo, trissecção do ângulo e quadratura do círculo, frizando a mobilização dos matemáticos ao longo da história para tentar explicar tais problemas, acarretando um alto desenvolvimento da Matemática.This work addresses the three classic problems ancient Greek geometry bringing the main stories and concepts needed to understand them. Geometric constructions with non-graded ruler and compass, building numbers, bodies, complex numbers and polynomials are some of the issues that precede the statements of problems. The buildings are displayed using the relationships in arithmetic operations, the options of how to represent geometrically the four basic operations and extraction of square roots, shows that every problem can be modeled in such conditions solucionas through Euclidean tools. This view comes against constructive rising numbers which the main thoughts of constructions with ruler and compass, making clear the definition of geometric constructions for the Greeks. It also present properties of abstract algebra involving numerical sets that have body characteristics, including complex numbers, also explains the importance of polynomials in the statement of classical impossibilities building the definition of degree of extension. Finally this research will clarify the integration of all the contents mentioned above and how every theory can be organized in the realization of doubling the cube demonstrations, angle trisection and squaring the circle, plus the mobilization of mathematicians throughout history for trying to explain such problems causing a high development of mathematics
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Vala, Jan. "Parametrický geometrický 3D kreslicí nástroj." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2014. http://www.nusl.cz/ntk/nusl-236087.
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Purpose of this thesis is to introduce reader to 3D parametric construction tools and their application with dynamic geometry. Project introduces basic concepts of parametric construction in computer geometry, summary of the state of the art, description of selected parametric geometry software, evaluation of its features and design of 3D parametric geometry library for use in computer graphics followed by implementation of said library and user interface application for evaluation.
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Bojorquez, Betzabe. "Geometric Constructions from an Algebraic Perspective." CSUSB ScholarWorks, 2015. https://scholarworks.lib.csusb.edu/etd/237.
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Many topics that mathematicians study at times seem so unrelated such as Geometry and Abstract Algebra. These two branches of math would seem unrelated at first glance. I will try to bridge Geometry and Abstract Algebra just a bit with the following topics. We can be sure that after we construct our basic parallel and perpendicular lines, bisected angles, regular polygons, and other basic geometric figures, we are actually constructing what in geometry is simply stated and accepted, because it will be proven using abstract algebra. Also we will look at many classic problems in Geometry that are not possible with only straightedge and compass but need a marked ruler.
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Graham, S. L. "The application of geometric modelling to motor vehicle construction." Thesis, Coventry University, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.233947.
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Patel, Pritesh V. "Stepwise construction and spectroscopy of geometrically constrained bimetallic molecular triads." Thesis, University of Newcastle Upon Tyne, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.427410.
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Jesus, Gilson Bispo de. "Construções geométricas: uma alternativa para desenvolver conhecimentos acerca da demonstração em uma formação continuada." Pontifícia Universidade Católica de São Paulo, 2008. https://tede2.pucsp.br/handle/handle/11316.
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Previous issue date: 2008-06-30Conselho Nacional de Desenvolvimento Científico e Tecnológico
The purpose of this study is to analyze a sequence of activities carried out with in service teachers, aiming the construction of the definition of line bisector of a segment and, from this definition, to allow them to demonstrate inherent properties of this mathematical object. Moreover, the study also aimed that the teachers were able to justify it mathematically, based on plane Geometry, some geometric constructions in which this object was the main tool to solve the problem. Our research question was: Can a teaching sequence, carried out with in service teachers, and focus on geometric constructions, contribute for the development of knowledge about demonstration in Geometry? In order to answer this question, we developed a sequence with a group of in-service teachers of Mathematics for Elementary and secondary school. To reach such aim, we base our study on the theoretical approach of Duval (2003) and Brousseau (1986), about Semiotics Representation Registers, and the Didactic Situation Theory respectively. We also used the Duval and Egret (1989) and De Villiers (2001; 2002) ideas about demonstrations. Finally, we still used some authors ideas about teacher s formation. The methodological choice was research-action and Didactic Engineering, which had contributed to achieve the objective of this study. The analysis of the discussions and the behaviors of the teachers during the formation reveled that the activities had caused reciprocal reflections about definitions, properties, theorems, mathematical justifications, demonstrations. Moreover, the sequence allowed these teachers to discover and to construct some plane Geometry concepts, whilst they made geometric constructions. In this sense, we do highlight to the importance of material representation register. We conclude that this formation contributed for the autonomy of these teachers
O presente trabalho tem como objetivo analisar uma sequência de atividades desenvolvidas em uma formação continuada para professores. Esta seqüência visava que os participantes construíssem a definição de mediatriz de um segmento e, a partir desta, demonstrassem propriedades inerentes a esse objeto matemático. Além disso, objetivava que os professores justificassem matematicamente, com base na Geometria plana, algumas construções geométricas em que esse objeto era a principal ferramenta para a resolução do problema. A questão pesquisada foi: uma seqüência de ensino com enfoque em construções geométricas pode contribuir para o desenvolvimento de conhecimentos acerca da demonstração em Geometria em uma formação continuada de professores? Assim, aplicamos junto a um grupo de professores de Matemática (Ensino Fundamental e Médio) em formação continuada, a seqüência de atividades. Para tal, nos baseamos nos estudos de Duval (2003) e Brousseau (1986), sobre os registros de representação semiótica e a Teoria das Situações Didáticas respectivamente. Trabalhamos também com Duval e Egret (1989) e De Villiers (2001; 2002), no que diz respeito às demonstrações e com autores especializados em formação de professores, para a fundamentação teórica dessa pesquisa. A escolha metodológica pela pesquisa-ação e pelos pressupostos da Engenharia Didática contribuíram para o alcance dos objetivos desse estudo. A análise das discussões e comportamentos dos professores durante a formação revelou-nos que as atividades provocaram reflexões sobre definições, propriedades, teoremas recíprocos, justificativas matemáticas, demonstrações, além de oportunizar a descoberta e construção de alguns conceitos da Geometria plana ao realizarem construções geométricas. Nesse sentido, pudemos destacar o registro material de representação, identificado por nós, e inferir que essa formação contribuiu para a autonomia dos professores
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Saquet, Pierre. "Further developments of the AcBuilder tool for constructing geometrical models of aircraft." Thesis, KTH, Aerodynamik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-48578.
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This report, along with Laurent Gourc’s and Ben Marchant’s reports, presents the work done on the development of the new AcBuilder, realized for CEASIOM. CEASIOM is a package of different modules, developed as part of the SimSAC project, which aims to Simulate Stability And Control Characteristics for Use in Conceptual Design. First, the CEASIOM software is introduced in the context of the SimSAC project and, to know where the development of the aircraft builder tool (AcBuilder) is, an overview of the previous version is shown. Then, based on the issues noticed by the users and the programmers of CEASIOM, the goals of the project are presented in listing some modifications and improvements to bring to the software. Secondly, the document treats about the requirements for the new AcBuilder development in order to reach the goals of the project. Those requirements come from both the programming languages used (Matlab and Java) and from the technical parts of the project (geometrical construction of aircraft). Finally, this report presents the new AcBuilder tool, its new design interface, its new functionalities and the remaining improvements to implement in order to make the module compatible with the changes brought by the new requirements.
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Makeev, Andrew. "Geometrically nonlinear analysis of laminated composites with extension-twist coupling." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/12028.
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Berlinkov, Artemi. "Dimensions in Random Constructions." Thesis, University of North Texas, 2002. https://digital.library.unt.edu/ark:/67531/metadc3160/.
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We consider random fractals generated by random recursive constructions, prove
zero-one laws concerning their dimensions and find their packing and Minkowski dimensions. Also we investigate the packing measure in corresponding dimension. For a class of random distribution functions we prove that their packing and Hausdorff dimensions coincide.
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Ibtiouene, Rachid. "Contribution au dimensionnement électromagnétique d'une machine synchrone autopilotée à aimants insérés." Vandoeuvre-les-Nancy, INPL, 1993. http://www.theses.fr/1993INPL109N.
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Le coût relativement élevé des aimants modernes incite à en minimiser la taille tout en conservant des performances acceptables pour la machine. D'autre part, la machine doit être adaptée à son alimentation. Dans cette optique, nous avons développé des modèles d'étude permettant de déterminer l'influence des paramètres géométriques d'un moteur synchrone autopiloté à aimants insérés dans l'armature rotorique (le cas limite d'un rotor lisse ainsi que le couple de détente sont également étudiés). Les méthodes proposées constituent une contribution à la définition des paramètres optimaux
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Benkert, Marc [Verfasser], and A. [Akademischer Betreuer] Wolff. "Construction and Analysis of Geometric Networks / Marc Benkert ; Betreuer: A. Wolff." Karlsruhe : KIT-Bibliothek, 2007. http://d-nb.info/1186010932/34.
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MOREIRA, JOHANN SENRA. "CONSTRUCTION OF THE CONICS USING THE GEOMETRIC DRAWING AND CONCRETE INSTRUMENTS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2017. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=33061@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCOORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
PROGRAMA DE MESTRADO PROFISSIONAL EM MATEMÁTICA EM REDE NACIONAL
O presente trabalho tem como objetivo facilitar o estudo das cônicas e ainda despertar o interesse do aluno para o desenho geométrico. Será apresentado que as curvas cônicas estão em nosso dia a dia, não só como beleza estética, mas também provocando fenômenos físicos amplamente utilizado pela arquitetura e engenharia civil, como acústica e reflexão da luz. Utilizaremos instrumentos para desenhar curvas que despertem a curiosidade dos alunos e faremos uso das equações e lugares geométricos a fim de demostrar tais recursos. Pretende-se assim que ao adquirir tais conhecimentos o aluno aprimore seu entendimento matemático e amplie seu horizonte cultural.
The present research aims to facilitate the study of the conics and also to arouse the interest of the student for the geometric drawing. The conic curves will be presented not only as they are in our day to day as aesthetic beauty but also as responsible for the physical phenomena widely used by architecture and civil engineering as well as acoustics and reflection of light. We will use instruments to draw curves that arouse the curiosity of the students, making use of the equations and locus in order to demonstrate such resources. It is intended that the student acquire this knowledge, improving his mathematical understanding and broadening his cultural horizon.
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Baldwin, Elizabeth. "A Geometric Invariant Theory Construction of Moduli Spaces of Stable Maps." Thesis, University of Oxford, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.487135.
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We construct the moduli spaces of stable maps, Mg,n(pr, d), via geometric invariant theory (GIT). This construction is only valid over Spec C, but a special case is a GIT presentation of Mg,n, which is valid over any algebraically closed field. Our method follows that of Gieseker in [G] and Swinarski in [Sw2], though our proof that the semistable set is nonempty is different.
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Chislenko, Julia. "On geometric constructions of the universal enveloping algebra U(sln̳)." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/28097.
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Sousa, Cristiano Benevides de. "Inversão Geométrica Aplicada à Resolução dos Problemas de Apolônio." Universidade Federal da Paraíba, 2014. http://tede.biblioteca.ufpb.br:8080/handle/tede/7570.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
This work was developed with the aim of presenting a new approach within the Geometry, the Inversion. The Inversive Geometry is a non-Euclidean geometry that has several applications, mainly related to problems of tangency. This new Geometry is presented throughout this work in order to solve the ten problems of Apollonius. All constructions are carried out with the aid of a Dynamic Geometry software, Geogebra. Since the work is directed to teachers and students of basic education, then there is a proposed roadmap for the reader to participate in the construction of the solutions of these problems process, which will enable the development of creativity, logical thinking, reasoning and practice of geometric constructions.
O presente trabalho foi desenvolvido com o objetivo de apresentar uma nova abordagem dentro da Geometria; a Inversão. A Geometria Inversiva é uma Geometria não Euclidiana que possui inúmeras aplicações, principalmente relacionada a problemas de tangência. Essa nova Geometria é apresentada ao longo desse trabalho com o objetivo de solucionar os dez problemas de Apolônio. Todas as construções são realizadas com o auxílio de um software de Geometria Dinâmica; o Geogebra. Como o trabalho é direcionado para professores e alunos do ensino básico, então há uma proposta de roteiro para que o leitor possa participar do processo de construção das soluções dos referidos problemas, o que possibilitará o desenvolvimento da criatividade, do pensamento lógico, da argumentação e da prática em construções geométricas.
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Piah, Abd Rahni bin Mt. "Construction of smooth closed surfaces by piecewise tensor product polynomials." Thesis, University of Dundee, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.295312.
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Awuah-Baffour, Robert. "Investigation on kinematic determination of highway geometric characteristics by attitude GPS." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/21657.
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Leung, Hoi-cheung, and 梁海翔. "Enhancing students' ability and interest in geometry learning through geometric constructions." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2011. http://hub.hku.hk/bib/B48367746.
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Students nowadays are relatively confident in directly applying geometrical theorems and theories. Nevertheless, it has been a common phenomenon that students are not confident in constructing geometric proofs. They lack the confidence and sufficient experience and knowledge in conducting deductive geometrical proofs. To some students, they treat proofs simply as another type of examination questions which they can tackle by repeated drillings.
Students make use of straightedges and compasses to construct different geometry figures in geometric constructions. Through geometric constructions, we can train our prediction and logical thinking skills when investigating the properties of geometric figures. Geometric constructions provide students with hands-on experience to geometry learning which requires students to have more in-depth thinking.
This is an empirical study on the implementation of geometric construction workshops among junior secondary students in Hong Kong. Results have shown that students enjoyed the construction tasks during the workshops. Analysis has implied that geometric constructions help improve students’ ability in constructing geometric proofs and to raise their interests in geometry learning.published_or_final_version
Education
Master
Master of Education
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Rubinstein, Yanir Akiva. "Geometric quantization and dynamical constructions on the space of Kähler metrics." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/44270.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.Includes bibliographical references (p. 185-200).
This Thesis is concerned with the study of the geometry and structure of the space of Kihler metrics representing a fixed cohomology class on a compact Kähler manifold. The first part of the Thesis is concerned with a problem of geometric quantization: Can the geometry of the infinite-dimensional space of Kähler metrics be approximated in terms of the geometry of the finite-dimensional spaces of FubiniStudy Bergman metrics sitting inside it? We restrict to toric varieties and prove the following result: Given a compact Riemannian manifold with boundary and a smooth map from its boundary into the space of toric Kähler metrics there exists a harmonic map from the manifold with these boundary values and, up to the first two derivatives, it is the limit of harmonic maps from the Riemannian manifold into the spaces of Bergman metrics. This generalizes previous work of Song-Zelditch on geodesics in the space of toric Kähler metrics. In the second part of the Thesis we propose the study of certain discretizations of geometric evolution equations as an approach to the study of the existence problem of some elliptic partial differential equations of a geometric nature as well as a means to obtain interesting dynamical systems on certain infinite-dimensional spaces. We illustrate the fruitfulness of this approach in the context of the Ricci flow as well as another flow on the space of Kähler metrics. We introduce and study dynamical systems related to the Ricci operator on the space of Kähler metrics that arise as discretizations of these flows. As an application, we address several questions in Kähler geometry related to canonical metrics, energy functionals, the Moser-Trudinger-Onofri inequality, Nadel-type multiplier ideal sheaves, and the structure of the space of Kähler metrics.
by Yanir Akiva Rubinstein.
Ph.D.
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Mehrotra, Anuj. "A geometric programming based procedure to design bridge superstructures." Thesis, Virginia Tech, 1988. http://hdl.handle.net/10919/44081.
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The routine procedure for designing bridge superstructures relies heavily on the
past experience of the designer and is extremely time consuming and costly to try out
alternative designs. Typically, a designer is more concerned about satisfying the design
requirements laid down by the American Association of State Highway and Transportation
Officials (AASHTO) than in coming up with the best possible design from the
economic point of view. Thus, application of suitable mathematical programming
techniques to determine optimal designs can result in tremendous savings.
In this thesis, a procedure based on Generalized Geometric Programming (GGP)
is developed to optimally design and select bridge superstructures. The bridge superstructure
design problems are formulated as GGP problems incorporating all the design
considerations as specified by AASHTO and the Virginia Department of Transportation
(VDOT). A primal based algorithm is used in which, the resulting optimization problems
are transformed to the solution of a series of Linear Programming problems that
are easy to solve.
A computer implementation of the algorithm is also developed. The software is
extremely versatile and user friendly. It provides several options to help determine the
optimal solution under varying design conditions, and is implemented on several representative problems provided by VDOT. Comparison of the resulting optimal with
the existing designs promises huge savings in terms of both cost and effort. The methodology that is developed can be used to solve other Engineering Designs Problems as well.Master of Science
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Jeong, Namin. "A surfacelet-based method for constructing geometric models of microstructure." Diss., Georgia Institute of Technology, 2015. http://hdl.handle.net/1853/54438.
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Integration of material composition, microstructure, and mechanical properties with geometry information enables many product development activities, including design, analysis, and manufacturing. To address such needs, models of material composition have been integrated into CAD systems, creating systems called heterogeneous CAD modeling. In order to support the heterogeneous CAD system, extensive process-structure-property relationships have to be captured and integrated into current CAD system. A new method for reverse engineering of materials will be presented such that microstructure models can be constructed and used in the heterogeneous CAD system.
Reverse engineering of material consists of three parts: image analysis, structure-property-process relationship, and repository. In this research, an image processing method, which comprises the Radon transform and the wavelet transform, will be used in order to recognize geometric features from a microstructure image. Recognizing geometric features can be obtained by combinations of three techniques, masking, clustering, and high frequency component on wavelet transform, that are integrated with the Radon transform. Then, recognized geometric features can be used to construct an explicit geometric model of microstructure. The proposed work will provide an explicit mathematical method to recognize and to quantify microstructure features from an image. In addition, explicit geometric models of microstructure can be automatically constructed and utilized to get effective mechanical properties, establishing structure-property relationship of the material. In order to demonstrate this, polymer nano-composite sample and metal alloy sample will be used.
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Girotto, Naira. "O desenvolvimento de hábitos de pensamento : um estudo de caso a partir de construções geométricas no GeoGebra." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2016. http://hdl.handle.net/10183/151045.
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Esta dissertação apresenta, a partir de atividades de construções geométricas no software GeoGebra, uma proposta de desenvolvimento de hábitos do pensamento matemático no Ensino Fundamental. Nos fundamentos teóricos trazemos, de documentos oficiais, recomendações específicas sobre o trabalho escolar com construções geométricas usando régua e compasso, seguidos de alguns recortes que ilustram a presença de tais construções nos livros didáticos; também tratamos das regras de construção com a régua e o compasso, exemplificando com algumas construções clássicas, seguidas de demonstração; e finalmente apresentamos o potencial do software GeoGebra e, no contexto das construções geométricas, identificamos os diferentes hábitos de pensamento propostos no trabalho de Goldenberg. São com estes fundamentos que concebemos a sequência didática que foi colocada sob experimentação e avaliação em uma turma de 9º ano de uma escola de Ensino Fundamental, no município de Porto Alegre. Na análise do experimento, tendo-se como material as produções dos alunos realizadas no GeoGebra, foi possível observar estratégias que revelam raciocínios que fazem parte dos hábitos do pensamento elencados, especialmente aqueles que dizem respeito a visualização, exploração e experimentação geométrica.Based on geometric constructions activities with GeoGebra software, this dissertation presents a proposal for the development of mathematical thinking in elementary school. The theoretical approach of this work considers three aspects: the recommendations given at official documents about ruler and compass constructions as school activities; principles of the ruler and compass constructions, illustrated with some examples and their mathematical proofs; the potential of the GeoGebra software as a tool for geometric reasoning, in particular as a tool for development of the habits of reasoning proposed by Goldenberg. Based on those theoretical considerations, it was designed a didactic sequence that was placed under experimentation and evaluation in a class of 9th grade of elementary school in the city of Porto Alegre. Using as data base the productions of the students it was possible to observe in their strategies the presence of mathematical reasoning discussed by Goldenberg, especially those concerning to visualization and geometric exploration.
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Santana, Marciano AraÃjo. "Proposta de abordagem do teorema do Ãngulo externo na formaÃÃo continuada de professores de matemÃtica da educaÃÃo a distÃncia (ead) com o uso do geogebra." Universidade Federal do CearÃ, 2015. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=13731.
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O uso da geometria no dia a dia das pessoas tem importÃncia significativa por ser um assunto que utiliza desenhos, formas e teoremas como elementos de estudos para comprovar sua atuaÃÃo nos mais diversos campos da sociedade tais como engenharias, siderÃrgicas, arquiteturas, topografias, etc. Neste contexto, podemos afirmar que construÃÃes geomÃtricas propiciam a descoberta de valiosas ideias que auxiliam à compreensÃo das propriedades geomÃtricas. As avaliaÃÃes em larga escala apresentadas nos indicadores da educaÃÃo pÃblica no Estado do Cearà retratam claramente as dificuldades de aprendizagem por parte dos alunos quando relacionados aos conceitos geomÃtricos especificamente o teorema do Ãngulo externo tanto na teoria (conceito algÃbrico) como na prÃtica (conceito geomÃtrico). A partir desta analise, propomos realizar uma investigaÃÃo atravÃs da presente pesquisa que conseguisse identificar possÃveis entraves existentes no ensino de geometria para que pudesse obter avanÃos que visam melhorar no ensino relacionado ao Teorema do Ãngulo Externo e suas ConsequÃncias usando os ambientes de aprendizagens Velho Papel e Caneta (VPC) e o Ambiente virtual de Aprendizagem (AVA) com a operacionalidade do software educativo de geometria dinÃmica GeoGebra. O trabalho teve a participaÃÃo de um grupo de 12(doze) professores de matemÃtica em formaÃÃo continuada de um Curso de EspecializaÃÃo no Ensino de MatemÃtica da Universidade Vale do Acaraà (UVA) na cidade de Cascavel-Ce. O uso operacional e pedagÃgico do software de geometria dinÃmica GeoGebra foi aplicado em aulas expositivas com questionÃrios de problemas envolvendo o teorema do Ãngulo externo que busca avaliar o desempenho dos estudantes participantes da pesquisa em relaÃÃo suas prÃticas de sala de aula com o ensino de geometria. Adotamos abordagens qualitativa, exploratÃria e pesquisa-aÃÃo para caracterizar a pesquisa e buscamos tomar como base os pressupostos teÃricos e reflexivos segundo as concepÃÃes de Valente, Michele Artigue, Pais e Fiorentini e Lorenzato. A pesquisa revelou avanÃos no processo de aprendizagem dos estudantes participantes que se mostraram entusiasmados com os conhecimentos que construÃram e que os possibilitou estabelecerem um relacionamento colaborativo entre os grupos envolvidos (estudantes e professor-pesquisador)The use of geometry in everyday life people have significant importance because it is a subject that uses designs, shapes and theorems as studies of evidence to make its activities in various fields of society such as engineering, steel, architecture, topography, etc. In this context, we can say that geometric constructions provide the discovery of valuable ideas that help the understanding of geometric properties. The large-scale assessments presented in public education indicators in the State of Ceara clearly portray the difficulties of learning by students when related to geometric concepts specifically the exterior angle theorem in theory (algebraic concept) and in practice (geometric concept). From this analysis, we propose to conduct an investigation through this research that could identify possible barriers in existing geometry teaching so he could obtain advances to improve the teaching related to the External Angle Theorem and its Consequences using the old learning environments and Paper pen (VPC) and the virtual Learning Environment (VLE) with the operation of educational software of dynamic geometry GeoGebra. The work was attended by a group of twelve (12) mathematics teachers in continuing education of a Specialization Course in Teaching of Mathematics at the University Vale do Acaraà (UVA) in the city of Cascavel-Ce. The operational and pedagogical use of dynamic geometry software GeoGebra was applied in lectures with questionnaires problems involving the exterior angle theorem that seeks to assess the performance of students participating in the survey regarding their classroom practices with the teaching of geometry. We adopted a qualitative, exploratory and action research approaches to characterize the research and seek to build on the theoretical and reflexive assumptions according to Valente conceptions, Michele Artigue, Parents and Fiorentini and Lorenzato. The survey showed progress in the learning process of participating students that were excited by the knowledge that built and that allowed establish a collaborative relationship between the groups involved (students and teacher-researcher).
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Hausgen, Paul E. "A thermal analysis of an alkali metal thermal to electric converter with geometrically designed interior surfaces exhibiting directionally dependent radiative properties." Diss., Georgia Institute of Technology, 2000. http://hdl.handle.net/1853/16701.
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Lauterbach, Dominic [Verfasser]. "Singular Mixture Copulas - A Geometric Method of Constructing Copulas / Dominic Lauterbach." München : Verlag Dr. Hut, 2014. http://d-nb.info/1052375359/34.
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Gill, Olivia Jo. "Geometric and homological methods in group theory : constructing small group resolutions." Thesis, London Metropolitan University, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.573402.
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Given two groups K and H for which we have the free crossed resolutions, B* ɛ K and C* ɛ H respectively. Our aim is to construct a free crossed resolution, A* ɛ G, by way of induction on the degree n, for any semidirect product G = K >
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Martin, Benjamin C. "Geometric Design Optimization of Brushless Permanent Magnet Motors." Fogler Library, University of Maine, 2009. http://www.library.umaine.edu/theses/pdf/MartinBC2009.pdf.
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Lischewski, Andree. "Geometric constructions and structures associated with twistor spinors on pseudo-Riemannian conformal manifolds." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2015. http://dx.doi.org/10.18452/17132.
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Die Arbeit untersucht lokale Geometrien, die Twistorspinoren zulassen auf pseudo-Riemannschen Mannigfaltigkeiten beliebiger Signatur. Hierzu entwickeln wir die benötigten Methoden, nämlich das konforme Traktorkalkül, welches eine konform-invariante Beschreibung von Twistorspinoren als parallele Objekte ermöglicht, weiter. In diesem Zusammenhang ist unser erstes zentrales Resultat ein Klassifikationssatz für konforme Strukturen, deren Holonomiegruppen einen total ausgearteten Unterraum beliebiger Dimension invariant lassen. Hierauf aufbauend können wir einen partiellen Klassifikationssatz für konforme Strukturen mit Twistorspinoren beweisen. Weiterhin studieren wir die Nullstellenmenge eines Twistorspinors unter Nutzung der Theorie der Orbitzerlegungen für parabolische Geometrien. Wir können die lokale geometrische Struktur der Nullstellenmenge vollständig beschreiben und zeigen, dass lokal jeder Twistorspinor mit Nullstelle konform äquivalent zu einem parallelem Spinor ist. Eine Anwendung dieser Resultate auf niedrig-dimensionale Split-Signaturen führt zu einer vollständigen geometrischen Beschreibung von Mannigfaltigkeiten mit nicht-generischen Twistorspinoren in den Signaturen (3,2) und (3,3) durch parallele Spinoren, was die schon bekannte Analyse des generischen Falls komplementiert. Darüberhinaus wenden wir das Traktorkalkül an, um einer konformen Spin- Mannigfaltigkeit auf natürliche Weise eine konforme Superalgebra zuzuordnen. Dieser Zugang führt zu verschiedenen Resultaten, die algebraische Eigenschaften dieser Superalgebra mit speziellen Geometrien auf der zugrundeliegenden Mannigfaltigkeit in Verbindung bringen. Weiterhin erhält man so neue Konstruktionsprinzipien für Twistorspinoren und konforme Killingformen. Zuletzt führen wir den Begriff der konformen Spin-c-Geometrie ein. Unter anderem liefern spezielle Spin-c-Twistorspinoren eine neue Charakterisierung von Fefferman-Räumen.The present thesis studies local geometries admitting twistor spinors on pseudo- Riemannian manifolds of arbitrary signature. To this end, we refine and extend the necessary machinery of first prolongation of conformal structures and conformal tractor calculus which allows a conformally-invariant description of twistor spinors as parallel objects. In this context, our first main theorem is a classification result for conformal geometries whose conformal holonomy group admits a totally degenerate invariant subspace of arbitrary dimension. Based on this we are able to prove a partial classification result for conformal structures admitting twistor spinors. Moreover, we study the zero set of a twistor spinor using the theory of curved orbit decompositions for parabolic geometries. We can completely describe the local geometric structure of the zero set and show that locally every twistor spinor with zero is equivalent to a parallel spinor off the zero set. An application of these results in low-dimensional split-signatures leads to a complete geometric description of manifolds admitting non-generic twistor spinors in signatures (3,2) and (3,3) in terms of parallel spinors which complements the well-known analysis of the generic case. Moreover, we apply tractor calculus for the construction of a conformal superalgebra naturally associated to a conformal spin structure. This approach leads to various results linking algebraic properties of the superalgebra to special geometric structures on the underlying manifold. It also exhibits new construction principles for twistor spinors and conformal Killing forms. Finally, we introduce and elaborate on the notion of conformal Spin-c-geometry. Among other aspects, this gives rise to a new characterization of Fefferman spaces in terms of distinguished Spin-c-twistor spinors.
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Moro, Ana Cecilia Del. "Geometria das dobraduras e aplicações no Ensino Médio." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/55/55136/tde-03102017-172103/.
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Este trabalho tem como foco a dobradura em sala de aula, auxiliando o professor em sua prática docente. Com dobras simples de serem realizadas a dobradura pode auxiliar o aluno a desenvolver a concentração, estimular a criatividade, concretizar uma ideia ou pensamento no momento em que surge a foma no papel e, consequentemente, o aluno interioriza o aprendizado desejado. Os tópicos estudados versam sobre a construção dos principais polígonos regulares e de um sólido espacial, o tetraedro. São também estudadas algumas aplicações aritméticas, como divisão de segmentos e raízes quadradas e cúbicas.This work aims to study the activity of paper folding in the classroom as an auxiliary resource for the teacher. The folders are quite simple and will improve the students skills on concentration, creativity, and the ability to realize on paper his/her thoughts and ideas. The covered topics range from the construction of the main regular poligons, a spatial solid (tetrahedron), through some arithmetic applications, like division of a segment and square and cubic roots.
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Rastogi, Ashwin. "Brane Constructions and BPS Spectra." Thesis, Harvard University, 2013. http://dissertations.umi.com/gsas.harvard:10836.
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The object of this work is to exploit various constructions of string theory and M-theory to yield new insights into supersymmetric theories in both four and three dimensions. In 4d, we extend work on Seiberg-Witten theory to study and compute BPS spectra of the class of complete N = 2 theories. The approach we take is based on the program of geometric engineering, in which 4d theories are constructed from compactifications of type IIB strings on Calabi-Yau manifolds. In this setup, the natural candidates for BPS states are D3 branes wrapped on supersymmetric 3-cycles in the Calabi-Yau. Our study makes use of the mathematical structure of quivers, whose representation theory encodes the notion of stability of BPS particles. Except for 11 exceptional cases, all complete theories can be constructed by wrapping stacks of two M5 branes on Riemann surfaces. By exploring the connection between quivers and M5 brane theories, we develop a powerful algorithm for computing BPS spectra, and give an in-depth study of its applications. In particular, we compute BPS spectra for all asymptotically free complete theories, as well as an infinite set of conformal \(SU(2)^k\) theories with certain matter content. From here, we go on to apply the insight gained from our 4d study to 3d gauge theories. We consider the analog of the M5 brane construction in the case of 3d N = 2 theories: pairs of M5 branes wrapped on a 3-manifold. Using the ansantz of R-flow, we study 3-manifolds consisting of Riemann surfaces fibered over R. When the construction is non-singular, the resulting IR physics is described by a free abelian Chern-Simons theory. The mathematical data of a tangle captures the data of the gauge theory, and the Reidemeister equivalances on tangles correspond to dualities of physical descriptions. To obtain interacting matter, we allow singularities in the construction. By extending the tangle description to these singular cases, we find a set of generalized Reidemeister moves that capture non-trivial mirror symmetries of 3d gauge theories. These results give a geometric origin to these well-known 3d dualities.Physics
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Marca, Aline. "Construções geométricas como recurso pedagógico no ensino médio." Universidade Tecnológica Federal do Paraná, 2015. http://repositorio.utfpr.edu.br/jspui/handle/1/1692.
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CAPESEste trabalho tem como principal objetivo proporcionar aos alunos do ensino médio um crescimento em seus conhecimentos matemáticos e geométricos, através da utilização das Construções Geométricas como recurso pedagógico nas aulas de Matemática. Primeiramente foi realizada uma pesquisa bibliográfica para compreender como surgiu e evoluiu o campo da Geometria, bem como as Construções Geométricas. Também através da pesquisa bibliográfica foram diagnosticadas as formas como o ensino da Geometria aconteceu em nosso país, além disso foram estudadas algumas teorias relacionadas `a aprendizagem e em particular a Teoria Van Hiele que trata sobre a aprendizagem geométrica. São analisadas duas formas de abordagem das Construções Geométricas em sala de aula: através dos instrumentos manuais de desenho - régua e compasso - e através do instrumento computacional - software geométrico - sendo que optamos por abordar utilizando os instrumentos régua e compasso. É proposta uma oficina com nove atividades de Construções Geométricas que foi aplicada com uma turma da 3ª série do ensino médio, da Escola de Educação Básica Professor Anacleto Damiani, na cidade de Abelardo Luz, estado de Santa Catarina. Cada atividade da oficina conta com os seguintes tópicos: Objetivos da Atividade, Folha da Atividade, Passos da Construção, Justificativa da Atividade e Solução da Atividade. Após a aplicação da oficina os dados foram analisados através da Análise de Conteúdo segundo três categorias: Instrumentos de Desenho, Ângulos e suas Implicações e Paralelas e suas Implicações. Foi possível perceber que a maioria dos alunos conseguiu atingir os objetivos da pesquisa, e tiveram uma melhora em seus conhecimentos matemáticos e geométricos, o que pode ser percebido através da análise de questionários aplicados com os alunos, gravações de áudio, observações feitas durante a oficina e principalmente através da melhora apresentada pelos alunos no desenvolvimento das atividades propostas.
This work aims to provide high school students an development in his mathematical and geometrical knowledge, through the use of Geometric Constructions as a teaching resource in Mathematics classes. First a literature search to understand how it emerged and evolved the field of geometry was carried out and the Geometric Constructions. The ways in which the teaching of geometry happened in our country, also were studied some theories related to learning and in particular the Van Hiele theory which deals with the geometric learning also through the literature search were diagnosed. Two forms of the Geometric Constructions approach are analyzed in class: through the design of hand tools - ruler and compass - and through the computational tool - geometric software - being that we chose to approach using the ruler and compass instruments. It is proposed a workshop with nine Geometric Construction activities which was applied with a group of 3rd year of high school, the Escola de Educac¸ ˜ao B´asica Professor Anacleto Damiani in the city of Abelardo Luz, Santa Catarina. Each workshop activity includes the following topics: Activity Goals, Activity Sheet, Steps of Construction Activity Background and activity of the solution. After application of the workshop, the data were analyzed through content analysis according to three categories: Drawing Instruments, angles and their implications and Parallel and its Implications. Was observed that most of the students managed to achieve the research objectives, and had an development in their mathematical and geometrical knowledge, which can be perceived through the analysis of questionnaires administered to students, audio recordings, observations made during the workshop and especially through the improvement of the students in the development of the proposed activities.
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Arenas, Ruben. "Constructing a Matrix Representation of the Lie Group G2." Scholarship @ Claremont, 2005. https://scholarship.claremont.edu/hmc_theses/166.
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We define the Lie group G2 and show several equivalent ways to view G2. We do the same with its Lie algebra g2. We identify a new basis for g2 using Bryant’s view of g2 and geometric considerations we develop. We then show how to construct a matrix representation of G2 given our particular basis for g2. We examine the geometry of 1 and 2-parameter subgroups of G2. Finally, we suggest an area of further research using the new geometric characterization we developed for g2.
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Hernandez, Gabriel. "Platform design for customizable products as a problem of access in a geometric space." Diss., Georgia Institute of Technology, 2001. http://hdl.handle.net/1853/16760.
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Oliveira, Mateus Rodrigues de. "Explorando lugares geométricos através da resolução de problemas." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/55/55136/tde-26102016-143505/.
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Este trabalho visa resgatar a importância do ensino do desenho geométrico em especial dos Métodos dos Lugares Geométricos, aplicado à resolução de problemas de construção geométrica plana. A abordagem apresentada é tradicional, com o uso da régua e do compasso. Nesse sentido, o trabalho é composto da apresentação(conceito e construção), de vários Lugares Geométricos que podem ser considerados fundamentais para a resolução de problemas elementares de Desenho Geométrico, e a apresentação de construções das cônicas como algo mais elaborado destes lugares geométricos considerados fundamentais. Para a fixação dos conceitos, cada Lugar Geométrico (L.G.) contará com alguns exemplos de aplicação e, ao final dos capítulos, serão apresentados alguns exercícios propostos (para o leitor que se interessar em praticar os conceitos e as construções abordadas). Finalizando será feito um breve comentário das origens do desenho geométrico, bem como seu ensino no Brasil, evidenciando a resolução de problemas como método eficaz para o ensino da geometria.This study reviews the importance of education in special geometric design of the \"Methods of Geometric Places\", applied to the resolution of flat geometric construction problems. The presented approach is traditional, using ruler and compass. In this sense, the work consists of the presentation (concept and construction), several Geometric places that may be considered fundamental to solving elementary geometric design problems, and the presentation of conical constructions as something more elaborate of these loci considered fundamental. For fixing the concepts, each geometric place will feature some application examples and at the end of chapters, some proposed exercises will be presented ( to the reader who is interested iun practing the concepts and addressed buildings). Finalizing will be a brief review of the origins of geometric design and its teaching in Brazil, emphasizing problem solving as an effective method for teaching geometry.