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1
Jadda, Zoubida. "Constructions de places reelles et geometrie semi-algebrique." Rennes 1, 1986. http://www.theses.fr/1986REN10102.
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Cette these a pour objet de montrer l'existence d'une chaine d'anneaux de valuations reels d'un corps de fonctions r(v) d'une variete algebrique affine irreductible v, qui sont convexes pour un meme ordre sur r(v) et dont le centre, la dimension, le rang et le rang rationnel, verifiant certaines conditions, sont donnes. La technique de demonstration est un pur produit de la geometrie algebrique reelle. Elle utilise le spectre et la triangulation par un homeomorphisme semi-algebrique
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Löfstedt, Tommy. "Fractal Geometry, Graph and Tree Constructions." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-51347.
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In the 18th and 19th centuries the branch of mathematics that would later be known as fractal geometry was developed. It was the ideas of Benoˆıt Mandelbrot that made the area expand so rapidly as it has done recently, and since the publication of his works there have for fractals, and most commonly the estimation of the fractal dimension, been found uses in the most diverse applications. Fractal geometry has been used in information theory, economics, flow dynamics and image analysis, among many different areas. This thesis covers the foundations of fractal geometry, and gives most of the fun- damental definitions and theorems that are needed to understand the area. Concepts such as measure and dimension are explained thoroughly, especially for the Hausdorff di- mension and the Box-counting dimension. An account of the graph-theoretic approach, which is a more general way to describe self-similar sets is given, as well as a tree- construction method that is shown to be equivalent to the graph-theoretic approach.
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Strawn, Nathaniel Kirk. "Geometry and constructions of finite frames." [College Station, Tex. : Texas A&M University, 2007. http://hdl.handle.net/1969.1/ETD-TAMU-1335.
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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
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Master of Education
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O'Neill, Edward Finbar. "Geometry based constructions for curves and surfaces." Thesis, University of Birmingham, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.251132.
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Jacobs, Andrew D. "Nonstandard quantum groups : twisting constructions and noncommutative differential geometry." Thesis, University of St Andrews, 1998. http://hdl.handle.net/10023/13693.
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The general subject of this thesis is quantum groups. The major original results are obtained in the particular areas of twisting constructions and noncommutative differential geometry. Chapters 1 and 2 are intended to explain to the reader what are quantum groups. They are written in the form of a series of linked results and definitions. Chapter 1 reviews the theory of Lie algebras and Lie groups, focusing attention in particular on the classical Lie algebras and groups. Though none of the quoted results are due to the author, such a review, aimed specifically at setting up the paradigm which provides essential guidance in the theory of quantum groups, does not seem to have appeared already. In Chapter 2 the elements of the quantum group theory are recalled. Once again, almost none of the results are due to the author, though in Section 2.10, some results concerning the nonstandard Jordanian group are presented, by way of a worked example, which have not been published. Chapter 3 concerns twisting constructions. We introduce a new class of 2-cocycles defined explicitly on the generators of certain multiparameter standard quantum groups. These allow us, through the process of twisting the familiar standard quantum groups, to generate new as well as previously known examples of non-standard quantum groups. In particular we are able to construct generalisations of both the Cremmer-Gervais deformation of SL(3) and the so called esoteric quantum groups of Fronsdal and Galindo in an explicit and straightforward manner. In Chapter 4 we consider the differential calculus on Hopf algebras as introduced by Woronowicz. We classify all 4-dimensional first order bicovariant calculi on the Jordanian quantum group GL[sub]h,[sub]g(2) and all 3-dimensional first order bicovariant calculi on the Jordanian quantum group SL[sub]h(2). In both cases we assume that the bicovariant bimodules are generated as left modules by the differentials of the quantum group generators. It is found that there are 3 1-parameter families of 4-dimensional bicovariant first order calculi on GL[sub]h,[sub]g(2) and that there is a single, unique, 3-dimensional bicovariant calculus on SL[sub]h(2). This 3-dimensional calculus may be obtained through a classical-like reduction from any one of the three families of 4-dimensional calculi on GL[sub]h,[sub]g(2). Details of the higher order calculi and also the quantum Lie algebras are presented for all calculi. The quantum Lie algebra obtained from the bicovariant calculus on SL[sub]h(2) is shown to be isomorphic to the quantum Lie algebra we obtain as an ad-submodule within the Jordanian universal enveloping algebra U[sub]h(sl[sub]2(C)) and also through a consideration of the decomposition of the tensor product of two copies of the deformed adjoint module. We also obtain the quantum Killing form for this quantum Lie algebra.
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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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Renaudineau, Arthur. "Constructions de surfaces algébriques réelles." Thesis, Paris 6, 2015. http://www.theses.fr/2015PA066249/document.
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Cette thèse est motivée par les problèmes de constructions de surfaces algébriques réelles. Nous nous intéressons plus particulièrement au problème de construire des surfaces algébriques réelles avec un grand nombre d'anses. Ce problème est relié à la conjecture de Viro, dont un contre exemple a été construit pour la première fois par I. Itenberg en 1993. L'outil fondamental de nos constructions est le patchwork de Viro, qui peut également s'interpréter par la géométrie tropicale. En utilisant la géométrie tropicale, et plus particulièrement les modifications tropicales, nous donnons une nouvelle construction d'une famille de courbes algébriques réelles planes avec un nombre asymptotiquement maximal d'ovals pairs. Cette famille avait été construite initialement en 2006 par E. Brugallé. En utilisant la méthode générale du patchwork, nous donnons ensuite une construction d'une sextique réelle avec 45 anses, améliorant ainsi un résultat de 2001 de F. Bihan. Enfin, nous nous penchons sur l'étude des surfaces algébriques réelles dans P1xP1xP1 et nous construisons notamment une famille de surfaces algébriques réelles de tridegré (2k,2l,2) dans P1xP1xP1 avec un premier nombre de Betti asymptotiquement maximal. Cette construction utilise une généralisation de la méthode du patchwork de Viro faite par E. Shustin en 1998In this thesis, we focus on constructions of real algebraic surfaces. The main problem we focus on is to construct real algebraic surfaces with a big number of handles. This problem is related to Viro's conjecture. A couterexample to Viro's conjecture was constructed at the first time by I. Itenberg in 1993. The fundamental tool to our constructions is Viro's patchworking. Viro's patchworking can be reformulated in terms of tropical geometry. Using tropical geometry, and more precisely tropical modifications, we give a new construction of a family of real algebraic plane curves with asymptotically a maximal number of even ovals. This family was first constructed in 2006 by E. Brugallé. Using Viro's patchworking, we construct a real sextic with 45 handles, improving a result of F. Bihan obtained in 2001. At least, we focus on the study of real algebraic surfaces in P1xP1xP1. More precisely, we construct a family of real algebraic surfaces of tridegree (2k,2l,2) in P1xP1xP1 with asymptotically a maximal first Betti number. This construction uses a more general version of Viro's patchworking due to E. Shustin in 1998
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Fehlinger, Luise. "Boundary constructions for CR manifolds and Fefferman spaces." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2014. http://dx.doi.org/10.18452/17020.
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In dieser Dissertation werden Cartan-Ränder von CR-Mannigfaltigkeiten und ihren Fefferman-Räumen besprochen. Der Fefferman-Raum einer strikt pseudo-konvexen CR-Mannigfaltigkeit ist als das Bündel aller reellen Strahlen im kanonischen, komplexen Linienbündel definiert. Eine andere Definition nutzt die Cartan-Geometrie und führt zu einer starken Beziehung zwischen den Cartan-Geometrien der CR-Mannigfaltigkeit und des zugehörigen Fefferman-Raumes. Allerdings wird hier die Existenz einer gewissen Wurzel des antikanonischen, komplexen Linienbündels, dessen Existenz nur lokal gesichert ist, vorausgesetzt. Für Randkonstruktionen benötigen wir jedoch eine globale Konstruktion des Fefferman-Raumes. Dennoch können lokale Resultate zum Fefferman-Raum von einer Konstruktion zur anderen übertragen werden können, da konforme Überlagerungen von beiden vorliegen. Der Cartan-Rand einer Mannigfaltigkeit wird mithilfe der zugehörigen Cartan-Geometrie konstruiert, welche eine globale Basis und damit auch eine Riemannsche Metrik auf dem Cartan-Bündel definiert, welches per Cauchy-Vervollständigung abgeschlossen wird. Division durch die Strukturgruppe ergibt den Cartan-Rand der Mannigfaltigkeit. Der Cartan-Rand ist eine Verallgemeinerung des Cauchy-Randes, da beide im Riemannschen übereinstimmen. Allgemein ist der Cartan-Rand nicht unbedingt Hausdorffsch, was nicht wirklich überrascht, sind doch Rand-Phänomene "irgendwie singulär". Wir stellen fest, dass für CR-Mannigfaltigkeit und ihre Fefferman-Räume die Projektion des Cartan-Randes des Fefferman-Raumes den Cartan-Rand der CR-Mannigfaltigkeit enthält. Schließlich betrachten wir die Heisenberg-Gruppe, eines der grundlegenden Beispiele für CR-Mannigfaltigkeiten. Sie ist flach aber - anders als der homogene Raum - nicht kompakt. Wir finden, dass der Cartan-Rand der Heisenberg-Gruppe ein einzelner Punkt und der Cartan-Rand des zugehörigen Fefferman-Raumes eine nicht-ausgeartete Faser über diesem ist.The aim of this thesis is to discuss the Cartan boundaries of CR manifolds and their Fefferman spaces. The Fefferman space of a strictly pseudo-convex CR manifold is defined as the bundle of all real rays in the canonical complex line bundle. Another way of defining the Fefferman space of a CR manifold uses the tools of Cartan geometry and leads to a strong relationship between the Cartan geometries of a CR manifold and the corresponding Fefferman space. However here the existence of a certain root of the anticanonical complex line bundle is requested which can solely be guarantied locally. As we are interested in boundaries we need a global construction of the Fefferman space. Still we find that local results on the Fefferman space can be transferred from one construction to the other since we have conformal coverings of both. The Cartan boundary of a manifold is constructed with the help of the corresponding Cartan geometry, which defines a global frame and hence a Riemannian metric on the Cartan bundle which can be completed by Cauchy completion. Division by the structure group gives the Cartan boundary of the manifold. The Cartan boundary is a generalization of the Cauchy boundary since both coincide in the Riemannian case. In general the Cartan boundary is not necessarily Hausdorff, which is not really surprising since boundary phenomena are somehow ``singular''''. For CR manifolds and their Fefferman spaces we especially prove that the projection of the Cartan boundary of the Fefferman space contains the Cartan boundary of the CR manifold. We finally discuss the Heisenberg group, one of the basic examples of CR manifolds. It is flat but - contrary to the homogeneous space - not compact. We find that the Cartan boundary of the Heisenberg group is a single point and the Cartan boundary of the corresponding Fefferman space is a non degenerate fibre over that point.
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Pedersen, H. "Geometry and magnetic monopoles : Constructions of Einstein metrics and Einstein-Weyl geometries." Thesis, University of Oxford, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.353118.
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Tabera, Alonso Luis Felipe. "Two tools in algebraic geometry : construction of configurations in tropical geometry and hypercircles for the simplification of parametric curves." Rennes 1, 2007. http://www.theses.fr/2007REN1S045.
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On étudie deux problèmes en géométrie algébrique. Le premier est la comparaison des géométries tropicale et algébrique. En particulier, on compare les configurations d'incidence, la règle de Cramer et les résultants. On présente la notion de construction géométrique et on traduit, sous plusieurs restrictions, des théorèmes classiques d'incidence dans le contexte tropical, comme le théorème de Pappus, de Fano ou de Cayley-Bacharach. La deuxième partie traite des hypercercles. Ces courbes ont été introduites par Andradas, Recio et Sendra et sont employées dans le problème de trouver des reparamétrisations de courbes rationnelles avec des coefficients algébriquement optimaux à partir d'une paramétrisation donnée. On étude la variété de Weil dans le cas paramétrique (hyperquadriques), la géométrie des hypercercles et on donne une méthode pour obtenir des reparamétrisations optimales en utilisant uniquement des reparamétrisations affines de la courbeThis thesis deals with two problems in algebraic geometry. The first one is the comparison of tropical and algebraic geometry. In particular, we study the relationship between incidence configurations, Cramer's rule and the notion of resultant. We introduce the notion of geometric construction and we transfer, under some assumptions, classical incidence theorems to the tropical framework, such as Pappus, Fano of Cayley-Bacharach theorems. The second part relates to hypercircles. These curves where introducedby Andradas, Recio and Sendra, that are used in the problem of computing reparametrizations of rational curves with optimal algebraic coefficients from a given non optimal parametrization. We study the Weil variety in the parametric case (hyperquadric), the geometry of hypercircles and we provide an algorithm to compute an optimal reparametrization using only affine reparametrization of the curve
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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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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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SALGADO, Jacymar de Almeida. "Reflex?es quanto ? import?ncia das Constru??es Geom?tricas no ensino da Geometria Plana." Universidade Federal Rural do Rio de Janeiro, 2013. https://tede.ufrrj.br/jspui/handle/jspui/1954.
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The present work was carried out in three stages, which are the theoretical, research with professionals of education (mathematics teachers from public schools in the metropolitan region of Rio de Janeiro) and performing diagnostic and educational activities at the Municipal School Cruzeiro do Sul, Mesquita, Rio de Janeiro, with students from the 6th grade of elementary school. The work has shown promise in identifying a strong tendency of mathematics teachers in this region promote their practice in teaching Plane Geometry, highly influenced by a process algebrization this science and its teaching. This study aimed to promote reflection on the current teaching of Plane Geometry in elementary school in the metropolitan area of Rio de Janeiro, as well as provide a strong tool to minimize disability in its teaching. It is speculated, with strong evidence, that the abandonment occurred in Brazil, particularly in the region where the study was promoted, the use of Geometric Constructions in teaching plane geometry is, perhaps, the main factor that affects the teaching and learning of this discipline.
O presente trabalho foi realizado em tr?s etapas, que s?o parte te?rica, pesquisa com profissionais de educa??o (professores de matem?tica da rede p?blica da regi?o metropolitana do Rio de Janeiro) e realiza??o de atividades diagn?sticas e pedag?gicas na Escola Municipal Cruzeiro do Sul, Mesquita, Rio de Janeiro, com alunos do 6? ano do ensino fundamental. O trabalho mostrou-se promissor ao identificar uma forte tend?ncia dos professores de Matem?tica dessa regi?o em promoverem sua pr?tica pedag?gica, no ensino da Geometria Plana, altamente influenciados por um processo de algebriza??o desta ci?ncia e do seu ensino. Este trabalho teve como objetivo promover reflex?es sobre o atual ensino da Geometria Plana no ensino fundamental da regi?o metropolitana do Rio de Janeiro, bem como apresentar uma forte ferramenta para minimizar a defici?ncia no ensino da mesma. Especula-se, com forte ind?cio, que o abandono ocorrido no Brasil, em particular da regi?o no qual o estudo foi promovido, do uso das Constru??es Geom?tricas no ensino da Geometria Plana ?, talvez, o principal fator que afeta o ensino e aprendizagem desta disciplina.
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Milici, Pietro. "A quest for exactness : machines, algebra and geometry for tractional constructions of differential equations." Thesis, Paris 1, 2015. http://www.theses.fr/2015PA010675.
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Dans La Géométrie de 1637, Descartes a trouvé un “équilibre” entre constructions géométriques et manipulation symbolique au moyen de l’introduction d’opportunes machines idéales. En particulier, les instruments de Descartes étaient l’algèbre polynomiale (analyse) et une classe de constructions diagrammatiques (synthèse). Cette approche implique une classification des courbes, suivant laquelle les courbes algébriques peuvent être considérées comme “purement géométriques”. Cette limite a été dépassée à l’aide d’une méthode générale par Newton et Leibniz, en introduisant l’infini dans la partie analytique, tandis que la perspective synthétique a graduellement et de plus en plus perdu de son importance par rapport à la perspective analytique (la géométrie devient un moyen de visualisation et cesse d’être un moyen de construction). L’approche fondationnelle de Descartes (analyse par éléments finis et synthèse par constructions diagrammatiques) a été tout de même étendue au-delà des limites des courbes algébriques, bien qu’en deux périodes distinctes. Vers la fin du XVII siècle la partie synthétique a été étendue avec le “mouvement tractionnel” (construction de courbes transcendantes à l’aide de machines idéalisées) et vers le début du XX siècle la partie analytique a été étendue avec l’“algèbre différentielle” (de nos jours, considérée comme une branche de l’algèbre computationnelle). L’objectif de cette thèse est de prouver comment il est possible d’obtenir un nouvel équilibre entre ces extensions (synthétique et analytique) des instruments cartésiens, un équilibre dépassant la limite des courbes algébriques et permettant de traiter une classe de problèmes transcendants. En d’autres termes, le but est de mettre en exergue comment une nouvelle convergence de machines, algèbre et géométrie est possible, permettant une fondation d’une partie de l’analyse infinitésimale sans exigence conceptuelle de l’infini. Ce travail se caractérise par l’attention qui est portée sur le rôle constructif de la géométrie (en tant qu’idéalisation du comportement de machines opportunes) à des fins fondationnelles. Cette approche, suite à la “dé-géométrisation” des mathématiques, se détache fortement du courant principal des discussions sur les mathématiques, notamment du point de vue fondationnel. Toutefois, même si aujourd’hui cette question est tombée dans l’oubli, le problème de définir des critères de constructions appropriés, très débattu à l’âge classique, a eu de profondes influences sur la façon dont les objets et les méthodes mathématiques de l’époque ont été définis. D’après la définition de Bos [2001], ce sont là les “problèmes d’exactitude” de la géométrie. Ces problèmes d’exactitude ont trait aux interprétations philosophiques et psychologiques, c’est pourquoi ils sont normalement considérés comme externes aux mathématiques. Toutefois, même si je ne vais pas apporter de réponse exhaustive, dans mes conclusions je propose une approche algorithmique (très primitive) pour cerner ces problèmes, que j’espère pouvoir approfondir dans des travaux à venir. Depuis la perspective des sciences cognitives, cette approche par rapport à l’analyse infinitésimale ne demande pas l’infini et, grâce aux machines idéalisées, peut être conçue au travers d’opportunes “métaphores fondatrices” (selon la terminologie de Lakoff and Núñez [2000]). Ce caractère concret peut avoir des retombées utiles dans la didactique des mathématiques, grâce à l’usage d’artefacts tant physiques que numériques (cette partie ne sera abordée que de façon marginale)In La Géométrie, Descartes proposed a “balance” between geometric constructions and symbolic manipulation with the introduction of suitable ideal machines. In particular, Cartesian tools were polynomial algebra (analysis) and a class of diagrammatic constructions (synthesis). This setting provided a classification of curves, according to which only the algebraic ones were considered “purely geometrical.” This limit was overcome with a general method by Newton and Leibniz introducing the infinity in the analytical part, whereas the synthetic perspective gradually lost importance with respect to the analytical one—geometry became a mean of visualization, no longer of construction. Descartes’s foundational approach (analysis without infinitary objects and synthesis with diagrammatic constructions) has, however, been extended beyond algebraic limits, albeit in two different periods. In the late 17th century, the synthetic aspect was extended by “tractional motion” (construction of transcendental curves with idealized machines). In the first half of the 20th century, the analytical part was extended by “differential algebra,” now a branch of computer algebra. This thesis seeks to prove that it is possible to obtain a new balance between these synthetic and analytical extensions of Cartesian tools for a class of transcendental problems. In other words, there is a possibility of a new convergence of machines, algebra, and geometry that gives scope for a foundation of (a part of) infinitesimal calculus without the conceptual need of infinity. The peculiarity of this work lies in the attention to the constructive role of geometry as idealization of machines for foundational purposes. This approach, after the “de-geometrization” of mathematics, is far removed from the mainstream discussions of mathematics, especially regarding foundations. However, though forgotten these days, the problem of defining appropriate canons of construction was very important in the early modern era, and had a lot of influence on the definition of mathematical objects and methods. According to the definition of Bos [2001], these are “exactness problems” for geometry. Such problems about exactness involve philosophical and psychological interpretations, which is why they are usually considered external to mathematics. However, even though lacking any final answer, I propose in conclusion a very primitive algorithmic approach to such problems, which I hope to explore further in future research. From a cognitive perspective, this approach to calculus does not require infinity and, thanks to idealized machines, can be set with suitable “grounding metaphors” (according to the terminology of Lakoff and Núñez [2000]). This concreteness can have useful fallouts for math education, thanks to the use of both physical and digital artifacts (this part will be treated only marginally)
Ne La Géométrie del 1637 Descartes ha proposto un “equilibrio” tra costruzioni geometriche e manipolazioni simboliche con l’introduzione di opportune macchine ideali. In particolare gli strumenti di Descartes erano l’algebra polinomiale (analisi) e una classe di costruzioni diagrammatiche (sintesi). Questa impostazione implica una classificazione delle curve, secondo cui solo quelle algebriche possono essere considerate “puramente geometriche”. Questo limite è stato superato con un metodo generale da Newton e Leibniz introducendo l’infinito nella parte analitica, mentre la prospettiva sintetica ha gradualmente sempre più perso importanza rispetto a quella analitica (la geometria diventa un mezzo di visualizzazione e non più di costruzione). L’approccio fondazionale di Descartes (analisi con oggetti finiti e sintesi con costruzioni diagrammatiche) è stato comunque esteso oltre i limiti delle curve algebriche, anche se in due periodi distinti. Nel tardo XVII secolo la parte sintetica è stata estesa con il “movimento trazionale” (costruzione di curve trascendenti con macchine idealizzate), e nella prima metà del XX secolo la parte analitica è stata estesa con la “algebra differenziale” (oggigiorno considerata una branca dell’algebra computazionale). L’obiettivo di questa tesi è di provare come sia possibile ottenere un nuovo equilibrio tra queste estensioni (sintentica e analitica) degli strumenti Cartesiani, un equilibrio che superi il limite delle curve algebriche e permetta di trattare una classe di problemi trascendenti. In altre parole, l’obiettivo è di evidenziare come sia possibile una nuova convergenza di macchine, algebra e geometria che permetta una fondazione di (parte della) analisi infinitesimale senza il bisogno concettuale dell’infinito. La caratteristica di questo lavoro è l’attenzione al ruolo costruttivo della geometria (come idealizzazione del comportamento di opportune macchine) per fini fondazionali. Questo approccio, dopo la “de-geometrizzazione” della matematica, è molto distante dal filone principale delle discussioni sulla matematica, specie dal punto di vista fondazionale. Comunque, anche se oggigiorno caduto in oblio, il problema di definire degli appropriati canoni di costruzioni era molto sentito nel periodo della prima età moderna, ed ha avuto profonde influenze sul modo in cui sono stati definiti gli oggetti e i metodi matematici dell’epoca. Secondo la definizione di Bos [2001], questi sono i “problemi di esattezza” per la geometria. Questi problemi di esattezza riguardano interpretazioni filosofiche e psicologiche, pertanto sono solitamente considerati esterni alla matematica. Comunque, anche se senza una risposta esaustiva, nelle conclusioni propongo un approccio algoritmico (molto primitivo) per inquadrare tali problemi, che spero di approfondire in lavori futuri
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Gironella, Fabio. "On some constructions of contact manifolds." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLX045/document.
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Cette thèse est subdivisée en deux parties.La première partie porte sur l’étude de la topologie de l’espace des contactomorphismes pour quelques exemples explicites de variétés de contact en grandes dimensions. Plus précisément, en utilisant des constructions et résultats dus à Massot, Niederkrüger et Wendl, on construit, en chaque dimension impaire, une infinité d’exemples de contactomorphismes de variétés de contact vrillées fermées qui sont lissement isotopes mais pas contact-isotopes à l’identité. On donne aussi,en toutes dimensions impaires, des exemples de variétés de contact tendues fermées qui admettent un contactomorphisme tel que tous ses itérées sont lissement isotopes mais pas contacto-isotopes à l’identité ; ceci généralise un résultat en dimension 3 dû à Ding et Geiges.Dans la deuxième partie, on construit des exemples de variétés de contact fermées en grandes dimensions avec des propriétés particulières. Ceci nous amène à l’existence de structures tendues virtuellement vrillées en toutes dimensions impaires, et au fait que chaque variété de contact fermée de dimension 3 se plonge dans une variété de contact tendue fermée de dimension 5 avec fibré normal trivial. Pour cela, on utilise des constructions dues à Bourgeois (sur des produits avec des tores) et à Geiges (sur des revêtements ramifiés). On passe de ces constructions à des définitions ;ceci permet de prouver un résultat d’unicité dans le cas des revêtements ramifiés de contact, et d’étudier leurs propriétés globales, en montrant qu’elles ne dépendent d’aucun choix auxiliaire fait dans les procédures. Un deuxième but permis par ces définitions est l’étude des relations entre ces constructions et les notions de livre ouvert porteur, due à Giroux, et de fibré de contact, due à Lerman. Par exemple, on donne une définition de structure de contact de Bourgeois qui est locale,inclue (strictement) les résultats de la construction de Bourgeois et permet de récupérer une classe d’isotopie de livres ouverts porteurs sur les fibres ; ceci suit d’une réinterprétation, inspirée par une idée de Giroux, des livres ouverts porteurs en termes de paires de champs de vecteurs de contactThis thesis is divided in two parts.The first part focuses on the study of the topology of the contactomorphism group of some explicit high dimensional contact manifolds. More precisely, using constructions and results by Massot, Niederkrüger and Wendl, we construct (infinitely many) examples in all dimensions of contactomor-phisms of closed overtwisted contact manifolds that are smoothly isotopic but not contact-isotopicto the identity. We also give examples of tight high dimensional contact manifolds admitting a contactomorphism whose powers are all smoothly isotopic but not contact-isotopic to the identity ;this is a generalization of a result in dimension 3 by Ding and Geiges.In the second part, we construct examples of higher dimensional contact manifolds with specific properties. This leads us to the existence of tight virtually overtwisted closed contact manifolds in all dimensions and to the fact that every closed contact 3-manifold embeds with trivial nor-mal bundle inside a tight closed contact 5-manifold. This uses known construction procedures byBourgeois (on products with tori) and Geiges (on branched covering spaces). We pass from these procedures to definitions ; this allows to prove a uniqueness statement in the case of contact branched coverings, and to study the global properties (such as tightness and fillability) of the results of both constructions without relying on any auxiliary choice in the procedures. A second goal allowed by these definitions is to study relations between these constructions and the notions of supporting open book, due to Giroux, and of contact fiber bundle, due to Lerman. For instance,we give a definition of Bourgeois contact structures on flat contact fiber bundles which is local,(strictly) includes the results of Bourgeois’ construction, and allows to recover an isotopy class of supporting open books on the fibers. This last point relies on a reinterpretation, inspired by anidea by Giroux, of supporting open books in terms of pairs of contact vector fields
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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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Troscheit, Sascha. "Dimension theory of random self-similar and self-affine constructions." Thesis, University of St Andrews, 2017. http://hdl.handle.net/10023/11033.
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This thesis is structured as follows. Chapter 1 introduces fractal sets before recalling basic mathematical concepts from dynamical systems, measure theory, dimension theory and probability theory. In Chapter 2 we give an overview of both deterministic and stochastic sets obtained from iterated function systems. We summarise classical results and set most of the basic notation. This is followed by the introduction of random graph directed systems in Chapter 3, based on the single authored paper [T1] to be published in Journal of Fractal Geometry. We prove that these attractors have equal Hausdorff and upper box-counting dimension irrespective of overlaps. It follows that the same holds for the classical models introduced in Chapter 2. This chapter also contains results about the Assouad dimensions for these random sets. Chapter 4 is based on the single authored paper [T2] and establishes the box-counting dimension for random box-like self-affine sets using some of the results and the notation developed in Chapter 3. We give some examples to illustrate the results. In Chapter 5 we consider the Hausdorff and packing measure of random attractors and show that for reasonable random systems the Hausdorff measure is zero almost surely. We further establish bounds on the gauge functions necessary to obtain positive or finite Hausdorff measure for random homogeneous systems. Chapter 6 is based on a joint article with J. M. Fraser and J.-J. Miao [FMT] to appear in Ergodic Theory and Dynamical Systems. It is chronologically the first and contains results that were extended in the paper on which Chapter 3 is based. However, we will give some simpler, alternative proofs in this section and crucially also find the Assouad dimension of some random self-affine carpets and show that the Assouad dimension is always `maximal' in both measure theoretic and topological meanings.
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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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Submitted by Silvio Marcelino da Silva (silviomarcelinosilva@yahoo.com.br) on 2018-08-04T13:28:58Z
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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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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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Duy, Mai The [Verfasser]. "Some self-similar constructions in two and three dimensions and their neighbor geometry / Mai The Duy." Greifswald : Universitätsbibliothek Greifswald, 2011. http://d-nb.info/1012609359/34.
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Tipler, Carl. "Constructions de métriques extrémales : résolutions de singularités, déformations complexes." Phd thesis, Université de Nantes, 2011. http://tel.archives-ouvertes.fr/tel-00676452.
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Le problème abordé dans cette thèse est celui de l'existence de métriques extrémales. Si (M, J, g) est une variété kahlérienne compacte, une métrique extrémale est une métrique kählérienne dont la norme L2 de la courbure scalaire est minimale pour les métriques représentant la même classe de Kähler. On propose de nouvelles constructions de métriques extrémales utilisant des méthodes perturbatives. Dans un premier temps, on montre que si (M, J, g) est une surface orbifold extrémale qui ne possède que des singularités isolées de type Hirzebruch-Jung, alors une résolution de (M, J) admet une métrique extrémale. On donne des applications de ce résultat sur l'existence de métriques extrémales sur les éclatements de surfaces réglées paraboliques. Dans une seconde partie, on etudie la stabilié des métriques extrémales sous déformations complexes. Ceci est un travail réalisé en collaboration avec Yann Rollin et Santiago Simanca. On donne un critère suffisant pour assurer la stabilité d'une métrique extrémale lors d'une déformation complexe munie d'une action holomorphe d'un groupe compact. On généralise ainsi des résultats de S.Simanca et C.Lebrun. Ceci nous permet également de retrouver un résultat de S.Donaldson, a savoir une métrique Kähler-Einstein sur une déformation de la variété de Mukai et Umemura.
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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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Sousa, Filho João Rodrigues de. "Construções geométricas utilizando o aplicativo Euclidea." reponame:Repositório Institucional da UFC, 2017. http://www.repositorio.ufc.br/handle/riufc/26002.
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SOUSA FILHO, João Rodrigues de. Construções geométricas utilizando o aplicativo Euclidea. 54 f. Dissertação (Mestrado Profissional em Matemática) - Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2017.Submitted by Jessyca Silva (jessyca@mat.ufc.br) on 2017-09-15T04:41:13Z No. of bitstreams: 1 2017_dis_jrsousafilho.pdf: 1638940 bytes, checksum: 90574fddf2903840bfd512da93fb7993 (MD5)
Rejected by Rocilda Sales (rocilda@ufc.br), reason: Boa tarde, Estou devolvendo a Dissertação de JOÃO RODRIGUES DE SOUSA FILHO para que ele realize as correções que seguem listadas abaixo: 1- CAPA (altere o nome do curso que consta na capa PROGRAMA DE PÓS-GRADUAÇÃO EM MATEMÁTICA EM REDE NACIONAL) 2- FOLHA DE APROVAÇÃO (refaça a folha de aprovação colocando todos os seus elementos (nome do autor, título, descrição e nome dos membros da banca) em uma única página. OBS.: Verifique o modelo no GUIA DE NORMALIZAÇÃO DE TRABALHOS ACADÊMICOS DA UFC, disponível em: http://www.biblioteca.ufc.br/wp-content/uploads/2015/08/guia-normalizacao-trabalhos-ufc-2013.pdf 3- AGRADECIMENTOS (adicione ao termo AGRADECImEMTNOS a formatação CENTRALIZADO, NEGRITO e FONTE n 12) 4- EPÍGRAFE (coloque o a frase da epígrafe no seguinte formato: “A geometria é uma ciência de todas as espécies possíveis de espaços. ” (IMMANUEL KANT) 5- LISTA DE SÍMBOLOS (retire os parênteses que existem nas definições da lista de símbolos, iniciando cada definição com letra maiúscula. O termo LISTA DE SÍMBOLOS deve estar em negrito e fonte n 12) 6- NOMENCLATURA UTILIZADA (esta referida parte não pertence às seções da Dissertação, assim, coloque os símbolos e definições presentes nessa parte na LISTA DE SÍMBOLOS) 7- SUMÁRIO (veja o modelo correto de formatação do sumário no GUIA DE NORMALIZAÇÃO DA UFC) 8- CAPÍTULO 3 (as divisões do capítulo 3 que aparecem no sumário estão incorretas: primeiro, devem ser numeradas sucessivamente como: 3,1 ; 3.2 ; 3.2 ......... Acompanhadas do referido título que aparece no capítulo. Ex.: 3.1 Problema 1 – Dada uma circunferência r, construa o seu centro OBS.: ACRESCENTE A NUMERAÇÃO E A FORMATAÇÃO NEGRITO E FONTE N 12, TANTO NO SUMÁRIO COMO NAS SEÇÕES DO CAPÍTULO 3. 9- REFERÊNCIAS ( retire a numeração que acompanha o título das referências, tanto no sumário como na página referida, acrescente a formatação negrito, centralizado e fonte n 12. Atenciosamente, on 2017-09-15T16:36:12Z (GMT)
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Rejected by Rocilda Sales (rocilda@ufc.br), reason: Boa tarde, A Dissertação de JOÃO RODRIGUES DE SOUSA FILHO ainda apresenta a alguns erros a serem corrigidos, os mesmos seguem listados abaixo: 1- SUMÁRIO (o alinhamento do sumário não estar igual ao modelo do GUIA DE NORMALIZAÇÃO DA UFC: o início de cada título e a quebra de linha devem estar alinhados na mesma posição. EX.: 1 INTRODUÇÃO.................00 2 O APLICATIVO.................00 2.1 Comandos da tela inicial..............................00 3 RESOLUÇÃO.................00 2- NUMERAÇÃO DE CAPÍTULOS (revise a numeração dos capítulos pois está diferente da que aparece no sumário: tem dois capítulos com a mesma numeração) 3- REFERÊNCIAS (troque o termo REFERÊNCIAS BIBLIOGRÁFICAS apenas por REFERÊNCIAS) 4- NUMERAÇÃO DE PÁGINAS (retire a numeração indevida de página que aparece na página 5) Atenciosamente, on 2017-09-18T14:13:09Z (GMT)
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The present dissertation intends, in a first moment, to explain the Euclidea application as well as its use in the learning process of plane geometry, including the solution of problems involving this subject. This proposal intends to reach part of the young people who use smartphones, bringing a great opportunity to make Math classes more attractive. In a second moment we will solve sixteen problems of the application and give rigorous proofs of their constructions.
A presente dissertação pretende, em um primeiro momento, explicar o aplicativo Euclidea bem como sua utilização no processo de aprendizagem de geometria plana, incluindo a resolução de problemas envolvendo este conteúdo. Essa proposta pretende atingir parte do universo jovem que usa aparelhos smartphones, trazendo assim uma grande oportunidade de tornar as aulas de Matemática mais atrativas. Em um segundo momento, abordaremos a resolução de dezesseis problemas do aplicativo e daremos demonstrações rigorosas de suas construções.
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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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Will, Etienne. "Constructions tropicales de noeuds algébriques dans IRP3." Phd thesis, Université de Strasbourg, 2012. http://tel.archives-ouvertes.fr/tel-00733721.
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Cette thèse présente la construction de courbes tropicales réelles dans R^3 dont la projectivisation, qui est un entrelacs projectif dans IRP^3, est constituée de 2 composantes, I'une étant isotope à un noeud donné au départ. Dans le cas de certains noeuds toriques, il est possible de modifier cette construction pour que I'entrelacs projectif correspondant ait une seule composante isotope au noeud torique considéré. Pour chacune de ces courbes tropicales réelles, nous faisons appel au théorème récent de G. Mikhalkin, qui affirme l'existence d'une algébrique réelle non singulière dans IRP^3, de même genre et degré que la courbe tropicale réelle considérée, et qui est isotope à l'entrelacs projectif correspondant.
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Lundberg, Emilia. "A bar construction in Morse-Witten homology." Thesis, Uppsala universitet, Algebra och geometri, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-168218.
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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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Alves, Andréia Rodrigues. "O desenho geométrico no 9º ano como estratégia didática no ensino da geometria." Universidade Federal de Alagoas, 2017. http://www.repositorio.ufal.br/handle/riufal/1736.
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This research aims to present part of the history of the Geometric Design history in Brazil, passing through significant historical moments, that played a very important role in the development of nowadays Geometric Design, searching for its importance, as well as what it‟s into the National Curricular Parameters (PCNs).The Van Hiele's Theory is presented through its different levels and how the teacher can use this theory and provide a better use of learning in Geometry. The works shows a previous and posteriori evaluation to diagnose the level of geometric learning of the students before and after the activities proposed in this paper, with reference as evaluation criterion the Theory of Van Hiele. Some activities were applied in a state school in Arapiraca-AL, with a 9th grade class, which involved basic geometric constructions to aid in the learning of Geometry. As results some considerations were taken into account about the activities that were proposed in the classroom and how they could help in the process of teaching and learning Geometry.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Apresentamos, neste trabalho, um pouco da história do ensino do Desenho Geométrico no Brasil, que passando por momentos históricos significativos tiveram um papel muito importante no desenvolvimento do que se tem hoje sobre Desenho Geométrico, procurando sua importância, bem como o que dizem os Parâmetros Curriculares Nacionais. Mostramos, também, a Teoria de Van Hiele, passando por seus diferentes níveis e como o professor pode utilizar essa teoria e proporcionar um melhor aproveitamento de aprendizagem na Geometria. Apresentamos uma avaliação prévia e posteriori para diagnosticar o nível de aprendizagem geométrica dos alunos antes e depois da realização das atividades propostas nesta dissertação, tendo como critério de avaliação a Teoria de Van Hiele. Aplicamos algumas atividades em uma escola Estadual de Arapiraca-AL, com uma turma do 9º ano, que envolviam construções geométricas básicas para auxiliar na aprendizagem da Geometria. Finalizamos com as considerações sobre as atividades que foram propostas em sala de aula e como elas puderam auxiliar no processo de ensino e aprendizagem da Geometria.
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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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Descamps, Benoît. "Optimal shaping of lightweight structures." Doctoral thesis, Universite Libre de Bruxelles, 2013. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209362.
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Designing structures for lightness is an intelligent and responsible way for engineers and architects to conceive structural systems. Lightweight structures are able to bridge wide spans with a least amount of material. However, the quest for lightness remains an utopia without the driving constraints that give sense to contemporary structural design.Previously proposed computational methods for designing lightweight structures focused either on finding an equilibrium shape, or are restricted to fairly small design applications. In this work, we aim to develop a general, robust, and easy-to-use method that can handle many design parameters efficiently. These considerations have led to truss layout optimization, whose goal is to find the best material distribution within a given design domain discretized by a grid of nodal points and connected by tentative bars.
This general approach is well established for topology optimization where structural component sizes and system connectivity are simultaneously optimized. The range of applications covers limit analysis and identification of failure mechanisms in soils and masonries. However, to fully realize the potential of truss layout optimization for the design of lightweight structures, the consideration of geometrical variables is necessary.
The resulting truss geometry and topology optimization problem raises several fundamental and computational challenges. Our strategy to address the problem combines mathematical programming and structural mechanics: the structural properties of the optimal solution are used for devising the novel formulation. To avoid singularities arising in optimal configurations, the present approach disaggregates the equilibrium equations and fully integrates their basic elements within the optimization formulation. The resulting tool incorporates elastic and plastic design, stress and displacements constraints, as well as self-weight and multiple loading.
Besides, the inherent slenderness of lightweight structures requires the study of stability issues. As a remedy, we develop a conceptually simple but efficient method to include local and nodal stability constraints in the formulation. Several numerical examples illustrate the impact of stability considerations on the optimal design.
Finally, the investigation on realistic design problems confirms the practical applicability of the proposed method. It is shown how we can generate a range of optimal designs by varying design settings. In that regard, the computational design method mostly requires the designer a good knowledge of structural design to provide the initial guess.
Doctorat en Sciences de l'ingénieur
info:eu-repo/semantics/nonPublished
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Or, Chi-ming. "Experimentation, construction, conjecturing and explanation in a dynamic geometry environment." Click to view the E-thesis via HKUTO, 2005. http://sunzi.lib.hku.hk/hkuto/record/B35675007.
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Dangskul, Supreedee. "Construction of Seifert surfaces by differential geometry." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/20382.
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A Seifert surface for a knot in ℝ³ is a compact orientable surface whose boundary is the knot. Seifert surfaces are not unique. In 1934 Herbert Seifert provided a construction of such a surface known as the Seifert Algorithm, using the combinatorics of a projection of the knot onto a plane. This thesis presents another construction of a Seifert surface, using differential geometry and a projection of the knot onto a sphere. Given a knot K : S¹⊂ R³, we construct canonical maps F : ΛdiffS² → ℝ=4πZ and G : ℝ³ - K(S¹) → ΛdiffS² where ΛdiffS² is the space of smooth loops in S². The composite FG : ℝ³ - K(S¹) → ℝ=4πZ is a smooth map defined for each u∈2 ℝ³ - K(S¹) by integration of a 2- form over an extension D² → S² of G(u) : S1 → S². The composite FG is a surjection which is a canonical representative of the generator 1∈H¹(ℝ³- K(S¹)) = Z. FG can be defined geometrically using the solid angle. Given u ∈ ℝ³ - K(S¹), choose a Seifert surface Σu for K with u ∉ Σu. It is shown that FG(u) is equal to the signed area of the shadow of Σu on the unit sphere centred at u. With this, FG(u) can be written as a line integral over the knot. By Sard's Theorem, FG has a regular value t ∈ ℝ=4πZ. The behaviour of FG near the knot is investigated in order to show that FG is a locally trivial fibration near the knot, using detailed differential analysis. Our main result is that (FG)-¹(t)⊂ ℝ³ can be closed to a Seifert surface by adding the knot.
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Saeid, Nezhad Nazila [Verfasser], Christoph [Gutachter] Hoeschen, and Martin [Gutachter] Skalej. "Construction and geometric calibration of a new robot-driven scanning geometry / Nazila Saeid Nezhad ; Gutachter: Christoph Hoeschen, Martin Skalej." Magdeburg : Universitätsbibliothek Otto-von-Guericke-Universität, 2020. http://d-nb.info/1226932029/34.
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Barros, Ana Paula Rodrigues Magalhães de 1961. "Contribuições de um micromundo composto por recursos do GeoGebra e da coleção M³ para a aprendizagem do conceito de volume de pirâmide." [s.n.], 2013. http://repositorio.unicamp.br/jspui/handle/REPOSIP/253924.
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Orientadores: Rúbia Barcelos Amaral, Samuel Rocha de OliveiraDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Educação
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Resumo: Atualmente a internet tem se tornado cada vez mais atrativa aos nossos alunos, dentro e fora do ambiente escolar. O número de recursos digitais para o ensino da Matemática vem crescendo. Nesse sentido, ambientes de aprendizagem compostos por software e vídeos, online, podem ser materiais potenciais para o ensino. No entanto, é importante conhecermos tais potencialidades para o processo de aprendizagem dos alunos. Pesquisas apontam dificuldades para o ensino e a aprendizagem do conteúdo de Geometria Espacial e também identificam características fundamentais de software de Geometria Dinâmica para o estudo desse conteúdo. Nessa pesquisa, cuja abordagem foi qualitativa, um ambiente denominado micromundo composto por applets do software GeoGebra e vídeos da coleção M³ foi constituído sob lentes da teoria do Construcionismo e da Teoria Cognitiva de Aprendizagem Multimídia (TCAM) e aplicado em uma escola pública estadual localizada na cidade de Sumaré ¿ SP. Quatro duplas de estudantes do 2º ano do Ensino Médio participaram e foram observadas isoladamente. A investigação aconteceu em torno das contribuições desse micromundo em um estudo de volume de pirâmides. A pergunta que embasou a investigação foi: Como um micromundo composto por recursos do GeoGebra e da coleção M³ pode contribuir no processo de aprendizagem do aluno em um estudo sobre volume de pirâmides? Nessa direção, o objetivo foi analisar as condições criadas pelo micromundo nesse processo mediado por uma professora. Para tanto, observei a interação das duplas no micromundo e investiguei as contribuições das características sustentadas pelo Construcionismo e pela TCAM presentes nele. As dimensões construcionistas corroboraram o engajamento e interesse dos alunos em realizar as tarefas. A organização dos recursos em um ambiente on-line estimulou o interesse dos alunos. Os princípios da TCAM presentes nas multimídias aprimoraram, sobretudo, a ação reflexão dos alunos durante a realização das atividades, O micromundo proporcionou aos alunos a busca de conexões entre as multimídias e, assim, eles tomaram diferentes percursos enquanto buscavam compreender o conteúdo de volume de uma pirâmide. As características de um ambiente exploratório e interativo colaboraram para que os alunos pudessem visualizar e interpretar as figuras geométricas espaciais sob vários ângulos. O micromundo contribuiu para que as ações construcionistas ocorressem a partir da interação dos alunos, fomentando a construção do conhecimento nesse processo. Desta forma, foi possível observar indícios de aprendizagem
Abstract: Nowadays, the internet is becoming more and more attractive to our students, both inside or outside the school environment. Digital resources are growing for mathematical teaching. In this regard, online learning environments composed by software and video can be useful materials. However, it is important to know some potentialities for the students¿ learning. Researches address some difficulties for teaching and learning Euclidean Geometry and they also appoint some fundamental characteristics of one Interactive Geometry software in order to this use. In this qualitative research, an environment called microworld which is composed by applets, a software called GeoGebra and videos of M³ collection was built under the Cognitive Theory of Multimedia Learning (CTML) and it was used in a state public school located in Sumaré-SP. Four couples of second year high students participated in this research and they were observed separately. The investigation occurred around the contributions of this microworld in a study about the volume of a pyramid. The research question was: How a microworld composed by GeoGebra and M³ collection can contribute in the teaching and learning process of the student in a study about the volume of a pyramid? Thus, the objective was to analyze the conditions created by microworld in this process mediated by a teacher. In order to do that, I observed the interaction of the couples in the microworld and I investigated the contributions of the characteristics appointed by the Constructionist theory and TCMA that I could find. The constructionists dimensions confirm the engagement and interest of the students to do the tasks. The resources¿ organization in an online environment stimulated the students. TCAM¿s principles presented by the multimedia improved, above all, the student¿s reflection while they were doing the activities. Microworld provided to the students the opportunity to search for connections between the multimedia and, thereby, they could take different paths while they tried to comprehend the content of the volume of a pyramid. The characteristics of an exploratory and interactive environment collaborate to the visualization and interpretation of the Euclidean geometric illustrations under various lenses. Microworld contributed to the constructionist interactions as they could be made through the students, instigating knowledge construction in this process. Thus, it could be observed some learning signs
Mestrado
Ensino de Ciencias e Matematica
Mestra em Multiunidades em Ensino de Ciências e Matemática
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Yeh, Andy Ju-Chih. "Knowledge construction of 3D geometry in virtual reality microworlds." Queensland University of Technology, 2007. http://eprints.qut.edu.au/16648/.
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The recent development of virtual reality (VR) technology carries powerful potential that can be utilised to facilitate the learning of 3D geometry. Therefore, a new approach for teaching and learning of 3D geometry that utilises a virtual reality learning environment (VRLE) is proposed in this research study. This research study aimed to: (a) design and evaluate a VRLE to facilitate the learning of 3D geometry concepts and processes by upper primary school students, and (b) generate theoretical and design principles that will have application both within and beyond the immediate research study. The research methodology employed was design experiments or design-based research. Informed by this methodology, the research design consisted of iterative cycles of developing/revising a conceptual framework, designing/prototyping a VRLE, enacting/evaluating the VRLE, and reflecting/redesigning the research. An initial conceptual framework was generated through extensive literature review to inform the design and evaluation of a VRLE. Based on the conceptual framework, a prototype VRLE named VRMath was then designed and implemented. The enactment and evaluation of VRMath consisted of two iterations. Iteration 1 (six hours/sessions with two students of Year 5 and 6) was conducted using the prototype VRMath (Yeh & Nason, 2004). Based on the findings from Iteration 1, nine learning activities were developed and research protocols (e.g., observation and interview) were revised for Iteration 2. Iteration 2 involved six primary school students (Year 4-5) for eight weeks (two hours/sessions per week). Findings from Iteration 2 confirmed and identified some usability issues of VRMath system and many new ways of thinking and doing 3D geometry when students interacted with VRMath. These have implications on the design of VRMath and the teaching and learning of 3D geometry within the VRMath environment. Justifications about the conceptual framework and students' learning within VRMath were made after the two iterations of enactment and evaluation. The learning activities and VRMath were also revised and redesigned for the preparation of future iterations. After a full cycle of the design-experiments, this research study concluded with a proto-theory (semiotic framework) for the design of and learning within VRLEs, and visions for using VRLEs in mathematic and technology education.
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Ishikawa, Suguru. "Construction of general symplectic field theory." Kyoto University, 2019. http://hdl.handle.net/2433/242575.
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Schwartz, Alexander. "Constructions of cubical polytopes." [S.l.] : [s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=970075154.
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Or, Chi-ming, and 柯志明. "Experimentation, construction, conjecturing and explanation in a dynamic geometry environment." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2005. http://hub.hku.hk/bib/B35675007.
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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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Paffenholz, Andreas. "Constructions for posets, lattices, and polytopes." [S.l.] : [s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=975678299.
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Gardiner, John. "Dynamic geometry, construction and proof : making meaning in the mathematics classroom." Thesis, Sheffield Hallam University, 2002. http://shura.shu.ac.uk/6479/.
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The overall aim of this study was to investigate mathematical meaning making in relation to the areas of construction and proof through the use of a dynamic geometry environment (Cabri II as available on the TI 92 calculator). The experimental work was carried out with 11-14 year old pupils in four schools in the North of England between 1996 and 1999. The research involved working with whole classes and a range of groups of varying sizes. The research methodologies adopted were drawn from various areas (an approach advocated as suitable for classroom research by Klafid, 1998). The researcher acted as both teacher and participant observer. The study was conducted over several cycles, with previous cycles of analysis and reference to the literature being used to inform subsequent stages. After a pilot phase when recording methods and technical approaches were clarified, there were four cycles of investigation. Data collection was by means of participant observation, with audio recording of dialogue. Screens generated by pupils were recorded in field notes. There was emphasis from the outset of the study to relate the findings to classroom practice. This led to a consideration as an ongoing part of the study, of ideas of classroom and group dynamics and how these could be combined with, and related to, the use of the technology. The study illuminated two key areas; the processes of immediate individual and group meaning making and wider aspects of social dynamics in the mathematics classroom. Socio-cultural analysis of classroom and group discourses identified progression from spontaneous to scientific concepts, illuminating the development of pupils' powers of intuition and sense of conviction. The dynamic geometry environment was used to investigate constructions stable under drag, illuminating the way in which the dynamic aspects afforded by the technology affect pupils' appreciation of the relationship between construction and proof. Various aspects of proof were highlighted and in particular the function of proof as explanation was seen to be an important aspect in the development of pupils' mathematical meaning making. Further analysis illuminated a distinction between the immediate individual sense making of pupils and the way this sense making is brought to social and consensual meaning making. At the wider classroom level the study identified issue of transparency the importance of the social use of argumentation to take forward the 'taken as shared' and the development of socio-mathematical norms and whole-class zones of proximal development. These aspects of individual and group meaning-making and whole class dynamics are advanced as ways of promoting local communities of mathematical practice as advocated by Winbourne and Watson( 1998).
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Tidwell, Paul H. "Design and construction of a double-octahedral variable geometry truss manipulator." Thesis, Virginia Polytechnic Institute and State University, 1989. http://hdl.handle.net/10919/74544.
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This thesis deals with the design and construction of a variable geometry truss (VGT) of the double-octahedral (pyramid-pyramid) geometry. The truss is expected to be the focus of several experimental research projects. In this thesis, a kinematic model is formulated, and the forward and inverse kinematic problems are solved. Issues of motor and instrumentation choices are addressed. Dimensional choices and the important problems of joint design are examined. A computer simulation is performed for force and vibration analysis.
A fully collapsible double-octahedral variable geometry truss with three degrees of freedom was built using NC machining technologies. An improved second generation twenty-one degree-of-freedom truss will be built based on this original test article.Master of Science
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Chaachoua, Abdelhamid. "Fonctions du dessin dans l'enseignement de la géométrie dans l'espace : étude d'un cas : la vie des problèmes de construction et rapports des enseignants à ces problèmes." Université Joseph Fourier (Grenoble), 1997. http://www.theses.fr/1997GRE10050.
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Le travail present a pour objectif de cerner le role et l'usage des figures geometriques dans l'enseignement de la geometrie dans l'espace. Deux directions de recherche sont adoptees. La premiere s'interroge sur les fonctions du dessin papier-crayon dans les problemes de geometrie dans l'espace. La deuxieme etudie le role que peuvent jouer les environnements informatiques quant aux fonctions du dessin modele d'un objet geometrique dans l'espace. Dans les parties a et b, nous etudions l'evolution du statut du dessin dans l'enseignement et nous degageons les fonctions du dessin dans les problemes de geometrie. Ce travail nous conduit a l'etude de la vie des problemes de construction dans l'espace au cours de ce siecle. Nous utilisons essentiellement la theorie anthropologique de chevallard. Dans la partie c, l'analyse des programmes et des manuels, met en evidence l'evolution des problemes de construction dans l'espace au cours de ce siecle sous deux contraintes : dessin et solide. Elle montre aussi que des regles d'usage existent dans l'enseignement sur les constructions d'intersection de plans et de droites et qui varient suivant l'epoque. Nous analysons les attentes implicites des enseignants a propos de ces regles d'usage dont il s'avere qu'ils n'en ont pas conscience. Dans la partie d, nous entreprenons l'etude du role que peuvent jouer les environnements informatiques quant aux fonctions du dessin, modele d'un objet geometrique dans l'espace. Nous examinons comment un environnement informatique peut elargir le champ d'experimentation du dessin modele d'un objet geometrique dans l'espace. En particulier, nous analysons la vie des problemes de construction dans l'environnement informatique. Enfin, nous etudions les changements eventuels que peuvent introduire les environnements informatiques dans les rapports des enseignants aux problemes de construction.
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Kaasalainen, Mikko K. J. "On the construction of invariant tori and integrable Hamiltonians." Thesis, University of Oxford, 1994. http://ora.ox.ac.uk/objects/uuid:399aa26d-4f86-4100-81e2-ba34b6def947.
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The main principle of this thesis is to employ the geometric representation of Hamiltonian dynamics: in a broad sense, we study how to construct, in phase space, geometric structures that are related to a dynamical system. More specifically, we study the problem of constructing phase-space tori that are approximate invariant tori of a given Hamiltonian; also, using the constructed tori, we define an integrable Hamiltonian closely approximating the original one. The methods are generally applicable; as examples, we use gravitational potentials that are of interest in stellar dynamics. First, we construct tori for box and loop orbits in planar, barred potentials, thus demonstrating the applicability of the scheme to potentials that have more than one major orbit family. Also, we show that, in general, the construction scheme needs two types of canonical transformations together: point transformations as well as those expressed by generating functions. To complete the construction scheme, we show how to furnish the tori with consistent coordinate systems, i.e., how to recover the angle variables of a torus labelled by its actions. Next, the developed methods are employed in creating invariant phase-space tori in nonintegrable potentials supporting minor-orbit families. These tori are used to define an integrable Hamiltonian H0, and a modified form of the standard Hamiltonian perturbation theory is then used to demonstrate that a minor-orbit family can be treated as one made up of orbits trapped by a resonance of H0. Finally, we generalize the scheme further by constructing tori in time-reversal asymmetric Hamiltonians (by considering the motion in a rotating frame of reference), and study the transition from locally contained stochasticity to global chaos. Using both near-integrable 'laboratory' Hamiltonians and those for which we construct tori, we investigate the transition in the light of the resonance overlap criterion.
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Sharma, A. "Reconstructing the geometry of a 3-dimensional model using multiple visible surface representations." Thesis, De Montfort University, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.233862.
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Jasutė, Egle. "Interactive visualization model for the constructionist teaching and learning of geometry." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2014. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2014~D_20141209_111855-74602.
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Teaching of mathematics is one of the most complicated and demanding disciplines in a curriculum. The aim of a teacher is not only to communicate knowledge but also to engage the students, motivate them and involve in active learning process by encouraging them to construct their knowledge and competencies. Dynamic geometry systems based on the principle of constructionist learning enable to effectively involve students into the activity by constructing their mathematical knowledge and competencies. However, teachers of mathematics find it difficult to employ the systems since the technical skills of the teachers are inadequate. The visualization of secondary school geometry by using the systems of dynamic geometry systems, i.e. interactive microworlds, can help to solve the problem.
The dissertation has analysed the methods of informatics which are employed to develop learning software, the capacities of dynamic geometry systems and the concepts of constructionist teaching and learning as well as interactive visualization. A model to create interactive microworlds is presented with reference to the implemented technological capacities of dynamic geometry systems and the didactics of constructionist teaching of mathematics. The syntax and semantics of dynamic geometry objects has been formalized through the abstract data types which help to describe scenarios of interactive visualization according to a model.
The model has been implemented through the visualization of 9-10... [to full text]Matematikos mokymas viena iš sudėtingiausių ir daugiausiai dėmesio reikalaujanti disciplina mokykliniame kurse. Mokytojo tikslas ne tik perteikti žinias, bet sudominti, motyvuoti ir įtraukti klasės mokinius į aktyvų mokymosi procesą konstruojant savo žinias ir gebėjimus. Dinaminės geometrijos sistemos grįstos konstrukcionistinio mokymosi principu padeda efektyviai įtraukti mokinius į veiklą konstruojant matematines žinias ir gebėjimus. Tačiau matematikos mokytojui sudėtinga naudoti šias sistemas, nes dažnai mokytojo techniniai gebėjimai yra nepakankami. Šiai problemai išspręsti gali padėti mokyklinės geometrijos vizualizavimas panaudojant dinaminės geometrijos sistemas – sukurti interaktyvūs mikropasauliai. Disertacijoje išnagrinėti informatikos metodai taikomi kuriant skaitmenines priemones mokymuisi, dinaminių geometrijos sistemų galimybės, konstrukcionistinio mokymo(si), interaktyvaus vizualizavimo sąvokos. Pateikiamas modelis interaktyviems mikropasauliams kurti atsižvelgiant į naudojamos dinaminės geometrijos sistemos technologines galimybes ir konstrukcionistinio matematikos mokymo didaktiką. Formalizuota dinaminės geometrijos objektų sintaksė ir semantika abstrakčiaisiais duomenų tipais, kuri padeda aprašyti scenarijus interaktyviam vizualizavimui pagal modelį. Modelis įgyvendintas vizualizuojant 9-10 klasės matematikos kursą. Sukurta apie 400 interaktyvių mikropasaulių. Atliktas įvertinimas parodė, kad modelis gali būti įgyvendintas įvairiose dinaminės geometrijos... [toliau žr. visą tekstą]
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Oikawa, Stephen Oliver. "Design and construction of a four-bay variable-geometry-truss manipulator arm." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1995. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/MQ45463.pdf.
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Tucker, Gayle. "Mathematical modelling in neurophysiology : neuronal geometry in the construction of neuronal models." Thesis, University of Oxford, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.414405.
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Zhang, Pei. "Automatic construction of parts+geometry models for initialising groupwise non-rigid registration." Thesis, University of Manchester, 2012. https://www.research.manchester.ac.uk/portal/en/theses/automatic-construction-of-partsgeometry-models-for-initialising-groupwise-nonrigid-registration(854e154c-72c7-4c17-908c-cbcffa74c562).html.
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Groupwise non-rigid image registration is a powerful tool to automatically establish correspondences across sets of images. Such correspondences are widely used for constructing statistical models of shape and appearance. As existing techniques usually treat registration as an optimisation problem, a good initialisation is required. Although the standard initialisation---affine transformation---generally works well, it is often inadequate when registering images of complex structures. In this thesis we present a sophisticated system that uses the sparse matches of one or more parts+geometry models as the initialisation. We show that both the model/s and its/their matches can be automatically obtained, and that the matches are able to effectively initialise a groupwise non-rigid registration algorithm, leading to accurate dense correspondences. We also show that the dense mesh models constructed during the groupwise registration process can be used to accurately annotate new images. We demonstrate the efficacy of the proposed system on three datasets of increasing difficulty, and report on a detailed quantitative evaluation of its performance.