Geometrias não-eucludianas como anomalias: implicações para o ensino de geometria e medidas

This present research the aim to show to the reader the Geometry non-Euclidean while anomaly indicating the pedagogical implications and then propose a sequence of activities, divided into three blocks which show the relationship of Euclidean geometry with non-Euclidean, taking the Euclidean with respect to analysis of the anomaly in non-Euclidean. PPGECNM is tied to the line of research of History, Philosophy and Sociology of Science in the Teaching of Natural Sciences and Mathematics. Treat so on Euclid of Alexandria, his most famous work The Elements and moreover, emphasize the Fifth Postulate of Euclid, particularly the difficulties (which lasted several centuries) that mathematicians have to understand him. Until the eighteenth century, three mathematicians: Lobachevsky (1793 - 1856), Bolyai (1775 - 1856) and Gauss (1777-1855) was convinced that this axiom was correct and that there was another geometry (anomalous) as consistent as the Euclid, but that did not adapt into their parameters. It is attributed to the emergence of these three non-Euclidean geometry. For the course methodology we started with some bibliographical definitions about anomalies, after we ve featured so that our definition are better understood by the readers and then only deal geometries non-Euclidean (Hyperbolic Geometry, Spherical Geometry and Taxicab Geometry) confronting them with the Euclidean to analyze the anomalies existing in non-Euclidean geometries and observe its importance to the teaching. After this characterization follows the empirical part of the proposal which consisted the application of three blocks of activities in search of pedagogical implications of anomaly. The first on parallel lines, the second on study of triangles and the third on the shortest distance between two points. These blocks offer a work with basic elements of geometry from a historical and investigative study of geometries non-Euclidean while anomaly so the concept is understood along with it s properties without necessarily be linked to the image of the geometric elements and thus expanding or adapting to other references. For example, the block applied on the second day of activities that provides extend the result of the sum of the internal angles of any triangle, to realize that is not always 180° (only when Euclid is a reference that this conclusion can be drawn)

Plásticos reforçados a base de tecidos híbridos: efeitos da anisotropia e geometria normativa na caracterização mecânica e da fratura

As most current studies, reinforced plastics have been, in recent years, a viable alternative in building structural elements of medium and large, since the lightness accompanied by high performance possible. The design of hybrid polymer composites (combination of different types of reinforcements) may enable structural applications thereof, facing the most severe service conditions. Within this class of composite materials, reinforced the underlying tissues hybrid high performance are taking space when your application requires high load bearing and high rigidity. The objective of this research work is to study the challenges in designing these fabrics bring these materials as to its mechanical characterization and fracture mechanisms involved. Some parameters associated with the process and / or form of hybridization stand out as influential factors in the final performance of the material such as the presence of anisotropy, so the fabric weave, the process of making the same, normative geometry of the specimens, among others. This sense, four laminates were developed based hybrid reinforcement fabrics involving AS4 carbon fiber, kevlar and glass 49-E as the matrix epoxy vinyl ester resin (DERAKANE 411-350). All laminates were formed each with four layers of reinforcements. Depending on the hybrid fabric, all the influencing factors mentioned above have been studied for laminates. All laminates were manufactured industrially used being the lamination process manual (hand-lay-up). All mechanical characterization and study of the mechanism of fracture (fracture mechanics) was developed for laminates subjected to uniaxial tensile test, bending in three and uniaxial compression. The analysis of fracture mechanisms were held involving the macroscopic, optical microscopy and scanning electron microscopy

Música, filosofia, formação: por uma escuta sensível do mundo

La musique, plus qu`um mot et le texte écrit, a le pouvoir de produire le déplacement du sujet en relation aux contingences du temps e de l´espace. Entendre de la musique est plus que de l´amusement. Comme un artifice cognitif qui ultrapasse l´expérience analytique e métonymique, les formes tonales doublent la réalité, expandent les sens, actionent l´imagination, retotalisent les sentiments, amplient les expériences, permettent la rencontre du sujet avec les éssences des phénomènes qui ne sont pas traductibles par les mots. Nous écoutons de la musique pour restituer notre dignité e conférer à la vie plus de vérité, plus de concrétion (Santiago Kovadloff). La mélodie permet l´expérimentation des états de cohésion, de conéction pleine entre sens et intention, entre commencement et fin, de la finitude de la vie (Schopenhauer). Le phénomène musical provoque l´expréssion de la douleur, de la souffrance et, au même temps, du jubile et de la joie, réliant nature et homme (Nietzsche). Tenant comme base cette compréhension, la dissertation tient dans la musique une importante métaphore pour comprendre la complexité humaine, une fois qu´elle propicie une écoute sensible du monde et mobilise dans le sujet l´expérimentation de divers états de l´être. Nous pouvons dire que la musique est un opérateur de la conaissence parce qu´elle fait affleurer l´écoute intérieure, la rencontre du sujet avec lui même. Cet opérateur cognitif actione les pôles de l´ésprit qui font dialoguer sensibilité, éthique et esthétique, ordre et chaos, silence et bruit, mouvement et pause, repétition et inovation. Par l´expérience musicale, nous habitons des formes hibrides de sensibilité et raison. L´inachèvement, notre principal caractéristique comme humains, a, dans la musique, une image impair, parce que la musique est l´expression du dévir. Pour tisser ces arguments, la dissertation part des études de Schopenhauer et Nietzsche sur la musique, esthétique et métaphysique; Expose des fragments de la biographie de trois grands penseurs contemporains (Werner Heinsenberg, Ilya Prigogine et Edgar Morin) accentuant la présence de la musique en ses vies; et, par fin, présente ce que nous appelons biographies sonores de quatre artistes-musiciens brésiliens (Benedito Juarez et Gil Jardim, de São Paulo, et Ronaldo Ferreira de Lima et, Cleudo Freire, du Rio Grande do Norte)

O ensino de filosofia no ensino médio mediado pela literatura sartriana

On analyse une expérience de l enseignement de philosophie dans l enseignement secondaire par la littérature. La scène d intervention a été l Institut Fédéral d Éducation, Science et Technologie du Rio Grande do Norte (IFRN), dans l année 2008. L étude à caractère qualitatif a adopté un modèle de recherche participant, dans laquelle le chercheur a intervenu dans son propre contexte de classe. On a utilisé l investigation d un ouvrage existentialiste de Jean-Paul Sartre, le roman La Nausée, comme contribution méthodologique pour l enseignement de philosophie. On a adopté le recours de la littérature avec contenu philosophique à partir de la proposition apportée para les Paramètres Curriculaires Nationaux pour l Enseignement Secondaire (PCNEM) : celle qu on ne doit ni avoir la prétention de former de philosophes professionnels ni banaliser la philosophie auprès des élèves. En partant du principe que l existentialisme a été un courant philosophique qui a utilisé la littérature entant qu expression d idées philosophiques, on a envisagé le potentiel pédagogique du voisinage communicant entre la philosophie et la littérature que lie l expérience littéraire avec les textes qui montrent aussi la discussion philosophique. L idée force a été celle de traiter concepts philosophiques a partir de la littérature comme invitation à la réflexion, en analysant l élément ludique dans la littérature comme jeu de la pensée. La pensée considérée comme action ludique arriverait parmi l idéal d en chercher de meilleures manières à comprendre la réalité en étant cet idéal esthétique assumé dans l effort d imprimer sens au chaos des expériences. Les situations pédagogiques en classe comptent fréquemment avec moment de dialogue a propos des problèmes existentiels affrontés par le protagoniste du roman, Antoine Roquentin, considérés comme questions philosophiques et débattues par l investigation dialogique tout suite après la lecture des parties du livre. Dans ce sens, on a cherché à suivre les marches de la méthode socratique dans lequel questionner e questionner à soi même soient les moles propulseurs de la réflexion philosophique. L investigation dialogique a été étendue pendant cinq rencontres de quatre-vingt-dix minutes interprétés par une analyse discursive qui a essayé d établir des rapports entre le discours de l enseignant et des élèves avec le discours de la tradition philosophique. Cette recherche a aussi envisagé à produire une réflexion sur la pratique de l auteur lui-même de l étude. Celui-ci peut-être soit l objectif le plus largement atteint : prendre conscience de l importance de la formation d un enseignant réflexif qui associe dans sa praxis le savoir faire avec la critique honnête de sa propre capacité professionnel

História e filosofia da ciência nos currículos das licenciaturas em física e química da UFRN

Esta disertación es el resultado de un estudio de naturaleza de calidad que tuvo como objetivo analizar la estructura curricular de los cursos de Licenciatura en Física y en Química de Universidad Federal de Rio Grande del Norte en lo que se refiere a la inserción de disciplinas de contenido histórico y filosófico. La metodologia adoptada se constituye en un estudio de caso comparativo, pues procura establecer relaciones entre los dos cursos analizados. En este sentido, fueron consultados, para cada uno de los dos cursos, el Proyecto Político Pedagógico, el programa de La Disiplina y los materiales en ella utilizados. Se realizó también, la observación simple de clases de la disciplina y en seguida, una entrevista semi-estructurada con el profesor responsable por ella. Los resultados muestran que las disciplinas están inseridas en los currículos de los cursos de Física y de Química de maneras diferentes, principalmente en lo que se refiere a los enfoques teóricos-metodológicos asumidos por los profesores en el trabajo con los contenidos y en lo que se dice al respecto del papel desempeñado por la disciplina en la estructuta curricular. Hay por otro lado, puntos de convergencia, notadamente cuanto a la formación y al histórico de los profesores formadores, asi como en la relación a los modelos de formación subyacentes a la estructura curricular de los cursos. Se concluye que el conocimineto mútuo de los diferentes modelos de inserción de disciplinas de contenido histórico y filosófico en las Licenciaturas en Física y en Química de La UFRN podría contribuir para futuras reformulaciones curriculares, en el sentido del establecimiento de opciones claras y concientes acerca del papel a ser desempeñado por esas disciplinas en los cursos

Geometria e simetria nas rendas de bilro: contribuições para matemática escolar

A tese tem como objetivo descrever e analisar características e princípios dos padrões das rendas de bilro de modo a estabelecer relações com a Matemática escolar, principalmente, no que se refere aos tópicos como Geometria, simetria, isometria, área, perímetro, entre outros. Desse modo, elaboramos atividades didáticas, com base na Matemática explorada nos padrões da criação da renda de bilro, visando concretizar um exercício investigatório nas aulas de Matemática, de modo que, sejam estabelecidas relações conceituais entre a prática investigada e os conteúdos da Matemática escolar. Para satisfazer esses objetivos, buscamos apoio metodológico na pesquisa bibliográfica, do tipo documental em catálogos como o da Professora Valdelice Girão (1984) e também o de Dawson (1984). Realizamos também a pesquisa empírica durante as visitas ao Museu do Ceará e ao Centro das Rendeiras na Prainha, em Aquiraz, no Ceará. Para realizar as atividades didáticas, apoiamo-nos em Mendes (2009). Consideramos relevante essa abordagem de ensino porque pressupõe a experiência direta do aprendiz com situações reais vivenciadas, nas quais a abordagem instrucional é centrada no aluno. Desse modo, concluímos que para o ensino de conteúdos como Geometria, simetria, isometria, relação entre perímetro e área, entre outros que são abordados na Educação Básica, os modelos decorrentes da criação renda de bilro e outros modelos já descritos na tradição cearense podem ser usados como artefato cultural na criação de atividades didáticas

Uma proposta de FSS fractal com geometria simplificada

Frequency Selective Surfaces (FSS) are periodic structures in one or two dimensions that act as spatial filters, can be formed by elements of type conductors patches or apertures, functioning as filters band-stop or band-pass respectively. The interest in the study of FSS has grown through the years, because such structures meet specific requirements as low-cost, reduced dimensions and weighs, beyond the possibility to integrate with other microwave circuits. The most varied applications for such structures have been investigated, as for example, radomes, antennas systems for airplanes, electromagnetic filters for reflective antennas, absorbers structures, etc. Several methods have been used for the analysis of FSS, among them, the Wave Method (WCIP). Are various shapes of elements that can be used in FSS, as for example, fractal type, which presents a relative geometric complexity. This work has as main objective to propose a simplification geometric procedure a fractal FSS, from the analysis of influence of details (gaps) of geometry of the same in behavior of the resonance frequency. Complementarily is shown a simple method to adjust the frequency resonance through analysis of a FSS, which uses a square basic cell, in which are inserted two reentrance and dimensions these reentrance are varied, making it possible to adjust the frequency. For this, the structures are analyzed numerically, using WCIP, and later are characterized experimentally comparing the results obtained. For the two cases is evaluated, the influence of electric and magnetic fields, the latter through the electric current density vector. Is realized a bibliographic study about the theme and are presented suggestions for the continuation of this work

A modelagem matemática como alternativa de ensino e aprendizagem da geometria na educação de jovens e adultos

This is work itself insert in the mathematics education field of the youth and adult education to aim to practitioners of the educational action into the mathematics area performing to with this is teaching kind, adopting to as parameter the Mathematics Molding approach. The motive of the research is to draw up a application proposal of the molding mathematics as teaching and learning geometry alternative in the youth and adult education. The research it develops in three class of the third level (series 5th and 6th) of he youth and adults education in the one school municipal from the Natal outskirts. Its have qualitative nature with participating observation approach, once performing to directly in to research environment as a mathematics teacher of those same classes. We are used questionnaires, lesson notes and analyses of the officials documents as an basis of claim instruments. The results indicates that activity used the mathematic moldings were appreciated the savoir-faire of the student in to knowledge construction process, when search develop to significant learning methods, helping to student build has mathematics connections with other knowledge areas and inside mathematics himself, so much that enlarges your understanding and assist has in your participation in the other socials place, over there propitiate to change in student and teacher posture with relation to mathematic classroom dynamics

Geometria e arirmética numa visão multicultural: uma experiência pedagógica

This paper aims to build a notebook of activities that can help the teacher of elementary school mathematics. Topics covered are arithmetic and geometry and the activities proposed here were developed aiming print them a multicultural character. We take as a base line developed by Claudia Zaslavsky multiculturalism and reflected in his books "Games and activities worldwide" and "More games and activities worldwide." We structure our work around four themes: the symbol of the Olympic Games, the pyramids of Egypt, the Russian abacus abacus and Chinese. The first two themes allow you to explore basic concepts of geometry while the latter two themes allow us to explore numerical notation and arithmetic operations

A inferência causal na filosofia moral de Hume.

Starting from the idea that the result of the Humean analysis of causal inferences must be applied coherently to the remaining part of his work, including its moral theory, the present master thesis aims at investigating whether Hume´s moral philosophy is essentially based on feeling, or whether this would not be rather essentially a consequence of our causal inferences in human actions and deliberations. The main idea consists in showing that our moral inferences, to the extent that they are for Hume empirical , depend on our belief in a connexion between something which has been previously observed and something which is not being observed ( but that it is expected to occur or to be observed in the future). Thus, this very belief must base our moral inferences concerning the actions and deliberations of the individuals. Therefore, must e o ipso induce us to associate actions and behaviors, as well as character and moral claims of men to certain moral feelings. Accordingly, the thesis is unfolded in three chapters. In the first chapter Hume´s theory of the perception is reported as essential part of the explanation or the principles that bind ideas in our mind and constitute our inferences. In the second chapter, the Humean analysis of causal inferences is presented and the way they contribute in the formation of our moral inferences is explained. In the third and last chapter, the formation of our moral inferences and the real contribution of the doctrine of freedom and necessity for the examination or our actions are analysed and discussed.

A fundamentação metafísica do Direito na filosofia de Kant

A fundamentação metafísica do direito a que nos propomos a esclarecer na filosofia de Kant assume não somente uma análise de temas jurídicos. Temos uma questão filosófica de fundo a tratar: a justiça é possível? Tal indagação não é o tema do texto, mas o que está pressuposto. A análise kantiana, de certo modo, assume metafisicamente a possibilidade da justiça a partir do conceito de liberdade. Mas, com base na liberdade, demonstra a possibilidade da justiça na ética e no direito. A dissertação é composta por três capítulos. No primeiro capítulo, partindo da reconstrução inicial do conceito de liberdade na Crítica da Razão Pura, descrevemos a construção do conceito cosmológico de liberdade transcendental a partir do terceiro conflito antinômico e de sua solução na Dialética Transcendental. Feito isso, descrevemos o conceito de liberdade no capítulo do Cânon da Razão Pura e discutimos o problema de como compatibilizar liberdade transcendental e liberdade prática. No segundo capítulo, fazemos uma análise da distinção entre a legislação moral e a legislação jurídica das ações humanas partindo da análise da liberdade prática interna (moral) e distinguindo-a da liberdade prática externa (ou jurídica). Nesse contexto, desenvolvemos os pressupostos de uma metafísica do direito, tomando como ponto de partida o conceito de liberdade e o imperativo categórico como princípio da autonomia da vontade, base normativa para a lei universal do direito. No terceiro capítulo, a partir da relação entre ética e direito, reconstruímos o conceito de Direito e esclarecemos o fundamento da legitimidade da coerção a partir do princípio normativo de coexistência das liberdades individuais. Analisamos também os aspectos fundamentais do direito que derivam deste princípio, tal como os conceitos de Contrato Originário, Estado, Lei, Coerção,bem como a proposta kantiana de uma paz universal com base numa legislação internacional. No fim, discutimos o aspecto metafísico presente no fundamento do Direito

Medicina filosófica: as relações entre medicina e filosofia na Grécia antiga e em Kant

This work deals with the relationship between medicine and philosophy, which has existed since Antiquity, and will also be discussed here from Kant s perspective. It presents the historical context formed by reciprocal influences of common notions regarding health/disease, balance/justice, and just measure, which are present in the medical discourse as much as in the philosophical one. It considers that Hippocratic medicine emerges from concerns about dietetics, thus creating the link between philosophy and medicine, which is important for our analysis on Kant s contributions to Hippocratic legacy. Taking into account these considerations, the work distinguishes between two aspects which are associated within the dietetics presented by Kant in his work The conflict of the faculties, studied here in the light of his Doctrine of virtue, particularly the duties to oneself in regard the care of one s body and the teleological conception. In this sense, the work indicates the role of Kantian thinking not only to enrich medical dietetics, by lending to it moral value, but also to enrich philosophy by highlighting its therapeutic effects

Formatividade e interpretação: a filosofia estética de Luigi Pareyson

The concept of formativity, coined by Luigi Pareyson, is a key to the development of countless contemporary aesthetic studies. The aim of this dissertation is to present a deep understanding of the notion of Formativity and Interpretation, as evidenciated by the title Formativity and Interpretation: the aesthetical philosophy of Luigi Pareyson. The work Aesthetics - Theory of Formativity, first published in 1954, is considered a mark in the rebirth of aesthetics. In this dissertation, the concept of Formativity is examined as a component applicable to every human action, and not limited to pre-determined practices, nor referred to the application of preexisting. I ve performed an investigation of the triple concept of doing-inventing-interpreting, which simultaneously grounds Formativity. In the first section, Pareyson s Aesthetical Propaedeutic is presented; in the second, the Theory of Formativity: the aesthetical character of the whole human experience is analysed; and in the third chapter, The Aesthetical of Form and the Metaphysics of Figuration is related to the formativity character of the knowledge. Through this analysis, I ve intended to evidence how human operability can be understood as search and trial, figuration and invention, in the search for success. In this sense, this thesis seeks to present an interpretation of the idea of work-form, speculating the inexorability of invention and interpretation in an attempt to establish a new bottom line for the studies Pareyson s Aesthetics in Brazil

O PAPEL DO CETICISMO NA FILOSOFIA DO JOVEM HEGEL

Ce travail veut montrer que le scepticisme n‟est pas q‟un des principaux défis pour la philosophie moderne jusqu‟a la déflagration da la Reforme Protestante, la redecouverte et la traduction des textes de Sexte Empirique. La reception de ce scepticisme n‟est q‟un des principaux facteurs qui determinent le noveau fondament da la philosophie moderne avec base dans la subjectivité. Dans ce contexte d‟un nouveau fondament de la philosophie sous la base de la subjectivité, Hegel aborde le problème du scepticisme. La pensé developpé par Hegel dans période de Jena (1801-1807), principalement dans l‟écrit de la Differance parmi les philosophies de Fichte e Schelling, et dans les articles du Journal Critic de Philosophie, Relation du scepticisme avec la philosophie et Foi et Savoir, part du dialogue avec la philosophie d‟idealisme allemand, qui est le point plus haut du subjectivisme dans la philosophie developpé à partir du retour du scepticisme. Hegel essaye à travès l‟interpretation et la superation du scepticisme, établir une nouvelle base pour la philosophie. Alors, le scepticisme, dans cette période de la philosophie d‟Hegel, a la function d‟être la negativité propre à la authentique philosophie qui anéante le point de vue des les philosophies de la subjectivité. Cette manière comme Hegel intégre la scepticisme à sa philosophie, a son point plus haut dans la Phénoménologie de l Esprit. La figure du scepticisme parfait présenté dans l‟introduction de la Phénoménologie de l Esprit a la function de faire le passage du point de vue des philosophies de la subjectivité au point de vue espéculatif da la raison

Uma (re)leitura teleológica da filosofia moral em Kant : por uma necessidade de inclusão do homem na natureza

Made from the bases of metaphysics, this dissertation is related do Kant‟s moral philosophy. But the itinerary to reach the main speculation used to develop this current understanding of Kant‟s thoughts, it is nothing but an attempt to make the formal rigor more flexible, which has always been associated to Kantian ethics‟ perspectives. From the awareness of what this formalism could be, while a moral arrangement, it is how we will be able to come upon a teleological Kant. That is the fundamental element to comprehend some of the significant aspects in that ethical system, which necessarily comes through the effort to demonstrate the proximity between reason and sensibility, as well as nature and liberty. In this environment, the journey to achieve the autonomy, as the bedrock of liberty and morality, evokes the support of education in Kantian patterns, which enables a course of improvement of the human being, as an individual e, more significantly, as specie. This evolution progress, which tents to reveal the destiny of the humanity, is evolved in the relationship between necessity and finality, as a condition to make the structure of a project to humanity possible. We should mention that it is a rational, an educational and a moral project to be developed in the course of history. As a consequence, the amount of all these elements permits the development of the man‟s natural disposition as a creature that looks for self knowledge , becoming, afterward, dignified to be qualified as a human being. Finally, this study intent to figure out the necessity of the human being inclusion to nature, which happens throughout the acquirement of the individuals‟ conscience