CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / Neste trabalho, estudam-se de maneira sucinta as caracterÃsticas e os principais elementos algÃbricos e geomÃtricos das secÃÃes cÃnicas. Inicialmente, foram abordados os trÃs tipos gerais das secÃÃes cÃnicas, enfocando em princÃpio suas formas regulares para, em dado momento, tambÃm se discutir suas formas degeneradas. Verificou-se que, segundo um sistema cartesiano fixado, à possÃvel estabelecer uma representaÃÃo global das cÃnicas por meio de uma equaÃÃo algÃbrica do segundo grau em duas variÃveis, sendo que qualquer equaÃÃo desta forma,reciprocamente, pode ser identificada, por meio de rotaÃÃo ou translaÃÃo, com a equaÃÃo reduzida de algum tipo particular de cÃnica. Encerrando-se este trabalho, foi proposta uma abordagem inovadora para a lida no ensino mÃdio desse tÃpico de ensino-aprendizagem riquÃssimo em conceitos bÃsicos de Ãlgebra e geometria elementares, tÃo necessÃrios para uma boa formaÃÃo matemÃtica. Foi proposto que no estudo das cÃnicas se use de forma complementar a maneira alternativa de defini-las a partir de sua excentricidade, convergindo para a equaÃÃo geral unificada das cÃnicas em coordenadas polares. Essa forma generalizada e absolutamente simples de se representar as cÃnicas à tida como facilmente manipulÃvel e reflete em si mesma uma beleza singular da MatemÃtica, a Rainha das CiÃncias. Vale ressaltar que todo o enfoque dos conteÃdos aqui discutidos foi apresentado numa linguagem bastante simples e de fÃcil compreensÃo, uma vez que este trabalho se destina preferencialmente a alunos e professores da educaÃÃo bÃsica. / In this work, the features and the main algebraic and geometric elements of conic sections were succinctly studied. lnitially, the three general types of the conic sections were discussed, focusing at first on their regular forms and then, in certain moment, discussing about their degenerate forms. It was found that, according to a fixed Cartesian system, it is possible to establish a global representation of the conics through a two-variable algebraic quadratic equation, in a way that, in any equation of this form, reciprocally, can be identified by means of rotation or translation, with the reduced equation of any particular type of conic. At the end of this work, it was proposed an innovative approach of this rich teaching-leaming topic in basic concepts of elementary algebra and geometry to be applied in high school, as required for good mathematical training. lt was proposed that the study of conic would be used complementing the alternativa way to define them from their eccentricity, converging to a unified general equation of the conics in polar coordinates. This generalized way and absolutely simple to represent the conical is seen as easily manipulated and reflects on itself a singular beauty of mathematics, The Queen of Sciences. lt is worth to emphasize that the focus of the content discussed was presented in a very simple, easy to understand language, once this work is preferably intended for students and teachers of basic education.

In the present PhD work, three sophisticated models based on the "Engineering" modeling approach have been utilized to conveniently describe and thoroughly analyze details of Lightning events at the CN Tower. Both the CN Tower and the Lightning Channel are represented by a number of connected in series Transmission Line sections in order to account for the variations in the shape of the tower and for plasma processes that take place within the Lightning Channel. A sum of two Heidler functions is used to describe the "uncontaminated" Return Stroke current, which is injected at the attachment point between the CN Tower and the Lightning Channel. Reflections and refractions at all points of mismatched impedances are considered until their contribution becomes less than 1% of the originally injected current wave. In the proposed models, the problem with the current discontinuity at the Lightning Channel front, commonly taken care of by introducing a "turn-on" term when computing radiation fields, is uniquely treated by introducing reflected and transmitted components. For the first time, variable speed of propagation of the Return Stroke current front has been considered and its influence upon the predicted current distributions along the whole Lightning Channel path and upon the radiated distant fields analyzed. Furthermore, as another novelty, computation of the electromagnetic field is accomplished in Cartesian Coordinates. This fact permits to relax the requirement on the verticality of the Lightning Channel, normally imposed in Cylindrical Coordinates. Therefore, it becomes possible to study without difficulty the influence of a slanted Lightning Channel upon the surrounding electromagnetic field. Since the proposed sophisticated Five-Section Model has the capability to represent very closely the structure of the CN Tower and to emulate faithfully the shape of, as well as physical processes within the Lightning Channel, it is believed to have the potential of truthfully reproducing observed fields. The developed modeling approach can be easily adapted to study the anticipated radiated fields at tall structures even before construction.

Digital Clay represents a new type of 3-D human-computer interface device that enables tactile and haptic interactions. The Digital Clay kinematics structure is computer controlled and can be commanded to acquire a wide variety of desired shapes (shape display), or be deformed by the user in a manner similar to that of real clay (shape editing). The design of the structure went through various modifications where we finally settled on a crust matrix of spherical joint unit cells. After designing the kinematics structure, the next step is predicting the deformation of the crust matrix based upon a handful of inputs. One possible solution for predicting the shape outcome is considering minimizing the potential energy of the system. In this thesis two methods will be introduced. The first method will be an abstract model of the crust where the energy is calculated from a simplified model with one type of angular springs. The second method is the actual manufacturable crust model with two types of angular springs. From the implementation of these two methods, the output will be center-points of the unit cells. From the center-points, one can also calculate the joint angles within each unit cell.

In the present PhD work, three sophisticated models based on the "Engineering" modeling approach have been utilized to conveniently describe and thoroughly analyze details of Lightning events at the CN Tower. Both the CN Tower and the Lightning Channel are represented by a number of connected in series Transmission Line sections in order to account for the variations in the shape of the tower and for plasma processes that take place within the Lightning Channel. A sum of two Heidler functions is used to describe the "uncontaminated" Return Stroke current, which is injected at the attachment point between the CN Tower and the Lightning Channel. Reflections and refractions at all points of mismatched impedances are considered until their contribution becomes less than 1% of the originally injected current wave. In the proposed models, the problem with the current discontinuity at the Lightning Channel front, commonly taken care of by introducing a "turn-on" term when computing radiation fields, is uniquely treated by introducing reflected and transmitted components. For the first time, variable speed of propagation of the Return Stroke current front has been considered and its influence upon the predicted current distributions along the whole Lightning Channel path and upon the radiated distant fields analyzed. Furthermore, as another novelty, computation of the electromagnetic field is accomplished in Cartesian Coordinates. This fact permits to relax the requirement on the verticality of the Lightning Channel, normally imposed in Cylindrical Coordinates. Therefore, it becomes possible to study without difficulty the influence of a slanted Lightning Channel upon the surrounding electromagnetic field. Since the proposed sophisticated Five-Section Model has the capability to represent very closely the structure of the CN Tower and to emulate faithfully the shape of, as well as physical processes within the Lightning Channel, it is believed to have the potential of truthfully reproducing observed fields. The developed modeling approach can be easily adapted to study the anticipated radiated fields at tall structures even before construction.

My thesis is about functions, like linear functions, quadratic functions, goniometric functions etc. Goal of my work ist to design appropriate tasks with focus on function links. Students can with help of matematic program GeoGebra discover and adopt needed properties of functions. In this work you can find Cartesian coordinates and overview of basic properties of functions too.

Submitted by Emanuel Varela Cardoso (emanuel.varela@ufcg.edu.br) on 2018-06-11T23:25:51Z No. of bitstreams: 1 RUBENS MACIEL MIRANDA PINHEIRO – TESE (PPGEP) 2017.pdf: 3597155 bytes, checksum: c7a82fbab15a4a78e7d7a4dfdee185c5 (MD5) / Made available in DSpace on 2018-06-11T23:25:51Z (GMT). No. of bitstreams: 1 RUBENS MACIEL MIRANDA PINHEIRO – TESE (PPGEP) 2017.pdf: 3597155 bytes, checksum: c7a82fbab15a4a78e7d7a4dfdee185c5 (MD5) Previous issue date: 2017-03-03 / Objetivou-se com este trabalho avaliar o processo difusivo na desidratação osmótica , seguida de secagem em estufa, de melão cortado em formato de cubo com ênfase na modelagem matemática, análises físico-química e sensorial do produto obtido. As cinéticas características do processo de desidratação osmótica e da secagem em estufa são descritas por meio de dois modelos matemáticos que usam soluções analíticas da equação de difusão, em coordenadas cartesianas, com condição de contorno de primeiro e terceiro tipo. Às soluções analíticas foram acoplados algoritmos de otimização propostos neste trabalho, escritos na linguagem FORTRAN, que se baseiam na remoção ótima de pontos experimentais, visando-se à determinação dos parâmetros termofísicos para a descrição das cinéticas de absorção de sacarose e de remoção de água do melão. Foram realizados testes comparativos entre os otimizadores desenvolvidos com os resultados obtidos por outros softwares, os quais também utilizam as condições de contorno de primeiro (Prescribed) e terceiro tipo (Convective). Esta comparação possibilitou analisar a capacidade dos otimizadores propostos de encontrar os valores ótimos nos processos de transferência de massa. Adicionalmente, os cubos de melões desidratados foram submetidos à avaliação físico-química, pelas determinações de atividade de água, acidez, pH, açucares, cinzas, cor e firmeza, bem como, a avaliação sensorial pelos testes de aceitação e intenção de compra. Os dados foram obtidos em experimentos de desidratação osmótica de melão (cortados em pedaços de 10 mm de aresta) usando soluções osmodesidratante com teor de sólidos solúveis totais de 25, 45 e 65 ºBrix . A secagem posterior foi realizada em estufa, nas temperaturas de 50, 60 e 70 ºC. Os resultados indicaram que os otimizadores propostos têm capacidade para obter os parâmetros necessários ao estudo proposto neste trabalho. Constatou-se, através dos valores obtidos para o coeficiente de transferência convectiva, número de Biot e indicadores estatísticos que a condição de contorno mais adequada para descrever o processo que rege a transferência de massa é a condição de terceiro tipo. Verificou-se, através da análise sensorial, que a amostra com maior aceitação pelos provadores foi aquela submetida a desidratação osmótica na concentração de 65 ºBrix e secagem posterior na temperatura de 50 ºC, sendo que as maiores concentrações de sacarose e temperaturas de secagem favoreceram maior remoção da água, todavia as amostras submetidas às maiores temperaturas complementares apresentaram maior escurecimento enzimático. Todas as amostras apresentaram atividades de água dentro dos valores considerados microbiologicamente seguros após a secagem em estufa. / The present study makes an assessment of the diffusive process used in osmotic dehydration of melon sliced into cubes following kiln-drying based on mathematical modeling, considering the physicochemical and sensory properties of the product. The kinetic features of both osmotic dehydration and kiln-drying are described by means of two mathematical models using the analytical solution of the diffusion equation in conjunction with Cartesian coordinates of the first and third kind boundary conditions. In the present work, optimization algorithms have been correlated to analytical solutions. These algorithms were written in FORTRAN based on the optimum removal of experimental points so as to determine the thermophysical parameters with the purpose of describingthe melon solid absorption kinetics and moisture removal.Comparative tests have been conducted between the optimizers implemented for the present study. These were based on the results obtained by other software which also uses contour conditions of the first type (Prescribed) and the third type (Convective). As a result, it waspossible to analyze the efficiency of the proposed optimizers to determine the optimal values along mass transfer processes. In addition, the dehydrated melon cubes were submitted to physicochemical evaluation, considering water activity, acidity, pH, sugars, ash, color and firmness. They were also submitted to sensory evaluati on as determined bythe acceptance tests and purchase intention.The data were obtained via experiments conducted on the osmotic dehydration of melons (cut into pieces of 10 mm) using osmodesidratant solutions with total soluble solid contents of 25, 45 and 65 ºBrix. The drying was done in an oven at temperatures of 50, 60 and 70 ºC. Results demonstrated that the proposed optimizers can provide the necessary parameters for the study proposed in the present work. It has been verified, considering the values obtained for the convective transfer coefficient, Biot number and for the statistical indicators that the most adequate contour condition to describe the process governing mass transfer is that of the third kind condition. The sensorial analysis has also revealed that the sample with the greater acceptance by the testers was the one that underwe nt osmotic dehydration ata 65 ºBrix concentration and subsequent drying at a temperature of 50 ºC, considering as well that higher concentrations of sucrose and drying temperatures favored better water removal. However, the samples submitted to higher complementary temperatures displayed greater enzymatic browning. All samples have exhibited, after oven drying, water activities within values considered microbiologically safer.

Este trabalho apresenta uma proposta didática desenvolvida em uma escola da Rede Adventista de Educação no município de Cachoeirinha, que utilizou a linguagem LOGO em aulas de Matemática. O experimento prático, realizado com estudantes do sétimo ano do Ensino Fundamental e respaldado pelas teorias de Seymour Papert e Gèrard Vergnaud, buscou responder à seguinte questão: Como a utilização do ambiente LOGO auxilia na aprendizagem dos conceitos de Ângulos e Coordenadas Cartesianas, estudados durante o Ensino Fundamental? Outras investigações envolvendo a utilização da linguagem LOGO são mencionadas, bem como suas influências para o trabalho. A partir dos dados analisados qualitativamente, observou-se um crescente interesse pelo estudo dos tópicos de Geometria e um avanço nas elaborações de estratégias de soluções de problemas. Ao final deste trabalho, encontra-se a sequência didática elaborada e aplicada, produto desta dissertação. / This dissertation presents a didactic proposal developed in a school of Adventist Education in the city of Cachoeirinha, which used the LOGO language in Mathematic classes. The practical experiment was conducted with students in the seventh grade of elementary school and supported by the theories of Seymour Papert and Gerard Vergnaud, and tried to answer the following question: How the use of the LOGO environment can help the learning of the concepts of angles and Cartesian Coordinates, which were studied during elementary school? Further investigations involving the use of LOGO language are mentioned, as well as their influences for this paper. From the qualitatively analyzed data, it was noticed a growing interest in the study of topics of Geometry and an improvement in the elaboration of strategies for problem solving. At the final of this work, we can find the didactic sequence, made and applied, product of this dissertation.

Submitted by Alison Vanceto (alison-vanceto@hotmail.com) on 2016-10-26T10:46:14Z No. of bitstreams: 1 DissLCA.pdf: 9029830 bytes, checksum: 30432f39f78daa41661df8053a2b81dd (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-04-24T20:00:35Z (GMT) No. of bitstreams: 1 DissLCA.pdf: 9029830 bytes, checksum: 30432f39f78daa41661df8053a2b81dd (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-04-24T20:00:42Z (GMT) No. of bitstreams: 1 DissLCA.pdf: 9029830 bytes, checksum: 30432f39f78daa41661df8053a2b81dd (MD5) / Made available in DSpace on 2017-04-24T20:09:56Z (GMT). No. of bitstreams: 1 DissLCA.pdf: 9029830 bytes, checksum: 30432f39f78daa41661df8053a2b81dd (MD5) Previous issue date: 2016-09-06 / Não recebi financiamento / This dissertation has main goal analyze the Learning Situation “Cartesian coordinates and transformations in the plane” of Material Support Curriculum of the State of São Paulo, Student notebook, submit a proposal of a didactic sequence to the topic and check their effectiveness. The motivation for choosing this theme came from a study made of the results of SARESP, which present a low performance in the abilities involving this subject. The work begins with a study of issues on Cartesian coordinates of SARESP and Brazil Test, and official documents as PCN and Curriculum Proposal of the State of São Paulo. They are also appreciated opinions of some researchers in the field of education on the teaching of mathematics. We also make a brief analysis of how textbooks address the issue. Then described the planning of the teaching sequence that includes the Student Notebook activities as well as its application in two classes of students in Year 8. In implementing the activities we organize students into pairs, so that they could develop problems more autonomy and less interference from the teacher. After the implementation of the activities, students were evaluated by a test similar to the SARESP with some questions drawn from these tests and others built for myself. Using the results presented by the students in the activities and evidence did an analysis of trial and error. At the end we can conclude that our work is validated, because the students have obtained satisfactory results in the assessment, showing that the learning situation applied in the format presented propose an appropriate outcome compared with SARESP. To validate our research follow in big steps, the methodology proposed by didactic engineering. This educational product is available so that teachers can use it directly in their classes. / Esta dissertação tem como objetivo principal analisar a Situação de Aprendizagem “Coordenadas cartesianas e transformações no plano” do Material de Apoio ao Currículo do Estado de São Paulo, Caderno do Aluno, apresentar proposta de uma sequência didática para o tema e verificar sua eficácia. A motivação para escolha desse tema surgiu de um estudo que fiz dos resultados do SARESP, que apresentam um baixo desempenho nas habilidades envolvendo esse assunto. O trabalho inicia com um estudo de questões sobre Coordenadas Cartesianas do SARESP e Prova Brasil, e de documentos oficiais como PCN e Proposta Curricular do Estado de São Paulo. Também são apreciadas opiniões de alguns pesquisadores da área da educação sobre o ensino da Matemática. Fazemos ainda uma breve análise de como livros didáticos abordam o assunto. Em seguida descrevemos o planejamento da sequência didática que inclui as atividades do Caderno do Aluno assim como sua aplicação em duas classes de alunos de 8º Ano. Na aplicação das atividades organizamos os estudantes em duplas, de modo que puderam desenvolver os problemas com mais autonomia e com menor interferência do professor. Após a aplicação das atividades, os alunos foram avaliados por uma prova similar à do SARESP, com algumas questões extraídas desses testes e outras construídas por mim mesma. Usando os resultados apresentados pelos alunos nas atividades e na prova fiz uma análise dos acertos e erros. Ao final é possível concluir que nosso trabalho está validado, pois os alunos obtiveram resultados satisfatórios na avaliação, mostrando que a Situação de Aprendizagem aplicada no formato que propomos apresentou um resultado adequado comparado com o SARESP. Para validar nossa pesquisa seguimos, em grandes passos, a metodologia proposta pela engenharia didática. Esse produto didático está disponível para que docentes possam utilizá-lo diretamente em suas aulas.

Este trabalho apresenta uma proposta didática desenvolvida em uma escola da Rede Adventista de Educação no município de Cachoeirinha, que utilizou a linguagem LOGO em aulas de Matemática. O experimento prático, realizado com estudantes do sétimo ano do Ensino Fundamental e respaldado pelas teorias de Seymour Papert e Gèrard Vergnaud, buscou responder à seguinte questão: Como a utilização do ambiente LOGO auxilia na aprendizagem dos conceitos de Ângulos e Coordenadas Cartesianas, estudados durante o Ensino Fundamental? Outras investigações envolvendo a utilização da linguagem LOGO são mencionadas, bem como suas influências para o trabalho. A partir dos dados analisados qualitativamente, observou-se um crescente interesse pelo estudo dos tópicos de Geometria e um avanço nas elaborações de estratégias de soluções de problemas. Ao final deste trabalho, encontra-se a sequência didática elaborada e aplicada, produto desta dissertação. / This dissertation presents a didactic proposal developed in a school of Adventist Education in the city of Cachoeirinha, which used the LOGO language in Mathematic classes. The practical experiment was conducted with students in the seventh grade of elementary school and supported by the theories of Seymour Papert and Gerard Vergnaud, and tried to answer the following question: How the use of the LOGO environment can help the learning of the concepts of angles and Cartesian Coordinates, which were studied during elementary school? Further investigations involving the use of LOGO language are mentioned, as well as their influences for this paper. From the qualitatively analyzed data, it was noticed a growing interest in the study of topics of Geometry and an improvement in the elaboration of strategies for problem solving. At the final of this work, we can find the didactic sequence, made and applied, product of this dissertation.

Este trabalho apresenta uma proposta didática desenvolvida em uma escola da Rede Adventista de Educação no município de Cachoeirinha, que utilizou a linguagem LOGO em aulas de Matemática. O experimento prático, realizado com estudantes do sétimo ano do Ensino Fundamental e respaldado pelas teorias de Seymour Papert e Gèrard Vergnaud, buscou responder à seguinte questão: Como a utilização do ambiente LOGO auxilia na aprendizagem dos conceitos de Ângulos e Coordenadas Cartesianas, estudados durante o Ensino Fundamental? Outras investigações envolvendo a utilização da linguagem LOGO são mencionadas, bem como suas influências para o trabalho. A partir dos dados analisados qualitativamente, observou-se um crescente interesse pelo estudo dos tópicos de Geometria e um avanço nas elaborações de estratégias de soluções de problemas. Ao final deste trabalho, encontra-se a sequência didática elaborada e aplicada, produto desta dissertação. / This dissertation presents a didactic proposal developed in a school of Adventist Education in the city of Cachoeirinha, which used the LOGO language in Mathematic classes. The practical experiment was conducted with students in the seventh grade of elementary school and supported by the theories of Seymour Papert and Gerard Vergnaud, and tried to answer the following question: How the use of the LOGO environment can help the learning of the concepts of angles and Cartesian Coordinates, which were studied during elementary school? Further investigations involving the use of LOGO language are mentioned, as well as their influences for this paper. From the qualitatively analyzed data, it was noticed a growing interest in the study of topics of Geometry and an improvement in the elaboration of strategies for problem solving. At the final of this work, we can find the didactic sequence, made and applied, product of this dissertation.