CAPES / Este 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.

Esta dissertação apresenta, a partir da atividade de modelagem geométrica, uma proposta para o desenvolvimento de hábitos do pensamento matemático no Ensino Fundamental. Iniciamos o trabalho com reflexões que justificam a proposta: trouxemos a opinião de um grupo de professores acerca do trabalho com argumentações matemáticas na escola e as explicações apresentadas por um grupo de alunos do oitavo ano do Ensino Fundamental para justificar algumas propriedades matemáticas. Após estas reflexões, apresentamos os fundamentos teóricos da proposta: o trabalho de Goldenberg a respeito do desenvolvimento dos “hábitos do pensamento”, a serem entendidos como modos de pensar que contribuem para desenvolvimento do pensamento matemático. Avançamos com questões relativas à utilização de tecnologias no ensino e aprendizagem da Matemática e, em particular, tratamos do uso do software GeoGebra. Em continuidade, foi apresentado o site “Geometria em Movimento”, um material didático que trata de modelagem geométrica. Quanto à metodologia usada no desenvolvimento da proposta, nos inspiramos na Engenharia Didática e, com isso, concebemos, implementamos e validamos um experimento didático. Durante a realização do experimento, os alunos mostraram um gradativo desenvolvimento dos hábitos do pensamento. De início, construíram modelos apresentados no site “Geometria em Movimento” e ao final construíram seus próprios modelos e foram autores de projetos nos quais explicitaram, com desenvoltura, seus raciocínios matemáticos. / The aim of this work is to present an approach to the development of mathematical thinking in elementary school through the geometric modeling activity. In this study, we bring the opinion of a group of teachers about the work with mathematical arguments in school and the explanations that eighth grade students gave to justify some fundamental mathematical properties. This proposal is based on the work of Goldenberg about the development of learning habits, which contributes to the development of mathematical thinking. Also, in this study, we discuss technology in mathematics teaching and learning, using GeoGebra software, as well as the website Geometry on Motion, which is a teaching material about geometric modeling. We had look at Didactic Engineering to design, to implement, and to validate this teaching experiment. During this process, the students showed a gradual development of learning habits: initially they built models proposed, on the site Geometry in Motion and afterwards they built their own models and projects, when it was possible to observe their skills in mathematical reasoning.

Atualmente existe, praticamente, um consenso entre os pesquisadores de Ensino de Física, de que a metodologia tradicional não é a mais efetiva por não promover um real engajamento dos estudantes durante o processo de ensino/aprendizagem. Muitos pesquisadores denominam Aprendizagem Ativa (AA), os métodos que requerem tal engajamento e as pesquisas indicam que esta abordagem é mais efetiva. Ou seja, verifica-se um aumento da compreensão dos conceitos básicos de Física. Entretanto, ainda há pouca aplicação de novas metodologias em sala de aula, tanto no ensino médio quanto no superior. No nosso entender, as atividades experimentais (de laboratório ou demonstração) são as mais adequadas para a aplicação de metodologias de AA. Entretanto, particularmente no Brasil, existe pouco material didático experimental disponível que utilize essa metodologia. Este trabalho visa sanar tal necessidade no campo da Ótica Geométrica, oferecendo uma série de roteiros comentados para experimentos e demonstrações interativas. Estes roteiros usam a idéia de investigação orientada onde se pretende que os conhecimentos prévios dos alunos sejam expostos e confrontados com os conceitos científicos. Este material foi aplicado a estudantes do ensino médio (escolas públicas) e do curso de Licenciatura em Ciências Exatas do IFSC. Para a avaliação do mesmo foram realizados testes escritos e monitoramentos em sala de aula. / There is nowadays consensus among the physics education researchers that the traditional teaching methods are not the most effective in promoting real engagement of the students in the teaching/learning process. Several researchers named Active Learning (AL), methods that require this engagement and research evidences indicate that this approach is the most effective, a better comprehension of the basic physics concepts is verified. However, particularly in Brazil, there are few didactic materials available using AL approaches. This works aims to fulfill this need in the field of Geometrical Optics, offering a series of tutorials (guides) for experiments and interactive demonstrations. These tutorials are based in the idea of guided investigation where the students previous beliefs are exposed and confronted with the scientific concepts. This material was applied to high school students (in public schools) and college students (science teacher preparation course of IFSC). In order to evaluate this material, written tests were performed as well as observation of classrooms.

Neste trabalho são discutidos os aspectos inerentes à análise não-linear física (NLF) e geométrica (NLG) das estruturas de contraventamento em concreto armado. O estudo proposto tem como base a análise estrutural de pórticos planos de concreto armado, desenvolvendo-se uma ferramenta rigorosa capaz de analisar essas estruturas de forma elaborada e consistente. Com essa ferramenta serão avaliadas as reduções de inércia que ocorrem em pórticos planos de concreto armado, submetidos a diferentes condições de carregamento e a diferentes taxas de armadura, contribuindo para o estabelecimento de estimativas confiáveis dos efeitos da NLF nessas estruturas. Estes resultados, combinados com os parâmetros de estabilidade &#945 e &#947z - capazes de estimar com bastante precisão os efeitos devidos à NLG - permitem o estabelecimento de métodos simplificados para a análise não-linear física e geométrica das estruturas de contraventamento de edifícios em concreto armado, de grande utilidade para os projetistas. / In this work the inherent aspects to the physical nonlinear analysis (PNL) and geometric nonlinear analysis (GNL) of reinforced concrete bracing structures are argued. The considered study is based in the structural analysis of in reinforced concrete plane frames, developing a rigorous tool capable to analyze these structures of elaborated and consistent form. Using this tool, inertia reductions that occurs in reinforced concrete plane frames, submitted the different loading conditions and the different levels of reinforcement will be evaluated, contributing for the establishment of trustworthy estimates to the effects of PNL in these structures. These results, matched with the stability parameters &#945 e &#947z - capable to estimate with sufficient accuracy the effects of GNL - allow the establishment of simplified methods for physical and geometrical non-linear analysis of reinforced concrete buildings bracing structures, of great utility for the designers.

Esta dissertação apresenta, a partir da atividade de modelagem geométrica, uma proposta para o desenvolvimento de hábitos do pensamento matemático no Ensino Fundamental. Iniciamos o trabalho com reflexões que justificam a proposta: trouxemos a opinião de um grupo de professores acerca do trabalho com argumentações matemáticas na escola e as explicações apresentadas por um grupo de alunos do oitavo ano do Ensino Fundamental para justificar algumas propriedades matemáticas. Após estas reflexões, apresentamos os fundamentos teóricos da proposta: o trabalho de Goldenberg a respeito do desenvolvimento dos “hábitos do pensamento”, a serem entendidos como modos de pensar que contribuem para desenvolvimento do pensamento matemático. Avançamos com questões relativas à utilização de tecnologias no ensino e aprendizagem da Matemática e, em particular, tratamos do uso do software GeoGebra. Em continuidade, foi apresentado o site “Geometria em Movimento”, um material didático que trata de modelagem geométrica. Quanto à metodologia usada no desenvolvimento da proposta, nos inspiramos na Engenharia Didática e, com isso, concebemos, implementamos e validamos um experimento didático. Durante a realização do experimento, os alunos mostraram um gradativo desenvolvimento dos hábitos do pensamento. De início, construíram modelos apresentados no site “Geometria em Movimento” e ao final construíram seus próprios modelos e foram autores de projetos nos quais explicitaram, com desenvoltura, seus raciocínios matemáticos. / The aim of this work is to present an approach to the development of mathematical thinking in elementary school through the geometric modeling activity. In this study, we bring the opinion of a group of teachers about the work with mathematical arguments in school and the explanations that eighth grade students gave to justify some fundamental mathematical properties. This proposal is based on the work of Goldenberg about the development of learning habits, which contributes to the development of mathematical thinking. Also, in this study, we discuss technology in mathematics teaching and learning, using GeoGebra software, as well as the website Geometry on Motion, which is a teaching material about geometric modeling. We had look at Didactic Engineering to design, to implement, and to validate this teaching experiment. During this process, the students showed a gradual development of learning habits: initially they built models proposed, on the site Geometry in Motion and afterwards they built their own models and projects, when it was possible to observe their skills in mathematical reasoning.

This research thesis seeks to investigate a new method to sense the classical Hall effect in Hall devices under the influence of a magnetic field primarily manufactured in complementary metal oxide semiconductor (CMOS) technologies. The thesis poses a research question enabling the investigation into whether or not the geometrical factor in a classical Hall device can be improved by proposing a new method to sense the Hall effect indirectly in standard CMOS technology. State of the art Hall effect devices rely on low ohmic contacts to sense the Hall voltage effect. These contacts along with the geometry can have an adverse effect on the Hall device sensitivity. Furthermore, the Hall voltage in Silicon can be very limited in comparison to high mobility semiconductor materials. It was found that by replacing the highly doped n-type sensing contacts of the Hall device with highly doped p-type contacts, a vertical bipolar junction transistor could be formed. This transistor, normally considered a parasitic element, ultimately leads to a very useful sensing technique in which the Hall current is sensed and amplified by the transistor forward gain, β + 1. The Hall effect appears as a current through the emitter of the transistor. The major contribution of this research resides in a novel method to measure as well as amplify the Hall effect in a square n-well plate manufactured on a standard CMOS technology. The research also bridges the gap found in literature on the subject of direct versus indirect Hall sensing techniques. The outcome of the research also addresses practical implementations of such alternate methods as well as the effect the methods have on fundamental noise limits and differences in noise between the proposed method and traditional methods. The device although not improving the fundamental geometrical factor of the plate which was found to be dominated by the geometry itself, was proven to be functional as well as behaving according to Hall effect theory. Furthermore, the gain that even low forward gain bipolar transistors contribute to the signal, more than compensates for the loss of Hall effect contributed by the geometrical correction factor. The method also contributes less noise in comparison to typical traditional methods of Hall voltage amplification using operational amplifiers. The proposed method thus allows for a very simple measuring technique that is compatible with standard CMOS technology processes. ## Hierdie navorsings tesis is gemik daarop om 'n nuwe meetmetode te ondersoek om die klassieke Hall effek te meet in Hall toestelle onder die invloed van 'n magneetveld wat primér in komplementêre metaaloksied-halfgeleiertegnologie (CMOS) vervaardig word. Die tesis stel 'n navorsingsvraag wat lei tot die ondersoek van die vraag of die geometriese faktor in 'n klassieke Hall toestel verbeter kan word deur om 'n nuwe metode voor te stel om die Hall effek indirek te meet in standaard CMOS tegnologie. Nuutste navorsing oor meetmetodes in Hall effek toestelle, maak nog steeds staat op lae ohmiese kontakte om die Hall spanning effek te meet. Hierdie kontakte saam met die meetkunde van die toestel, het 'n nadelige uitwerking op die Hall toestel se sensitiwiteit. Verder is die Hall spanning in Silikon baie beperk met vergelyking tot hoë mobiliteit halfgeleier materiale. Daar is gevind dat deur die vervanging van die hoogs gedoteerde n-tipe meetkontakte van die Hall toestel met hoogs gedoteerde p-tipe kontakte, kan vertikale bipolêre transistors gevorm word. Hierdie transistor, gewoonlik beskou as 'n parasitiese element, lei tot 'n baie nuttige meet tegniek waarin die Hall stroom gemeet en versterk word deur die transistor se voorwaartse wins, β + 1. Die Hall effek verskyn as 'n stroom deur die emittor van die transistor. Die grootste bydrae van hierdie navorsing lê in 'n nuwe metode om die Hall effek in 'n vierkantige n-dam plaat wat in standaard CMOS tegnologie vervaardig is te meet sowel as om die sein te versterk. Die navorsing oorbrug ook die gaping gevind in literatuur oor die onderwerp van direkte teenoor indirekte Hall meet tegnieke. Die uitkoms van die navorsing spreek ook die praktiese implementering van die meetmetode aan sowel as die effek wat die meetmetode op fundamentele ruisgrense en verskille in ruis tussen die voorgestelde meetmetode en tradisionele meetmetodes het. Die toestel, hoewel nie gelei het tot ‘n verbetering van die fundamentele geometriese faktor van die plaat wat oorheers is deur die meetkunde van die plaat self, is wel funksioneel bewys, asook dat dit optree volgens Hall effek teorie. Verder is daar gevind dat die wins wat selfs lae voorwaartse wins bipolêre transistors bydra tot die sein, meer as die verlies wat die meetkundige faktor veroorsaak op die Hall effek kan herwin. Dié meetmetode dra ook minder ruis by met vergelyking tot tipiese tradisionele meetmetodes soos operasionele versterkers, wat vir Hall spanning versterking gebruik word. Die voorgestelde meetmetode skep dus ‘n baie eenvoudige meettegniek wat versoenbaar is met standaard CMOS tegnologie prosesse. / Thesis (PhD)--University of Pretoria, 2014. / lk2014 / Electrical, Electronic and Computer Engineering / PhD / unrestricted

Discharge of brine wastewater produced from industrial plants into adjacent coastal water bodies is considered as a preferable and common method currently used in many offshore industrial plants. Therefore, it is important to carefully study the behavior of jets and their environmental impacts on water bodies close to the discharge points, especially when the density is different between the jets and the receiving water. The main goal of this study is to improve the understanding of the mixing behaviour of jet trajectories for positively (offset) and negatively (inclined) buoyant jets when density is considered a significant factor, and also to examine the accuracy of some RANS turbulence models and one type of artificial neural network in predicting jet trajectory behaviours. In the first part of this study, experiments using a PIV system for offset buoyant jets were conducted in order to study the effect of the density differences (due to salinity [nonthermal] or temperature [thermal]) between the discharge and the receiving water body on the jet behavior, and the results showed that the nonthermal jets behaved differently as compared to the thermal jets, even though the densimetric Froude numbers (Frd) and density differences (∆ρ) were similar. In addition, a Reynolds-averaged Navier-Stokes (RANS) numerical model was performed using open-source CFD code (OpenFOAM) with a developed solver (modified form of the pisoFoam solver). The realizable k-ε model showed the best prediction among the models. Secondly, an extensive experimental study of an inclined dense jet for two angles (15°and 52°) was conducted to study the effect of these angles on the jets’ geometrical characteristics in the presence of a wide range of densimetric Froude numbers as well as with different discharge densities. More experimental data were obtained for these angles to be added to the previous data for the purpose of calibrating, validating, and comparing the various numerical models for future studies. The results of these experiments are used to evaluate the performance of a type of artificial neural network method called the group method of data handling (GMDH), and the GMDH results are then compared with existing analytical solutions in order to prove the accuracy of the GMDH method in simulating mixing behaviors in water bodies. Thirdly, a comprehensive study on predicting the geometrical characteristics of inclined negatively-buoyant jests using GMDH approach was conducted. The superiority of this model was demonstrated statistically by comparing to several previous analytical models. The results obtained from this study confirm that the GMDH model was highly accurate and was the best among others for predicting the geometrical characteristics of inclined negatively-buoyant jests.

This thesis deals with the analysis of retinal images from digital fundus camera, especially with structure of optic disc (OD). The theoretic part describes main features of the human visual system and princip of eyeground examination. The paper discussed available methods that have been used for localization of optic disc. For further work is selected proposal of the geometrical model of vessel structure by using the method of segmentation of vessels by matched filtering. Original images are tested with semi-automatic method for optic disc localization.

Master's thesis deals with the analysis of the impact of transport vehicle on a building structure. Transport vehicle is represented by an airliner and building structure is represented by a containment of a nuclear power plant. The aim of thesis was to explore the possibility of numerical simulation of an impact of transport vehicle on a building structure utilizing the RFEM program and evaluation of the damage extent.

The aim of this work is description of a device developed at Brno University of Technology, Faculty of Civil Engineering, Institute of Geodesy for the purpose of absolute calibration of geodetic GNSS antennas. Thanks to calibration it is possible to remove systematic error of antenna's phase centre. The device consists of moveable arm and processing unit. The moveable arm is able to set up calibrated antenna to required azimuth and elevation angle. This work introduces the issue of absolute calibration, describes the moveable arm and the process of its assembling. Further, it defines geometrical parameters of moveable arm, describes their determination and their independent verification by geodetic method. Finally, the model of movement of antenna's reference point is described.