Do modelo geométrico ao modelo físico: o tridimensional na educação do arquiteto e urbanista

In the teaching practice of architecture and urbanism in Brazil, educational legislation views modeling laboratories and workshops as an indispensable component of the infrastructure required for the good functioning of any architectural course of study. Although the development of information technology at the international level has created new possibilities for digital production of architectural models, research in this field being underway since the early 1990s, it is only from 2007 onwards that such technologies started to be incorporated into the teaching activity of architecture and urbanism in Brazil, through the pioneering experience at LAPAC/FEC/UNICAMP. It is therefore a recent experiment whose challenges can be highlighted through the following examples: (i) The implementation of digital prototyping laboratories in undergraduate courses of architecture and urbanism is still rare in Brazil; (ii) As a new developing field with few references and application to undergraduate programs, it is hard to define methodological procedures suitable for the pedagogical curricula already implemented or which have already been consolidated over the years; (iii) The new digital ways for producing tridimensional models are marked with specificities which make it difficult to fit them within the existing structures of model laboratories and workshops. Considering the above, the present thesis discusses the tridimensional model as a tool which may contribute to the development of students skills in perceiving, understanding and representing tridimensional space. Analysis is made of the relation between different forms of models and the teaching of architectural project, with emphasis on the design process. Starting from the conceptualization of the word model as it is used in architecture and urbanism, an attempt is made to identify types of tridimensional models used in the process of project conception, both through the traditional, manual way of model construction as well as through the digital ones. There is also an explanation on how new technologies for digital production of models through prototyping are being introduced in undergraduate academic programs of architecture and urbanism in Brazil, as well as a review of recent academic publications in this area. Based on the paradigm of reflective practice in teaching as designed by Schön (2000), the experiment applied in the research was undertaken in the integrated workshop courses of architectural project in the undergraduate program of architecture and urbanism at Universidade Federal do Rio Grande do Norte. Along the experiment, physical modeling, geometric modeling and digital prototyping are used in distinct moments of the design process with the purpose of observing the suitability of each model to the project s phases. The procedures used in the experiments are very close to the Action Research methodology in which the main purpose is the production of theoretical knowledge by improving the practice. The process was repeated during three consecutive semesters and reflection on the results which were achieved in each cycle helped enhancing the next one. As a result, a methodological procedure is proposed which consists of the definition of the Tridimensional Model as the integrating element for the contents studied in a specific academic period or semester. The teaching of Architectural Project as it is developed along the fifth academic period of the Architecture and Urbanism undergraduate program of UFRN is taken as a reference

A dinâmica do pensamento geométrico :aprendendo a enxergar meias verdades e a construir novos significados

This work is a case study to investigate the dynamics of the historians thought as they produce a knowledge about the history of the area measurement systems as forms of historical expressions and representations. We refer to some of the ideas of David Bohm (1989, 1992, 1994, 1996) to support our theoretical understanding about the operation of thought. We chose a period that is recognized by the theorists as the origin of the geometrical thought -embracing the knowledge developed by the Egyptians, Babylonians, Chinese, Hindus, Greeks and Romans- and is referred to as containing a cycle in the development of this knowledge, described as beginning, apogee and decline. We assume this history, as told by the theorists, as a version that we organize and tell with the help of three sets of categories. The first refers to the elements that take part in the measurement practices; the second refers to the historians understanding about the development of the scientific knowledge. This exercise allowed us to extract the theorists main beliefs, that we criticized in the light of the knowledge about Cubação (Dal Pian, 1990). We stress the importance of the methodological approach adopted in this study to the teaching of Geometry and its history

Do modelo geométrico ao modelo físico: o tridimensional na educação do arquiteto e urbanista

In the teaching practice of architecture and urbanism in Brazil, educational legislation views modeling laboratories and workshops as an indispensable component of the infrastructure required for the good functioning of any architectural course of study. Although the development of information technology at the international level has created new possibilities for digital production of architectural models, research in this field being underway since the early 1990s, it is only from 2007 onwards that such technologies started to be incorporated into the teaching activity of architecture and urbanism in Brazil, through the pioneering experience at LAPAC/FEC/UNICAMP. It is therefore a recent experiment whose challenges can be highlighted through the following examples: (i) The implementation of digital prototyping laboratories in undergraduate courses of architecture and urbanism is still rare in Brazil; (ii) As a new developing field with few references and application to undergraduate programs, it is hard to define methodological procedures suitable for the pedagogical curricula already implemented or which have already been consolidated over the years; (iii) The new digital ways for producing tridimensional models are marked with specificities which make it difficult to fit them within the existing structures of model laboratories and workshops. Considering the above, the present thesis discusses the tridimensional model as a tool which may contribute to the development of students skills in perceiving, understanding and representing tridimensional space. Analysis is made of the relation between different forms of models and the teaching of architectural project, with emphasis on the design process. Starting from the conceptualization of the word model as it is used in architecture and urbanism, an attempt is made to identify types of tridimensional models used in the process of project conception, both through the traditional, manual way of model construction as well as through the digital ones. There is also an explanation on how new technologies for digital production of models through prototyping are being introduced in undergraduate academic programs of architecture and urbanism in Brazil, as well as a review of recent academic publications in this area. Based on the paradigm of reflective practice in teaching as designed by Schön (2000), the experiment applied in the research was undertaken in the integrated workshop courses of architectural project in the undergraduate program of architecture and urbanism at Universidade Federal do Rio Grande do Norte. Along the experiment, physical modeling, geometric modeling and digital prototyping are used in distinct moments of the design process with the purpose of observing the suitability of each model to the project s phases. The procedures used in the experiments are very close to the Action Research methodology in which the main purpose is the production of theoretical knowledge by improving the practice. The process was repeated during three consecutive semesters and reflection on the results which were achieved in each cycle helped enhancing the next one. As a result, a methodological procedure is proposed which consists of the definition of the Tridimensional Model as the integrating element for the contents studied in a specific academic period or semester. The teaching of Architectural Project as it is developed along the fifth academic period of the Architecture and Urbanism undergraduate program of UFRN is taken as a reference

Desgaste de polímeros estruturais de engenharia em contato de deslizamento com cilindro metálico

Present work proposed to map and features the wear mechanisms of structural polymers of engineering derived of the sliding contact with a metallic cylindrical spindle submitted to eccentricity due to fluctuations in it is mass and geometric centers. For this it was projected and makes an experimental apparatus from balancing machine where the cylindrical counterbody was supported in two bearings and the polymeric coupon was situated in a holder with freedom of displacement along counterbody. Thus, the experimental tests were standardized using two position of the two bearings (Fixed or Free) and seven different positions along the counterbody, that permit print different conditions to the stiffness from system. Others parameters as applied normal load, sliding velocity and distance were fixed. In this investigation it was used as coupon two structural polymers of wide quotidian use, PTFE (polytetrafluroethylene) and PEEK (poly-ether-ether-ketone) and the AISI 4140 alloy steel as counterbody. Polymeric materials were characterized by thermal analysis (thermogravimetric, differential scanning calorimetry and dynamic-mechanical), hardness and rays-X diffractometry. While the metallic material was submitted at hardness, mechanical resistance tests and metallographic analysis. During the tribological tests were recorded the heating response with thermometers, yonder overall velocity vibration (VGV) and the acceleration using accelerometers. After tests the wear surface of the coupons were analyzed using a Scanning Electronic Microscopy (SEM) to morphological analysis and spectroscopy EDS to microanalysis. Moreover the roughness of the counterbody was characterized before and after the tribological tests. It was observed that the tribological response of the polymers were different in function of their distinct molecular structure. It were identified the predominant wear mechanisms in each polymer. The VGV of the PTFE was smaller than PEEK, in the condition of minimum stiffness, in function of the higher loss coefficient of that polymer. Wear rate of the PTFE was more of a magnitude order higher than PEEK. With the results was possible developed a correlation between the wear rate and parameter (E/ρ)1/2 (Young modulus, E, density, ρ), proportional at longitudinal elastic wave velocity in the material.

Otimização de forma aplicando B-splines sob critério integral de tensões

This work proposes a computational methodology to solve problems of optimization in structural design. The application develops, implements and integrates methods for structural analysis, geometric modeling, design sensitivity analysis and optimization. So, the optimum design problem is particularized for plane stress case, with the objective to minimize the structural mass subject to a stress criterion. Notice that, these constraints must be evaluated at a series of discrete points, whose distribution should be dense enough in order to minimize the chance of any significant constraint violation between specified points. Therefore, the local stress constraints are transformed into a global stress measure reducing the computational cost in deriving the optimal shape design. The problem is approximated by Finite Element Method using Lagrangian triangular elements with six nodes, and use a automatic mesh generation with a mesh quality criterion of geometric element. The geometric modeling, i.e., the contour is defined by parametric curves of type B-splines, these curves hold suitable characteristics to implement the Shape Optimization Method, that uses the key points like design variables to determine the solution of minimum problem. A reliable tool for design sensitivity analysis is a prerequisite for performing interactive structural design, synthesis and optimization. General expressions for design sensitivity analysis are derived with respect to key points of B-splines. The method of design sensitivity analysis used is the adjoin approach and the analytical method. The formulation of the optimization problem applies the Augmented Lagrangian Method, which convert an optimization problem constrained problem in an unconstrained. The solution of the Augmented Lagrangian function is achieved by determining the analysis of sensitivity. Therefore, the optimization problem reduces to the solution of a sequence of problems with lateral limits constraints, which is solved by the Memoryless Quasi-Newton Method It is demonstrated by several examples that this new approach of analytical design sensitivity analysis of integrated shape design optimization with a global stress criterion purpose is computationally efficient

Números complexos: uma proposta de mudança metodológica para uma aprendizagem significativa no ensino médio

This work presents a proposal of a methodological change to the teaching and learning of the complex numbers in the Secondary education. It is based on the inquiries and difficulties of students detected in the classrooms about the teaching of complex numbers and a questioning of the context of the mathematics teaching - that is the reason of the inquiry of this dissertation. In the searching for an efficient learning and placing the work as a research, it is presented a historical reflection of the evolution of the concept of complex numbers pointing out their more relevant focuses, such as: symbolic, numeric, geometrical and algebraic ones. Then, it shows the description of the ways of the research based on the methodology of the didactic engineering. This one is developed from the utilization of its four stages, where in the preliminary analysis stage, two data surveys are presented: the first one is concerning with the way of presenting the contents of the complex numbers in math textbooks, and the second one is concerning to the interview carried out with High school teachers who work with complex numbers in the practice of their professions. At first, in the analysis stage, it is presented the prepared and organized material to be used in the following stage. In the experimentation one, it is presented the carrying out process that was made with the second year High school students in the Centro Federal de Educação tecnológica do Rio Grande do Norte CEFET-RN. At the end, it presents, in the subsequent and validation stages, the revelation of the obtained results from the observations made in classrooms in the carrying out of the didactic sequence, the students talking and the data collection

Uma investigação histórica sobre os logaritmos com sugestões didáticas para a sala de aula

This study was conducted from a preliminary research to identify the conceptual and didactic approach to the logarithms given in the main textbooks adopted by the Mathematics teachers in state schools in the School of Natal, in Rio Grande do Norte. I carried out an historical investigation of the logarithms in order to reorient the math teacher to improve its educational approach this subject in the classroom. Based on the research approach I adopted a model of the log based on three concepts: the arithmetic, the geometric and algebraic-functional. The main objective of this work is to redirect the teacher for a broad and significant understanding of the content in order to overcome their difficulties in the classroom and thus realize an education that can reach the students learning. The investigative study indicated the possibility of addressing the logarithms in the classroom so transversalizante and interdisciplinary. In this regard, I point to some practical applications of this matter are fundamental in the study of natural phenomena as earthquakes, population growth, among others. These practical applications are connected, approximately, Basic Problematization Units (BPUs) to be used in the classroom. In closing, I offer some activities that helped teachers to understand and clarify the meaningful study of this topic in their teaching practice

Elaboração de uma sequência didática sobre os conceitos geométricos preliminares ao estudo da trigonometria

This study is qualitative, including literature search and preparation of teaching materials. Your goal is to report the study of geometric problems of character presented in the application of trigonometry and work on the preparation of detailed activities that help in overcoming these difficulties. For this, we read some papers on teaching and learning of trigonometry in order to identify the difficulties encountered during their journey. Then separate the geometric difficulties of character and prepare a list of geometric content and procedures associated with them. Thus, we can organize a notebook with activities that would address most of these concepts. Finally we present the specification of activities called Activity on introductory concepts to the study of trigonometry

Percolação convencional, percolação correlacionada e percolação por invasão num suporte multifractal

In this work we have studied the problem of percolation in a multifractal geometric support, in its different versions, and we have analysed the conection between this problem and the standard percolation and also the connection with the critical phenomena formalism. The projection of the multifractal structure into the subjacent regular lattice allows to map the problem of random percolation in the multifractal lattice into the problem of correlated percolation in the regular lattice. Also we have investigated the critical behavior of the invasion percolation model in this type of environment. We have discussed get the finite size effects

Condições de energia de hawking e ellis e a equação de raychaudhuri

In the Einstein s theory of General Relativity the field equations relate the geometry of space-time with the content of matter and energy, sources of the gravitational field. This content is described by a second order tensor, known as energy-momentum tensor. On the other hand, the energy-momentum tensors that have physical meaning are not specified by this theory. In the 700s, Hawking and Ellis set a couple of conditions, considered feasible from a physical point of view, in order to limit the arbitrariness of these tensors. These conditions, which became known as Hawking-Ellis energy conditions, play important roles in the gravitation scenario. They are widely used as powerful tools for analysis; from the demonstration of important theorems concerning to the behavior of gravitational fields and geometries associated, the gravity quantum behavior, to the analysis of cosmological models. In this dissertation we present a rigorous deduction of the several energy conditions currently in vogue in the scientific literature, such as: the Null Energy Condition (NEC), Weak Energy Condition (WEC), the Strong Energy Condition (SEC), the Dominant Energy Condition (DEC) and Null Dominant Energy Condition (NDEC). Bearing in mind the most trivial applications in Cosmology and Gravitation, the deductions were initially made for an energy-momentum tensor of a generalized perfect fluid and then extended to scalar fields with minimal and non-minimal coupling to the gravitational field. We also present a study about the possible violations of some of these energy conditions. Aiming the study of the single nature of some exact solutions of Einstein s General Relativity, in 1955 the Indian physicist Raychaudhuri derived an equation that is today considered fundamental to the study of the gravitational attraction of matter, which became known as the Raychaudhuri equation. This famous equation is fundamental for to understanding of gravitational attraction in Astrophysics and Cosmology and for the comprehension of the singularity theorems, such as, the Hawking and Penrose theorem about the singularity of the gravitational collapse. In this dissertation we derive the Raychaudhuri equation, the Frobenius theorem and the Focusing theorem for congruences time-like and null congruences of a pseudo-riemannian manifold. We discuss the geometric and physical meaning of this equation, its connections with the energy conditions, and some of its several aplications.

Caracterização multi-escalar de bandas de deformação nas tectonossequências paleozóica, pré- e sin-rifte da Bacia do Araripe, Nordeste do Brasil

Deformation bands are structures, developed in porous sandstones, that has small offsets and they are not shown on seismic section. The deformation bands of the pre and synrift sandstones of Araripe Basin were studied in outcrop, macroscopic and microscopic scales. The hierarchical, cinematic and spatial-geometric characteristics, and also the deformational mechanisms acting during its structural evolution were established too. In general, the mesoscopic scale observation allowed to discriminate deformation bands as singles or clusters in three main sets: NNE-SSW dextral; NE-SW normal (sometimes with strike-slip offset); and E-W sinistral; further a bed-parallel deformation bands as a local set. The microscopic characterization allowed to recognize the shearing and cataclastic character of such structures. Through the multi-scale study done in this work we verified that deformation bands analyzed were preferentially developed when sandstones under advanced stage of lithification. We also infer that the geometrical-spatial complexity of these bands, together with the presence of cataclastic matrix, can difficult the migration of fluids in reservoir rocks, resulting on their compartmentalization. Therefore, the study of deformation bands can aid researches about the structural evolution of sedimentary basin, as well as collaborate to understand the hydrodynamic behavior of reservoirs compartmented by these deformational structures

A produção do espaço rural no município de Ceará-Mirim

This research intended to study the process of production of the rural space in the municipal district of Little Ceará-Mirim, looking for to identify the transformations in him happened, above all in the last thirty years. Since the beginning of your historical formation, the area in study had as element modelador and transformer of the physiognomy of your territory the culture canavieira that printed in your economy and in your society marks of a powerful nobility. The sugar-cane is covered of a cyclical character facing acme phases and decadence, as the one that it happens at the present time. Simultaneously, the sphere rural cearimirinense is going by changes by the implantation of modern companies gone back to the papaya production destined to the internal market and more precisely to the external market. Of this context they also consist the supplying farms of this same product. In the group of the establishments in the rural landscape here analyzed, they still interfere the mixed farms, the ones that practice agriculture, the ones that were devoted to the livestock, as well as the farms and the ranches. Another innovation is the caprinocultura developed in modern molds, using the system voisin of pasture rodízio being constituted in a pioneering experience in Brazil. Of that reality they announce other elements, to example of the establishments, being configured as new forms of use of the soil. In the perspective of turning them productive, the challenge resides of overcoming the difficulties in them existent. The reality of the space in screen is replete of lacks in all the instances. It is inferred that the municipal district possesses an enormous potential, however the performance of the administrative components is seen as deficient. He becomes urgent that the municipal public power promotes changes, mainly in what it respects to the social area, with a better attendance to the rural communities, for them to act positively in the process of the development of this municipal district

Densificação e microestrutura de um compósito Mo-Cu preparado a partir de um pó de heptamolibidato de amônia e cobre

The Cu-Mo system is a composite used in the electrical industry as material for electrical contact and resistance welding electrode as well as the heat sink and microwave absorber in microelectronic devices. The use of this material in such applications is due to the excellent properties of thermal and electrical conductivity and the possibility of adjustment of its coefficient of thermal expansion to meet those of materials used as substrates in the semiconductor micoreletrônic industry. Powder metallurgy through the processes of milling, pressing shaping and sintering is a viable technique for consolidation of such material. However, the mutual insolubility of both phases and the low wettability of liquid Cu on Mo impede its densification. However, the mutual insolubility of both phases and the low wettability of liquid Cu on Mo impede its densification. The mechanical alloying is a technique for preparation of powders used to produce nanocrystalline composite powder with amorphous phase or extended solid solution, which increases the sinterability immiscible systems such as the Mo-Cu. This paper investigates the influence of ammonium heptamolybdate (HMA) and the mechanical alloying in the preparation of a composite powder HMA-20% Cu and the effect of this preparation on densification and structure of MoCu composite produced. HMA and Cu powders in the proportion of 20% by weight of Cu were prepared by the techniques of mechanical mixing and mechanical alloying in a planetary mill. These were milled for 50 hours. To observe the evolution of the characteristics of the particles, powder samples were taken after 2, 10, 15, 20, 30 and 40 hours of milling. Cylindrical samples 5 to 8 mm in diameter and 3 to 4 mm thickness were obtained by pressing at 200 MPa to the mixed powders so as to ground. These samples were sintered at 1200 ° C for 60 minutes under an atmosphere of H2. To determine the effect of heating rate on the structure of the material during the decomposition and reduction of HMA, rates of 2, 5 and 10 ° C / min were used .. The post and the structures of the sintered samples were characterized by SEM and EDS. The density of the green and sintered bodies was measured using the geometric method (weight / volume). Vickers microhardness with a load of 1 N for 15 s were performed on sintered structures. The density of the sintered structures 10 ° C / min. reached 99% of theoretical density, how the density of sintered structures to 2 ° C / min. reached only 90% of the theoretical density

Efeito da moagem de alta energia na densificação e microestrutura do compósito AI2O3-Cu

The Cu-Al2O3 composite ceramic combines the phase of alumina, which is extremely hard and durable, yet very brittle, to metallic copper phase high ductility and high fracture toughness. These characteristics make this material a strong candidate for use as a cutting tool. Al2O3-Cu composite powders nanocrystalline and high homogeneity can be produced by high energy milling, as well as dense and better mechanical structures can be obtained by liquid phase sintering. This work investigates the effect of high-energy milling the dispersion phase Al2O3, Cu, and the influence of the content of Cu in the formation of Cu-Al2O3 composite particles. A planetary mill Pulverisatte 7 high energy was used to perform the experiments grinding. Al2O3 powder and Cu in the proportion of 5, 10 and 15% by weight of Cu were placed in a container for grinding with balls of hard metal and ethyl alcohol. A mass ratio of balls to powder of 1:5 was used. All powders were milled to 100 hours, and powder samples were collected after 2, 10, 20, 50 and 70 hours of grinding. Composite powders with compact cylindrical shape of 8 mm diameter were pressed and sintered in uniaxial matrix resistive furnace to 1200, 1300 to 1350 °C for 60 minutes under an atmosphere of argon and hydrogen. The heating rate used was 10°C/min. The powders and structures of the sintered bodies were characterized by XRD, SEM and EDS. Analysis TG, DSC and particle size were also used to characterize the milled powders, as well as dilatometry was used to observe the contraction of the sintered bodies. The density of the green and sintered bodies was measured using the geometric method (mass / volume). Vickers microhardness with a load of 500 g for 10 s were performed on sintered structures. The Cu-Al2O3 composite with 5% copper density reached 61% of theoretical density and a hardness of 129 HV when sintered at 1300 ° C for 1h. In contrast, lower densities (59 and 51% of the theoretical density) and hardness (110 HV and 105) were achieved when the copper content increases to 10 and 15%.

Merleau-Ponty: uma ontologia do visível

This work discusses the ontology of the visible at the thought of Maurice Merleau-Ponty (1908-1961), which points to a depth and opacity of the perceived world that oppose transparency of geometric world thought by René Descartes (1596-1650). At first we approached the Cartesian discourse developed in Dioptrics Descartes, the first of three scientific discourses published in 1637, being introduced by the famous Discourse method. In this sense, this research discusses the mechanistic explanation that the modern philosopher has the vision, process comprising the formation of images on the retina and its communication to the brain, and the subsequent reading performed by an immaterial mind. Discusses the notion of image as a result of the interpretation of the spirit because, for Descartes, is not the eye that sees, but the spirit that reads and decodes the signals that the body receives the world. At another point, reflected on the criticism of the philosopher Maurice Merleau-Ponty at the thought of overflight present in Dioptrics Descartes. Therefore, it takes as its reference the third part of the book The Eye and the Spirit (1961), in which the intellectualist approach of vision is considered a failed attempt to move away from the visible to rebuild it from anywhere . In this sense, it reflects on a new ontology proposed by Merleau-Ponty thinking being without departing from the puzzles of the body and vision. Puzzles that show a promiscuity between the seer and the seen, between sentient and sensitive. Thus, this paper discusses how visibility was treated by the contemporary philosopher, not as something to be judged by the spirit to get a real nature of things, but as a manifestation of the same things. Finally, this research explores the ontology of the visible in merleaupontiano thought, an ontology that does not rebuild or appropriates visible by a thought of overflight, but what you do from your own visibility as compared original and constant with depth in the world.