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

Espirito de catimbo: a moral magico-religiosa da jurema

This participative research interested in the social praxis attempts to understand the moral principles that set the magic rituals and the places of worship of three jurema centers of the potiguar region of Canguaretama. Among other inner particularly aspects of each focused catimbó-jurema center, it is being discussed the collective standards involved in the reliance and fellowship values assumed in the private magical gatherings by the juremeiras leaders and their partners, in contrast to the prestige seeking and the individualism that influence both the symbolic competitions and the witchcraft works that link these agents to the broader catimbozeiro universe of this region. Finally, the moral practices which make part of the juremeiro left-right dualism are investigated based on the understanding that the referred native pantheonic-ritual dichotomy does not necessarily express two moralities substantially adversed in terms of benefits or harms, but a series of moral actions subject to the specular logic of the tit-for tat. Thus, this research seeks to prove that this moral structure of symbolic reciprocity, as well as the witchcraft centrality in the catimbozeiro world, finds a certain causal link in a world view which guiding principle is the ontological evil of the catholic cosmology

Simulação de fluxo de fluidos em meios porosos desordenados uma análise de efeito de escala na estimativa da permeabilidade e do coeficiente de arrasto

The present study provides a methodology that gives a predictive character the computer simulations based on detailed models of the geometry of a porous medium. We using the software FLUENT to investigate the flow of a viscous Newtonian fluid through a random fractal medium which simplifies a two-dimensional disordered porous medium representing a petroleum reservoir. This fractal model is formed by obstacles of various sizes, whose size distribution function follows a power law where exponent is defined as the fractal dimension of fractionation Dff of the model characterizing the process of fragmentation these obstacles. They are randomly disposed in a rectangular channel. The modeling process incorporates modern concepts, scaling laws, to analyze the influence of heterogeneity found in the fields of the porosity and of the permeability in such a way as to characterize the medium in terms of their fractal properties. This procedure allows numerically analyze the measurements of permeability k and the drag coefficient Cd proposed relationships, like power law, for these properties on various modeling schemes. The purpose of this research is to study the variability provided by these heterogeneities where the velocity field and other details of viscous fluid dynamics are obtained by solving numerically the continuity and Navier-Stokes equations at pore level and observe how the fractal dimension of fractionation of the model can affect their hydrodynamic properties. This study were considered two classes of models, models with constant porosity, MPC, and models with varying porosity, MPV. The results have allowed us to find numerical relationship between the permeability, drag coefficient and the fractal dimension of fractionation of the medium. Based on these numerical results we have proposed scaling relations and algebraic expressions involving the relevant parameters of the phenomenon. In this study analytical equations were determined for Dff depending on the geometrical parameters of the models. We also found a relation between the permeability and the drag coefficient which is inversely proportional to one another. As for the difference in behavior it is most striking in the classes of models MPV. That is, the fact that the porosity vary in these models is an additional factor that plays a significant role in flow analysis. Finally, the results proved satisfactory and consistent, which demonstrates the effectiveness of the referred methodology for all applications analyzed in this study.

Os filhos evangélicos do novo caldeirão do diabo: a conversão religiosa na penitenciária de alcaçuz

The theme of the research is inserted at a field of intersection between the Sociology of Religion and Sociology of Violence, having as the general objective study the sociological meaning of the conversion of prisoners that lives at the biggest prison (Prison of Alcaçuz) of Rio Grande do Norte to the evangelical churches. The research is justified, because Brazil shelter the fourth greater arrested population arrested of the world, with projections indicating that it can turn the greatest in 2034. Besides, this study about religious conversion of prisoners to the Social Sciences is too important, because is a theme little developed in Brazil and deserves attention, one time that as the arrested people as the evangelicals are in expansion in our country. Starting from the precedent observations, we guide ourselves by the following problematic of research: the religious practice in Alcaçuz presents a mere instrumental perspective, where the actions of prisoners converted was on purpose oriented to conquest material or symbolic privileges; or purely religious, where seek a moral renovation? To develop the work, the scientific methodology adopted was exploratory and explanatory, using the Goffman´s theory about total institutions and presentation of self, and Blumer´s doctrine relating to Symbolic Interacionism and the Story life method, besides considerations about evangelical religion. Having this theoretical basis, was accomplished the Field research, when were made interviews and applied questionnaires to 11 Jailer Agents, 31 prisoners, Director and Vice-Dictor (in November, 2011), the coordinator of social projects of the prison and the coordinator of evangelization at the prisons in Rio Grande do Norte. As results, it was seeing in Alcaçuz that the prisoners can be separated in two groups: the one of Pavilions and other one of the Medical Section. The Pavilions are branded for managerial and structural problems, where are found idle prisoners in collective cells and with a historical of escaping attempts, mutinies and murders. The Medical Section has some individual cells or destined for two people, besides few collective also, and the prisoners work and have a more disciplined behavior, there isn t escapes or rebellions and that, for these reasons end for have more confidence from the Administration. About the presence of evangelical prisoners, most are at Medical Section, where exist a specific place to the cults (what doesn t at Pavilions). At the end, the conclusion is that the prisoner that says himself evangelical in Alcaçuz, although can be seeing with distrust about your real conversion, he gets win a trust vote and until the opposite being demonstrated in other words, that he is not hiding himself behind the bible to divert the vigilance of Direction and practice disciplinary faults without make any suspicions, is treated with more respect and has more opportunities live at Medical Section; have work, that most of times is paid and guarantee the homologation of your payment of penalty with work, besides other benefits, diminishing his time in jail

A ética econômica das classes trabalhadoras: a gramática social do comportamento econômico da nova pequena burguesia comercial de Natal/RN

Rogram relying on sociological interface between Economic Sociology, Sociology of Moral Theory of Socialization and Social Stratification, this dissertation research makes use of theoretical contributions Luic Boltanski, Charles Taylor, Axel Honneth, Pierre Bourdieu and Bernard Lahire to problematize the generally about the physical and symbolic production and social reproduction of the type of "economic ethics" predominant in the new petite bourgeoisie Brazilian. In other words, the goal is to explain and analyze the objective conditions (economic needs and moral grammar) and intersubjective (modes of socialization and social networks) and update the social genesis and contextual transcontextual beliefs, biases, inclinations and cultural regularities observed the economic behavior of individual profiles for the fractions of the urban petty bourgeoisie and commercial upward Natal / RN. With regard to methodological strategies adopted in data collection will be conducted qualitative interviews (semistructured) and ethnographic notes. In turn, the analytical treatment of the collected empirical content is based on the approach dispositionalist (Pierre Bourdieu, Loïc Wacquant and Bernard Lahire) that emphasizes the study of the past embedded agents and the different contexts of incorporation / activation / inhibition of "provisions" individual cultural

Natal como destino turístico : um estudo das imagens (re)veladas pela mídia, pelos turistas e suas implicações educacionais e culturais

This thesis is a result of a research on Natal/RN as a tourist destination. We understand that cities are chosen as tourist destinations beyond its cartographic localization, from other dimensions of meanings that, in its set, constitute images. These images are, probably, very different of the images constructed by native and resident populations, who possess relations of identity with the place. The knowledge of the meanings that others attribute to this city as tourist destination, bring us near to the symbolic bonds established by individuals or social groups on the act of their choices, as well as bring us near to the interaction process city-tourists where the expectations are confirmed or not. The images divulgated by the media also participate of the complex formation of the tourist image that is being constructed and available for the different public, in different social contexts. The tourism constitutes a symbolic asset of the modern society, being considered by the studious, as one of the most expressive phenomena of the modernity, for involving each year displacement and the interaction of thousand of people of different cultures in the entire world. All this people s mobilization points to practical social related to personal motivations, to the entailed desired to the idea to travel and to exceed borders. It is already consensus that tourism is a phenomenon of economic growth, generating jobs, income, professional, qualification, bringing improvements for the host cities. Since 1995, in Brazil, the tourism as a sector of the economy, passed to be considered one of the national priorities, and in this perspective, the national politics of the tourism invested in infrastructure of Brazilian cities with high tourist potential, objecting to increase the flows of Brazilian and foreign tourists. Owing to this fact, the country still invests in programs of tourist marketing, mainly divulging the images of the natural beauties of Brazil abroad. And for Brazilians, the campaigns appeal to rescue the feeling to be Brazilian, associating the idea to travel and know its country. Natal city possesses an excellent positioning in the tourist marketing, being predominantly divulgated in national and international level, for its naturalistic singularity, where the images of its natural enchantments as warm water beaches, white dunes, warm weather, constant breeze and an always blue sky are shown as the favorite scene on this city. From what was viewed above that the choice of a tourist destination articulates from a determined imaginary of a place, already constructed or in process of construction, we consider the knowledge of this imaginary a basic learning for the population of the city and especially, for educators, in the formation of professionals in this area and for tourism managers, elaborators of public politics. Based on this estimative, we developed this research that had as a general objective to identify the images that illustrate Natal city as a tourist destination - our objective of study, particularly the meanings and senses attributed by the tourist marketing (hotel s folders) and by the tourists that visited the city during this study. The discussions and reflections that had guided this research had been given from the theoretical link between imaginary and social representation, also considering some interfaces between the fields of communication and symbol. From the studied authors, Baczko (1985) clarifies that the study of social imaginary is directed for the mechanisms and structures of the social life, especially for the intervention accomplishes and efficient of the representations and symbols in the practical collectives, as well as in its direction and orientation . Following this same thought, Moscovici (1978) says that the social representation are produced in communicational and symbolic contexts, and these representations once that already constituted circulate socially as almost tangible entities. Based on this fundament and on the analyze of Barthes (1990), particularly in the approach given to the reading of photographic image, we could observe on hotel s folders that each page evidences senses and meanings of functionality of internal and external spaces, pointing to the way of leisure offered by the keepers of city which is the hotels. About, the leisure that they offer, it is directed to young public, giving meaning to the young myth of personalized leisure tourism on children, young and adults images. The image about security that hotels offer and the singular image of Natal city as a paradise place, provide an idealization of pleasure through the sun, dunes, and beaches and also due to the hospitability of the natives who are assigned as educated . For the tourist that participated on this research, Natal city is tied only by the imaginary of leisure and nature which constitute the emotional link of the relation media-city-tourist. And with such force and fullness of directions the city discloses without tensions and contradictions as a place protected by a mythical and sacred aura. The study also demonstrates us that the potiguar culture remains (almost) forgotten, due to the silenced in this imaginary. In this perspective, we highlight that this culture silence is very close related to the disvalue of education in its general meaning. We defend that the imaginary apprehended constitutes a new reading and a new looking and understanding the tourist reality that comes historically consolidating in this city. In this direction, we glimpse that this study and its future dismemberments can collaborate with the process of rescue the cultural values of the potiguar people, in the way that the meaning of tourist may be redefined, and the tourist image of the city can be also disclosed for its identities particularities of its culture

Praxiologia, representação social de menopausa e práticas educativas de enfermeiras na estratégia saúde da família

This research, whose theme is related to climacteric, aims to know the social representation of menopause developed by the nurses working for Estratégia Saúde da Família (Family Health Strategy) in João Pessoa PB, as well as identifying its structure and verifying the way it interferes with the assistance and educational practices to the climacterial user. In the theoretical level, it is based on a model that articulates the social representations theory, the central nucleus complementary theory and the central concepts of Pierre Bourdieu s praxiology: habitus, cultural capital, social field and symbolic power. A hundred and forty-seven female nurses who work for Estratégia Saúde da Família (Family Health Strategy) in João Pessoa (PB) took part in this research, and the data collection period was from February 2008 to March 2009. As to the methods and techniques, we used the method to determine the central nucleus based on the free association of words, a questionnaire to identify certain regularities that constitute the nurses habitus, and the semi-structured interview to explore opinions and attitudes when facing assistance situations and educational practices and to collect other relevant information. The data analysis was developed, when referring to the free associations, with the help of the EVOC software, which is a group of articulated programs which carry out the statistical analysis of the evocations and the identification of the possible elements of both the central nucleus and the peripheral system of the social representation. As to the questionnaire, we used the descriptive statistical analysis and the analysis of correlation between the variables. The interviews were submitted to a categorical analysis of the content. The EVOC result indicated that the cognition hormone was the only element of the central nucleus of the social representation of menopause. Due to its symbolic value and structuring power, this central nucleus ensures the strict and, at the same time, flexible character of the representational content. The analysis of the social advancement, of some fundamental features of the group habitus, as well as the analysis of its insertion in the health field and of the attitudinal opinions and dispositions concerning the assistance given to the climacterial user, and the analysis of the pedagogical dimension of this assistance, all these analyses lead to the conclusion that the nurses who took part in this research share a social representation of the menopause resulting from the association of different technical and scientific knowledge. These derive from the biomedical pattern as well as from hegemonic values which disqualify old age and overvalue youth, from pedagogical conceptions arising from patterns that are presently regarded as authoritative and old-fashioned and from cultural references (responsible for the semantic variations concerning the central nucleus) which are specific to the subgroups the nurses belong to. This research enables the creation of opportunities for discussion between active nurses working for Estratégia Saúde da Família, and the nurses who are teachers at institutions of higher education, aiming at linking theory to practice, so that they can find ways of thinking about the climacteric and working, in a more comprehensive way, with users who are experiencing this stage of life

Construtivismo de marco teórico-pedagógico a grife: um estudo a partir das mensagens veiculadas na internet

This thesis is resulted of a research on propagated the social representations of constructivism in the Internet, which as had estimated basic the idea of Moscovici (1961) of that the media it has determinative paper in the popularization of the scientific theories, in formation e propagation of the social representations and in the construction of behaviors human beings. Understanding the Internet as latest space of circulation of social communications, therefore, privileged field (and still not explored) for studies of social representations, we choose this half midiático as investigative field of our research, it if it constitutes in the "great ocean of the new informational planet" (LEVY, 2000, p. 126), besides making possible the interaction with different forms of images, different individuals, different ' world ', configuring itself as important space of symbolic production e of analysis of the representational process in the world contemporary. Based in these questions, we trace as objective to analyze the circulating speech propagated on-line on the constructivism, searching to apprehend the social representations shared the respect. This objective was constructed in face of the insertion of the theory constructivist in the educational way has two decades more than, as well as of its consolidation as reference in different social contexts, mainly in midiático. The question that directed the research was: as this theory obtains to penetrate in some layers of our society, to influence the world readings e the behaviors of different people? That modifications it suffers in this trajectory and which the paper of the Internet in this process? The corpus of the research was constituted of the substances on the theory found in the Internet, in pages in Portuguese of Google, in the period of 27 of July of 2004 the 17 of August of 2004. The data they had been analyzed on the basis of the project of analysis of content elaborated for Moscovici (1961) and in the estimated theoreticians of the social communication, in special of the hypermedia. The results had disclosed that the Internet participates of determinative form in the process of popularization of the constructivism theory, not only spreading out its estimated theoretician- methodological for the domain public (diffusion), but propagating positive beliefs and images of its postulates (propagation) and using them it service of interests politicians e financiers (propaganda). The popularization of the constructivism in the Internet and social representations of this theory propagated configure one process in which the theory passes of pedagogical theoretical landmark for grief, assuming a commercial character extremely and the status of solution for problems of the education and the society, stirring up attitudes and behaviors in public, most general possible, that comes to take care of to the interests politicians e marketing. Recognizing the diversity, the permanent renewal of information and the negotiation of directions gifts in the Internet, as well as the innumerable ones forms of access to the information found by it, we consider results of the research as fruits of the inherent characteristics to this way midiático, to the time where we call the attention for relativity these results, for the plasticity of knowing them and sensible propagated on-line e for the great challenge that the hypermedia imposes to the study of communication phenomena, of the social representations and in educational quarrels and for the necessity of new research that they investigate the forms of socialization of the information and communication propitiated by hypermedia and its implications in the construction of the symbolic universes and in practical social

Praxiologia e representação social sobre formação de professores nas licenciaturas da UFPI

At this investigation it was analyzed the content and the organization of the social representation on the object teachers education, built by teachers of degree courses from Universidade Federal do Piauí(Ufpi), understanding such representation articulated to the teaching habitus of these educators of teachers, what takes under consideration the position that they hold in the structure of the national field and in the subfield of teachers education. For that, it is searched: a) to emphasize the properties of the place in which the trainers act Ufpi as the office of those field and subfield; b) to understand who are the trainers, that is, to grasp the teaching habitus of the trainers with a view of its origin, social trajectory and the specifics of their position in the analyzed field and the subfield and c) to know what they think about their work object, that is, identify and articulate the content and the organization of the social representation analyzed with their properties of field and subfield agents. The research includes the specific degree courses of the Campus Ministro Petrônio Portella , from Teresina(PI), and it was applied to 134 professors of degree courses from this Campus. The data collect joined to the participants happened on the second period of 2008 and on the first semester of 2009. The starting point of the study is the corroboration that the reform of Ufpi degree courses, determined by the legislation and stablished at this Institution in 2005, altered a little the previous situation. It is comprehended that Ufpi and its structures of teachers education as a trainer institution, is limited by the national academic field and by the subfield of teachers education. From this last one, it was listed some of its properties, to show that it is about an academic subfield in construction process. It is emphasized division of the subfield, that separates the trainers into two subgroups the ones who dedicate themselves to the specific education on the contents and those ones who are specialized on pedagogical education placed in antagonistic position and competing by the symbolic power of imposing the meaning and the sense of the teachers education in the degree courses. To understand the comprehension of the problem, it is searched for the models that are in the root of the construction of the University and its project of teachers education in the degree courses, to clarify the matrixes in which the social representation searched is stablished. The theoretical referential articulates the contributions of Moscovici, the theory of social representations, and of Bourdieu, with the concepts that compose its praxeology, as habitus, social field, capital, symbolic power and others, as well as their interpreters and continuators, as Domingos Sobrinho. From the literature about the university and teachers education, it was used Dermeval Saviani, Luiz Antônio Cunha, Maria Isabel da Cunha and Mirian Jorge Warde, besides others. Plurimethodological procedures were adopted, combining associative techniques adjusted to the access to the social representations, and a classic technique, a questionnaire about teaching habitus. The condition is that the teachers build different social representation of the object teachers education because of the distinct positions that they occupy in the structure of the academic field and the subfield of the teachers education. The reached positions in the field and subfield are due to the differences in the origin and social trajectory of these agents, who, therefore, have different teaching habitus from which they build their social representation about their work object. It is highlighted that the teaching habitus and the social representation of two subfields, identified by the belongings to different dimensions of the teachers education in the degree courses, they have similarities and, also, differences. These ones permit to support that the subjects are holders of distinct teaching habitus that conceive different practices, struggles, tensions and conflicts around the sense of teachers education

Inclusão e deficiência: em busca das representações sociais na mídia impressa em Natal/RN

This thesis is the result of an extensive research on print media discourse on the inclusion of disabled people in society. Articles published in the newspapers Diário de Natal/O Poti and Tribuna do Norte from 1992 to 2002 have been analyzed. Beginning with the very same questions that moved Moscovici (1978) in his classic study La Psychalyse son image et son public , according to which the media play a predominant role in the formation and propagation of social representations as well as in the construction of human behaviors, we have chosen this mass media as our investigation field. Understanding the importance of the communication theory, we intend to associate it to the social representation theory, since communication, as an aspiration, relates to the fundamentals of all humanity (WOLTON, 2004, p. 56). Moreover, means of communication represent an important space for symbolic production and representational process, allowing the analysis of the circulating discourses on social inclusion and disability. Based on these questions, we have determined social representations present in print media on the subject to be our study object. This objective was elected due to the fact that the thematic of disability and inclusion is scarcely and sporadically found in journalistic speech. The research questions have been: which is the representation of disabled people s condition in print media? What changes have occurred during the analyzed period and which was the role played by print media in this process? The research corpus was composed of newspaper articles about various aspects concerning disability and of free word association by reporters. We have analysed: 1) graphical language promoted by the picture of the substances propagated in the period from 1992 a 2002; 2) free word association experiments carried out with reporters of both newspapers; and 3) texts published from 1996 to 1997 using the high-tech program ALCESTE (Contextual Lexical Analysis of a Set of Segments of Texts). The results revealed that the print media in Natal/RN refer to the topic in a discontinuous way, and depend on specific events to highlight disabled people s fight for their rights. Social inclusion is still a great challenge for these people in all levels. We believe that this incapacity to overcome all kinds of obstacles is established in a dialectic relation between society and the media: society remains silent (the manifestation of interest for the cause only attracts some people s or groups attention) and the media, which selects which information is to be broadcasted, gives no evidence to the issue. This representation may be noticed in the infrequency in which articles about the subject are published, as well as in the emphasis to sports, a more important issue for the media. An implication of this study is that a new perspective is opened for analysis and reflection: the Paralympics games as both an inclusive and a segregating social phenomenon. It would be beautiful to have all of us together!

Vivendo o bem estar no desconhecido: experiência da mulher com a presença do acompanhante no processo de parto

The humanization of the birth process is a current health policy priority. Within that perspective, the presence of a partner during the birth is a benefit guaranteed by the Law 111008/05. The purpose of this study is to comprehend the woman s experience with the presence of a birth partner as a legal right. It is a qualitative descriptive study based on Symbolic Interactionism and conducted using the grounded theory methodology. Data were collected by semi-structured interviews conducted during August to December 2006, with women that had the presence of a partner during their birth experience and that were in the first 24 hours of puerperium. Data analysis resulted in the identification of the phenomena: FEELING GOOD, RECOGNIZING THE BOND WITH THE PARTNER, RECOGNIZING THE IMPORTANCE OF THE EXPERIENCE and NOT KNOWING THE RIGHT. These enabled the identification of the central phenomenon LIVING THE WELL-BEING IN THE UNKNOWN. The study demonstrated that the birth experience with the presence of partner is a positive one, resulting in benefits such as tranquility, support, and assurance, which, in that context, signify well-being. However, the women do not visualize the experience as a right, therefore remaining alienated from their civic practice. The understanding of the experience was enabled by the conceptual construction obtained from the categories of the interactions between the women and their birth partners during the event. The explanation of the phenomenon LIVING THE WELL-BEING IN THE UNKNOWN reflects the theoretical structure obtained from the integration of the identified concepts. The study points out the need for health professionals to improve the information given to women during the birth process and to work the civic duties of the women in reproductive health

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

Euler e os números pentagonais

The present investigation includes a study of Leonhard Euler and the pentagonal numbers is his article Mirabilibus Proprietatibus Numerorum Pentagonalium - E524. After a brief review of the life and work of Euler, we analyze the mathematical concepts covered in that article as well as its historical context. For this purpose, we explain the concept of figurate numbers, showing its mode of generation, as well as its geometric and algebraic representations. Then, we present a brief history of the search for the Eulerian pentagonal number theorem, based on his correspondence on the subject with Daniel Bernoulli, Nikolaus Bernoulli, Christian Goldbach and Jean Le Rond d'Alembert. At first, Euler states the theorem, but admits that he doesn t know to prove it. Finally, in a letter to Goldbach in 1750, he presents a demonstration, which is published in E541, along with an alternative proof. The expansion of the concept of pentagonal number is then explained and justified by compare the geometric and algebraic representations of the new pentagonal numbers pentagonal numbers with those of traditional pentagonal numbers. Then we explain to the pentagonal number theorem, that is, the fact that the infinite product(1 x)(1 xx)(1 x3)(1 x4)(1 x5)(1 x6)(1 x7)... is equal to the infinite series 1 x1 x2+x5+x7 x12 x15+x22+x26 ..., where the exponents are given by the pentagonal numbers (expanded) and the sign is determined by whether as more or less as the exponent is pentagonal number (traditional or expanded). We also mention that Euler relates the pentagonal number theorem to other parts of mathematics, such as the concept of partitions, generating functions, the theory of infinite products and the sum of divisors. We end with an explanation of Euler s demonstration pentagonal number theorem

O ensaio jornalístico na revista Veja: uma análise multidimensional

This work has as objective generality to make a multidimensional analysis in the genre journalistic assay, communicative genre that, beyond complex and multimodal, presents hybrid characteristics. Specifically, with the intention to propose defining criteria of the cited genre, this research looks for to establish differences and similarities between the assay and other genres of the same sphere, from the description and interpretation of used multimodal resources. The analysis of the formal, schematical and rhetorical resources identified in the formatting of the journalistic assay sample that the analyses are supported in the socio-semiotic and socio-rhetorical approaches. In the formal dimension, we contemplate elements that constitute design of the text, including the forms of representation from the typography, the colors, images, as well as the aspects communicative-linguistics: the modalization indices, the communicative operators and the category time; in the schematical dimension, we present the organizational structure, considering the rhetorical movements postulates for Swales (1990) and in the rhetorical dimension we observe the categories: who writes, for who it writes, on what it writes and where writes. The adopted methodologicals postulates are of qualitative nature and the procedure is documentary, data that in we are valid them written texts of this genre as analysis object. Corpus it is constituted by a composed sample for 14 extracted texts of a set of 173 propagated journalistic assays weekly for the magazine Veja, in the period between August of 2004 and January of 2008. The analysis of the data showed that the journalistic assay, object of this study, materializes through multiple symbolic representations and multiple subjects that turn since a small episode of the daily facts of great social relevance in the present time, of historical and cultural nature, nationwide or international. Used for the first time by Montaigne in 1580, to assign, in saying of the proper author, written fast on its life and historical events, which could nor be remembered later , the term `assay' was enriched with other specifications, of form to enclose the one that if they call scientific assay today, academic assay, journalistic assay and other types of specific assays. These denominations have to see with the enrollment of the members of diverse of practices communities, in virtue of the multiplicity of activities carried through in these spheres. The conclusions the one that we arrive had been the following ones: 1. the discursive genre is not a pure entity, in virtue of the multiplicity of situations where the sorts if insert in the social actions; 2. the institutions define the configuration of one definitive genre, also its proper assignment, since for backwards of all discursive genre a voice exists to discipline - institutional voice, and in the case of the assays for analyzed us, the institutional voice if it presents, really, as a defining trace; 3. the journalistic assay, for its multiple symbolic representations, multiple subjects and for passing explicit or implicit opinions of its author, resembles it other genres, being able, therefore, to be inserted in a colony of opinionatives genres

O afeto além dos muros e portões : o apego a vizinhanças na cidade do Natal

Place Attachment is a positive affective bond between people and environments, and its main characteristic is the desire to maintain closeness to the place of attachment. Neighborhoods, in turn, are spaces close to the dwelling, which varies according to environmental, social and cultural characteristics. Facing the contemporary scenario of diminishment of neighborhood relations and its importance to the understanding of cities social-environmental context, the present work aimed to investigate the attachment to neighborhoods at the city of Natal-RN. This study had two stages. The first stage consisted on investigating, through an experts panel, the main characteristics of attached neighborhoods, aspects that contributes to the development of these neighborhoods, the ones that difficult, as well as look for indications of neighborhoods at the city of Natal that may be identified by these elements. In the following stage I interviewed 11 residents of two indicated neighborhoods at the district of Alecrim, to better comprehend the main characteristics of this attachment and the elements of the context that enable its development. The content of the interviews, categorized and evaluated by judges, indicated that, due to the 10 participant experts, the main characteristics of attached neighborhoods encompass elements of socialization, cooperation, physical space usage, intimacy and identity. According to them, these are characteristics enabled by temporal and rootedness aspects, by spatial contact, familiarity between neighbors, and cultural inheritance. The interviews with residents showed that attachment to the studied neighborhoods is specially grounded on support and cooperation networks between neighbors, on satisfaction with the proximity of services, and on the bond to symbolic aspects and local traditions. In addition to be enabled by spatial organization, by low displacement of residents, and by the district s history, relations at these neighborhoods are fostered by an intention to establish this kind of ties, carried by cultural values