A obra de triangulis omnimodis libri quinque de Johann Müller Regiomontanus (1436 1476): uma contribuição para o desenvolvimento da trigonometria

Trigonometry, branch of mathematics related to the study of triangles, developed from practical needs, especially relating to astronomy, Surveying and Navigation. Johann Müller, the Regiomontanus (1436-1476) mathematician and astronomer of the fifteenth century played an important role in the development of this science. His work titled De Triangulis Omnimodis Libri Quinque written around 1464, and published posthumously in 1533, presents the first systematic exposure of European plane and spherical trigonometry, a treatment independent of astronomy. In this study we present a description, translation and analysis of some aspects of this important work in the history of trigonometry. Therefore, the translation was performed using a version of the book Regiomontanus on Triangles of Barnabas Hughes, 1967. In it you will find the original work in Latin and an English translation. For this study, we use for most of our translation in Portuguese, the English version, but some doubt utterance, statement and figures were made by the original Latin. In this work, we can see that trigonometry is considered as a branch of mathematics which is subordinated to geometry, that is, toward the study of triangles. Regiomontanus provides a large number of theorems as the original trigonometric formula for the area of a triangle. Use algebra to solve geometric problems and mainly shows the first practical theorem for the law of cosines in spherical trigonometry. Thus, this study shows some of the development of the trigonometry in the fifteenth century, especially with regard to concepts such as sine and cosine (sine reverse), the work discussed above, is of paramount importance for the research in the history of mathematics more specifically in the area of historical analysis and critique of literary sources or studying the work of a particular mathematician

Dificuldades no processo ensino aprendizagem de trigonometria por meio de atividades

This study analyses the difficulties that teachers of high school face in the process of the teaching of trigonometry through activities in a construtivist focus. It contains a review of some publications and dissertations related with the study of trigonometry elaborated in the last years by several authors. It resorts to the study of teaching engineering as an instrument used in the research. It also presents a set of activities which will serve as sample to other teachers of mathematics; and points ways for the overcome of the difficulties found

Construção e aplicação de uma sequência didática para o ensino de trigonometria usando software geogebra

The present study aims to analyze the potentialities and limitations of GeoGebra software on what concerns trigonometry s teaching and learning processes. Taking the present resources of public school from the state of Rio Grande do Norte, the research intends to answer the following question: Could we use the current conditions of public school and the Geogebra software to optimize the trigonometry s learning and teaching processes situation? . To make it a possible to answer the question above, a module of investigative activities was created and applied. The methodological intervention was made among second year High School students from a public school in Natal, RN. The theoretical reference of Mathematics Didactics was taken was a base, adopting the conceptions of Borba and Penteado (2001), Valente (1999) and Zulatto (2002, 2007) about the use of Information Technology (IT) on Mathematics classrooms. In order to create the investigative activities helped us to understand how the students make their constructions and their visual perception through the process of dragging images on the computer screen. Furthermore, the activities done with the GeoGebra software s resources facilitate the resolution of trigonometry situations

Elaboração e aplicação de uma sequência de atividades para o ensino da trigonometria numa abordagem histórica

The present work aims to report the construction of a workbook for teaching trigonometry focusing the possible mix between the historical approach to the teaching of mathematics and the professional master´s degree. For this, considerations about the history of mathematics as a teaching methodology, the education of the math teacher who will teach trigonometry and also about the course of elaboration and experimentation of the activities in the workbook were made (using the methodological strategy of action research). Finally, the workbook for the teaching of trigonometry in a historical approach is presented as an example of the above mentioned mix between the history of mathematics, mathematical school content and the professional master´s degree

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

La contra revolucion imaginaria: novela y film en Mexico (1910-1965)

COSTA, S. G. A. La contra Revolucion imaginaria: novela y film en Mexico (1910-1965). Revista Mediterranea de Comunicacion, n. 1, p.71-97, 2010. Disponivel em:. Acesso em: 04 nov. 2010.

A Eficácia dos direitos fundamentais nos contratos civis e de consumo: uma teoria contratual baseada na colisão dos direitos ou bens constitucionalmente protegidos

The apparent virtuosity that if could wait of the globalization and the neoliberalism has given signals of deterioration in the contractual relations, especially in contracts of mass consumption, generating innumerable offensive situations to the basic rights and the goods constitutionally protected of the contractors. In the world of today, still that it does not reveal any desire, the individual practically is compelled to contract, for force of necessities and customs completely imposed, mainly in face of the essentiality of the services or agreed to goods. Ahead of as much and unexpected changes in the civil liames and of consumption, dictated for the globalization, it comes to surface the reflection if the private law e, more specifically, the civil law, meet prepared adequately to deal with these new parameters of the economy. The present dissertation has the intention to investigate if the globalization and the consequent neoliberalism, in this beginning of third millennium, will imply to revive of the principles and the basics paradigms of the contracts that consolidated and had kept, for more than two centuries, the liberal State. One notices that the study of this phenomenon it gains importance to the measure where if it aggravates the decline of the social State (Welfare State), with the embrittlement and the loss of the autonomy of the state authority, over all in countries of delayed modernity, as it is the case of Brazil, that presents deep deficiencies to give or to promote, with a minimum of quality and efficiency, essential considered public services to the collective and that if they find consecrated in the Federal Constitution, as basic rights or as goods constitutionally protecting, the example of the health, the education, the housing, the security, the providence, the insurance, the protection the maternity, the infancy and of aged and deficient. To the end, the incidence of constant basic rights of the man in the Constitution is concluded that, in the process of interpretation of the right contractual conflicts that have as object rights or goods constitutionally proteges, in the universe of the globalized perhaps economy and of the neoliberalismo, it consists in one of the few ways - unless the only one - that still they remain to over all deal with more adequately the contractual relations, exactly that if considers the presence of clauses generalities in the scope of the legislation infraconstitutional civil and of consumption, front the private detainers of social-economic power. To be able that it matters necessarily in disequilibrium between the parts, whose realignment depends on the effect and the graduation that if it intends to confer to the basic right in game in the private relation. The Constitution, when allowing the entailing of the basic rights in the privates relations, would be assuming contours of a statute basic of all the collective, giving protection to the man against the power, if public or independently private

Habitus docente e representação social do ensinar Geografia na Educação Básica de Teresina - Piauí

The literature about the Geography teaching has shown that most male and female teachers of this subject go on guiding their teaching practice based on the traditional Geography fundamentals, whose main characteristic consist in the description of places. The incorporation of scientific standards that change the old principles and concepts have not been happening, unless in a punctual way. The overcoming of the traditional Geography, related to the aspects accepted by the scientific field have not happened in Brazil yet, not only because of certain obvious obstacles, as the literature has been pointed out but also by symbolic obstacles, which block the incorporation of the new, of the non habitual action. One of those obstacles that motivated the accomplishment of this study was the social representations that are theoretically studied here under the perspective developed by Serge Moscovici. Then, the focus of this doctorate study is concentrated in the apprehension of the content and structure of the social representation of teaching of Geography and its relation with the habitus that gives form and social visibility to the ones who are teachers of that subject in Teresina. The consecution of this work was especially based on the Pierre Bourdieu´s praxiology, mainly on the concepts of social field, habitus and capital, as well as the theory of social representations, specifically on the approach of central nucleus developed by Jean-Claude Abric and Jean-Claude Flament. The initial hypothesis pointed out the existence of a Geographer´s primary habitus built through the development process of the geographic science field in Brazil, as a basis of production of a social representation of teaching geography . That representation, however, would act as a symbolic obstacle to the incorporation of the new scientific contents and pedagogical practice, which require from the teacher investigative and questionable attitude in the presence of the reality and contents approached in the classroom. That initial hypothesis laid on the theoretical purpose that it has been developed by Domingos Sobrinho (1997), which states that there is a narrow relationship between the habitus and social representation. The study was developed with male and female teachers of Geography from public schools of Teresina. The methodology involved the use of a questionnaire, the free-word association technique and deep interviews. The achieved results showed the presence of a complex process of representational construction and its articulation with a habitus produced by the synthesis of several situational and cultural referents, from among of them we can point out an insertion in a social field of practice exclusively related to the teaching and the reproduction of a professoral teaching (SILVA, 2003), built through the school development process, which those male and female teachers were exposed. The initial hypothesis that considered the local reproduction of a primary habitus of the Geography was denied, therefore, it was verified that there is not in Teresina the production/reproduction of the structures, rules and practice of the national scientific field, in which this subject is inserted. Hence, the incorporation of the new patterns of the geographic scientific knowledge is difficult because of the inexistence of a scientific habitus, that is, mental schema systems that would let the teachers mentioned above connect themselves appropriately to the science and its practices. So, it has gotten a social representation of teaching geography based on contents strictly related to the reproduction of structures, mental schema from the educational field which attach themselves to the hegemonic pedagogical practices in the national scope

A leitura de fontes antigas como possibilidade didatica: um exemplo a partir do Almagesto de Ptolomeu

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

O imaginário da mediunidade no processo de escritura em Fernando Pessoa

The answer to creating a fictional world? Repulsion or form of reaction to an outside world? Mental illness, whose brand can be symbolic simulation or depersonalization? Hard to take a stand when the deed is a poet Fernando Pessoa as what is at stake. Notes Schlafman Léo (1998) who, at the age of 20 years, Fernando Pessoa wrote in English, in his diary, "One of my mental complications is the fear of madness, which in itself already is crazy." What rid of madness, notes Robert Bréchon (1986), was the taste of the game and was playing it for your writing. Even though it has rid the madness, the poet does not quit seeking explanations - or provide it - for the phenomena much bother him, or defined.'s where we come across the alignment of Fernando Pessoa within philosophical as occultism and reading about psychological and mental disorders treated. paths were pursued by him to explain the existence of his heteronyms and its entry process. This work therefore presents main objective: to analyze the personal papers of Fernando Pessoa, whose outstanding feature is the presence of occult and alleged mediumship demonstrations held in response to non-literary and heteronímicas. Therefore, I focused on specific goals, which are: a) to study the speech of Fernando Pessoa on his mediumship / occult b) analyzing specific texts that are, for the poet, psychic demonstrations, c) study of a series of excerpts personal letters in which Fernando Pessoa suggested to be a medium. Admittedly, this essay will touch many arguments already made by scholars and experts of Fernando Pessoa, but consider the possibility of developing issues and contribute to the critical fortune of the poet. We assume that announces the Portuguese scholar Jerome Pizarro (2006), one of the greatest scholars of the work Pessoan: those interested in Fernando Pessoa be lost in the maze created by him. It is the image of a person-Minotaur, devouring all but, holding us in its labyrinthine tessitura, as marked by mystery. Will draw on our analysis, a theory aligned themselves to objects of research, whose main authors are Sigmund Freud (1908) Carl Jung (1991.1996). Gaston Bachelard (1996), Helena Blavatsky (2008), among others

O ensino de funfições trigonometricas através do software geogebra

In this study, we sought to address the weaknesses faced by most students when they were studying trigonometric functions sine and cosine. For this, we proposed the use of software Geogebra in performing a sequence of activities about the content covered. The research was a qualitative approach based on observations of the activities performed by the students of 2nd year of high school IFRN - Campus Caicfio. The activities enabled check some diculties encountered by students, well as the interaction between them during the tasks. The results were satisfactory, since they indicate that the use of software contributed to a better understanding of these mathematical concepts studied

Rio Grande do Norte: interações urbanas e os centros de gestão do território

The state of Rio Grande do Norte has been undergoing transformations in their territory, they are promoted by the installation of new infrastructure equipment, which in turn cause changes in the dynamic spatial and social hour set, causing new arrangements and new dynamics between cities. The overall goal of the research is to understand, at present, the urban network of the Rio Grande do Norte, from the centers of territory management. The picture presented in the paper reveals a network of cities that has gained a material basis urban, with the installation of new objects macro state structures (roads, ports, wind farms, banks, pipelines, internet access) that enable a relationship more intense between the urban centers of the state and other cities in the world, that the current structure characteristic of the urban network, its global nature, since the possibility of relations between the centers is greater. Such a relationship is indeed possible because the characteristics of the current historical period, with the high density of the tripod technique, science and information controlled by the market. In Rio Grande do Norte intentionality of the new arrangement that is configured is not other but meet market demands