Adrien-Marie Legendre (1752-1833) e suas obras em Teoria dos Números

The present thesis is an analysis of Adrien-Marie Legendre s works on Number Theory, with a certain emphasis on his 1830 edition of Theory of Numbers. The role played by these works in their historical context and their influence on the development of Number Theory was investigated. A biographic study of Legendre (1752-1833) was undertaken, in which both his personal relations and his scientific productions were related to certain historical elements of the development of both his homeland, France, and the sciences in general, during the 18th and 19th centuries This study revealed notable characteristics of his personality, as well as his attitudes toward his mathematical contemporaries, especially with regard to his seemingly incessant quarrels with Gauss about the priority of various of their scientific discoveries. This is followed by a systematic study of Lagrange s work on Number Theory, including a comparative reading of certain topics, especially that of his renowned law of quadratic reciprocity, with texts of some of his contemporaries. In this way, the dynamics of the evolution of his thought in relation to his semantics, the organization of his demonstrations and his number theoretical discoveries was delimited. Finally, the impact of Legendre s work on Number Theory on the French mathematical community of the time was investigated. This investigation revealed that he not only made substantial contributions to this branch of Mathematics, but also inspired other mathematicians to advance this science even further. This indeed is a fitting legacy for his Theory of Numbers, the first modern text on Higher Arithmetic, on which he labored half his life, producing various editions. Nevertheless, Legendre also received many posthumous honors, including having his name perpetuated on the Trocadéro face of the Eiffel Tower, which contains a list of 72 eminent scientists, and having a street and an alley in Paris named after him

A difícil aceitação dos números negativos: um estudo da teoria dos números de Peter Barlow (1776-1862)

The present study seeks to present a historico-epistemological analysis of the development of the mathematical concept of negative number. In order to do so, we analyzed the different forms and conditions of the construction of mathematical knowledge in different mathematical communities and, thus, identified the characteristics in the establishment of this concept. By understanding the historically constructed barriers, especially, the ones having ontologicas significant, that made the concept of negative number incompatible with that of natural number, thereby hindering the development of the concept of negative, we were able to sketch the reasons for the rejection of negative numbers by the English author Peter Barlow (1776 -1862) in his An Elementary Investigation of the Theory of Numbers, published in 1811. We also show the continuity of his difficulties with the treatment of negative numbers in the middle of the nineteenth century

Uma filosofia da história tornada sóbria sobre o papel da filosofia da história na teoria crítica da sociedade de Jürgen Habermas

Após uma parte introdutória sobre o estatuto da filosofia da história como conhecimento, o texto procura analisar o corte efetuado por Habermas em sua trajetória teórica visando livrar sua teoria social daquela filosofia e, consequentemente, superar as teses acerca da construção de um sujeito da história e da exequibilidade da história. Com essa análise procura-se diagnosticar as transformações fundamentais que esse corte ou rejeição, por parte de Habermas, do pensamento próprio da filosofia da história trouxe para a sua teoria crítica da sociedade, e também apontar os rudimentos e traços daquela filosofia nessa teoria.

De solutione problematum diophanteorum per números integros : o primeiro trabalho de Euler sobre equações diofantinas

The present dissertation analyses Leonhard Euler´s early mathematical work as Diophantine Equations, De solutione problematum diophanteorum per números íntegros (On the solution of Diophantine problems in integers). It was published in 1738, although it had been presented to the St Petersburg Academy of Science five years earlier. Euler solves the problem of making the general second degree expression a perfect square, i.e., he seeks the whole number solutions to the equation ax2+bx+c = y2. For this purpose, he shows how to generate new solutions from those already obtained. Accordingly, he makes a succession of substitutions equating terms and eliminating variables until the problem reduces to finding the solution of the Pell Equation. Euler erroneously assigns this type of equation to Pell. He also makes a number of restrictions to the equation ax2+bx+c = y and works on several subthemes, from incomplete equations to polygonal numbers

Os artigos de Euler sobre os números amigáveis

Among the many methodological resources that the mathematics teacher can use in the classroom, we can cite the History of Mathematics which has contributed to the development of activities that promotes students curiosity about mathematics and its history. In this regard, the present dissertation aims to translate and analyze, mathematically and historically, the three works of Euler about amicable numbers that were writed during the Eighteenth century with the same title: De numeris amicabilibus. These works, despite being written in 1747 when Euler lived in Berlin, were published in different times and places. The first, published in 1747 in Nova Acta Eruditorum and which received the number E100 in the Eneström index, summarizes the historical context of amicable numbers, mentions the formula 2nxy & 2nz used by his precursors and presents a table containing thirty pairs of amicable numbers. The second work, E152, was published in 1750 in Opuscula varii argument. It is the result of a comprehensive review of Euler s research on amicable numbers which resulted in a catalog containing 61 pairs, a quantity which had never been achieved by any mathematician before Euler. Finally, the third work, E798, which was published in 1849 at the Opera postuma, was probably the first among the three works, to be written by Euler

Tópicos de teoria dos números algébricos e aplicações em reticulados e equações diofantinas

Pós-graduação em Matemática Universitária - IGCE

Uma contribuição a teoria dos números e reticulados

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A história escolar e a teoria da atividade: relações e possibilidades formativas no ensinar e aprender

This study investigates the manner in which the Activity Theory by Alexei Nikolaevich Leontiev contributed to the performance of a teacher who teaches History at the 8th year of elementary school, Escola Estadual Coronel Fernandes, in Luís Gomes - RN city. Her goal is to analyze the contributions of this theory in her teaching practice. It was opted by collaborative approach as formative strategy and was used as procedures for training of knowing the courses of study and thoughtful reflection sessions. It was used as techniques in the development of these cycles, the semistructured interview and the reflection sessions, the autoscopy and observation in real life. Regarding the theoretical foundation, held in these cycles, the teacher demonstrated to have appropriated some contributions from Activity Theory, besides relating them to her practice and understanding her importance to the improvement of teaching and learning of History. Concerning to the reflection sessions, the analysis showed that the participant has used of constructions of this theory and improved their practice, developing lessons of History so as to encourage student participation in oral and promote his integral development. The educational process, carried out on the practice of teacher, has shown an increase in her conscious learning that contributed to the improvement in their professional development. Before these findings, as needs for new thinking, this research recommends, especially the organization of teaching activities, based on this theory, which allows the teacher to improve the teaching and learning process contributing to student's full education

Taxa de câmbio: uma abordagem integrada - teoria e história econômica

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Um tratamento para os números reais via medição de segmentos: uma proposta, uma investigação

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Teoria e metodologia na escrita da História do Brasil: Afonso de Taunay e a Academia Brasileira de Letras

The history of historiography in recent decades has the breathing space needed in the concerns of historians and has been transformed into a research field with its own issues. Uploaded this in perspective, this paper aims to understand how aspects of the theory of history and methodology have been addressed by Afonso de Escragnolle Taunay (1876-1958). We selected the letters exchanged by the author, the speeches of acceptance at the ABL, some articles and books produced by Taunay in the 1930s. In the first decades of the twentieth century, when it sought to define the historiography and its limits in both the literature and social science sources, the subjectivity is presented as the final decision making of the author, especially those related to the new site production Taunay, the Brazilian Academy of Letters.

Era uma vez... uns números

Este artigo aborda os números de Friedman, sua história e curiosidades. Os números de Friedman são números inteiros positivos que podem ser expressos, numa determinada base de um sistema de numeração, como uma combinação dos seus algarismos e dos símbolos das quatro operações aritméticas elementares, bem como a potenciação e o uso de parêntesis.

Uma análise histórico-epistemológica do conceito de grupo

This work aims to analyze the historical and epistemological development of the Group concept related to the theory on advanced mathematical thinking proposed by Dreyfus (1991). Thus it presents pedagogical resources that enable learning and teaching of algebraic structures as well as propose greater meaning of this concept in mathematical graduation programs. This study also proposes an answer to the following question: in what way a teaching approach that is centered in the Theory of Numbers and Theory of Equations is a model for the teaching of the concept of Group? To answer this question a historical reconstruction of the development of this concept is done on relating Lagrange to Cayley. This is done considering Foucault s (2007) knowledge archeology proposal theoretically reinforced by Dreyfus (1991). An exploratory research was performed in Mathematic graduation courses in Universidade Federal do Pará (UFPA) and Universidade Federal do Rio Grande do Norte (UFRN). The research aimed to evaluate the formation of concept images of the students in two algebra courses based on a traditional teaching model. Another experience was realized in algebra at UFPA and it involved historical components (MENDES, 2001a; 2001b; 2006b), the development of multiple representations (DREYFUS, 1991) as well as the formation of concept images (VINNER, 1991). The efficiency of this approach related to the extent of learning was evaluated, aiming to acknowledge the conceptual image established in student s minds. At the end, a classification based on Dreyfus (1991) was done relating the historical periods of the historical and epistemological development of group concepts in the process of representation, generalization, synthesis, and abstraction, proposed here for the teaching of algebra in Mathematics graduation course

A Teoria dos jogos e as ciências sociais

Pós-graduação em Ciências Sociais - FFC

Números complexos e geogebra

Pós-graduação em Matemática em Rede Nacional - IBILCE