Guilherme de La Penha: uma história do seu itinerário intelectual em três dimensões

This study focuses on the central Brazilian historiography of science, focusing specifically on the life and work of a contemporaneous mathematician-physicist, and becomes part of the set of research results that investigate, organize and describe personal, intellectual and professional itineraries of Brazilian scientists and educators. The theme chosen for the study ran from seminars on Mathematics in Pará and is up to organize and describe the life history, education, professional experience and scientific production of William Mauricio Souza Marcos de La Penha (Guilherme de La Penha), considering their academic, professional and intellectual life history, so that their academic and intellectual production be spread over the Brazilian scientific and academic community. We adopted the historical research as theoretical and methodological base for the development of this study, rising arguments about the profile of Guilherme de La Penha to characterize him as a multiskill intellectual and to reveal that his thoughts about science, technology, training scientists and educators were in accordance with their writings and their professional practice in order to build a first story about the life and work of William de La Penha. In this sense, we took the theoretical aspects related to historical research, biographies, intellectual itineraries, files and inventories as sources and historical construction vehicles in order to point out the essential elements to form a profile of the transdisciplinary intellectual historians, ie a profile scientist who carries out the research, management and administration, as well as a committed educator to the on-going training and forming process. The results pointed in different directions, among which we highlight the creation of Seção Guilherme de La Penha at Universidade da Amazonia, producing several articles about the life and work of William de La Penha presented at national and international conferences and the proposal for documentary displays which could contribute to understanding the implementation of a scientific area in Pará State, an area that would not only be restricted to the production of knowledge, but more than that, it would include the spreading, which provides various means, primarily through education. Thus it was possible to ensure that La Penha has an intellectual profile that can be considered a multi-and transdisciplinary intellectual who defends the possibility of forming a scientist one and multiple, non-linear attitudes and dialogues with all other areas in order to be understood under a model scientist for the twenty-first century based on the model clearly inspired by the scientist authors with which he identified throughout their training and professional activities, like the three that stood out in their relationship science: Archimedes, Leonhard Euler and Cliford Ambrose Truesdell

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

Fernando Fajnzylber: una visión renovadora del desarrollo en América Latina

Incluye Bibliografía

Los mercados y el Estado en la evolución del "manifiesto" de Prebisch

Ensayo presentado en homenaje a Raúl Prebisch

A representação do feio na arte: um breve estudo sobre quatro gravuras de Francisco Goya

Pós-graduação em Artes - IA

Pintura Naïve: características e análises - quatro exemplos em São Paulo

Pós-graduação em Artes - IA

Vozes do tempo em Octavio Paz

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Astrojildo Pereira e a formação do Partido Comunista Brasileiro

Pós-graduação em História - FCLAS

O vôo da trapezista alada: uma leitura da trajetória de Fevvers em Noites no circo de Angela Carter

Pós-graduação em Letras - FCLAS

Phoenissae de Sêneca: estudo introdutório, tradução e notas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Laurindo Almeida: dos trilhos de Miracatu às trilhas em Hollywood

Pós-graduação em Música - IA

O estranho perfeito: a música orquestral de Franz Zappa. -

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Um palimpsesto em andamento: formas e reformas de uma personagem azevediana

Pós-graduação em Estudos Literários - FCLAR

Guerreiro Ramos e a redenção sociológica: capitalismo e sociologia no Brasil

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Laurindo Almeida: dos trilhos de Miracatu às trilhas em Hollywood

Pós-graduação em Música - IA