O uso pedagógico de uma seqüência didática para a aquisição de algumas idéias relacionadas ao conceito de números complexos

The aim of the present work is to contribute to the teaching-learning process in Mathematics through an alternative which tries to motivate the student so that he/she will learn the basic concepts of Complex Numbers and realize that they are not pointless. Therefore, this work s general objective is to construct a didactic sequence which contains structured activities that intends to build up, in each student s thought, the concept of Complex Numbers. The didactic sequence is initially based on a review of the main historical aspects which begot the construction of those numbers. Based on these aspects, and the theories of Richard Skemp, was elaborated a sequence of structured activities linked with Maths history, having the solution of quadratic equations as a main starting point. This should make learning more accessible, because this concept permeates the students previous work and, thus, they should be more familiar with it. The methodological intervention began with the application of that sequence of activities with grade students in public schools who did not yet know the concept of Complex Numbers. It was performed in three phases: a draft study, a draft study II and the final study. Each phase was applied in a different institution, where the classes were randomly divided into groups and each group would discuss and write down the concepts they had developed about Complex Numbers. We also use of another instrument of analysis which consisted of a recorded interview of a semi-structured type, trying to find out the ways the students thought in order to construct their own concepts, i.e. the solutions of the previous activity. Their ideas about Complex Numbers were categorized according to their similarities and then analyzed. The results of the analysis show that the concepts constructed by the students were pertinent and that they complemented each other this supports the conclusion that the use of structured activities is an efficient alternative for the teaching of mathematics

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

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

Corpos brincantes: a cultura corporal do pastoril potiguar

Pastorais, Bailes Pastoris, Festa da Lapinha, Terno de Reis, Pastor, Pastoril Religioso ou Profano... Pastoris do Norte e Nordeste brasileiro. M ário de Andrade designou-o de Pastoril, folguedo de origem ibérica, tendo sua raiz primeira nos villancico. Considerando que o Pastoril é um folguedo popular, porque nele seus participantes engajam sua vida pessoal, sua cultura e suas influências, revelando modos de ser e compreender, que são interiorizados pelos brincantes a partir da vivência de seu contexto social múltiplo e de diferentes sentidos, é que situamos esse folguedo no mundo vivido fenomenológico. A investigação é de natureza fenomenológica, elucidando os elementos citados como cenário do vivido e do sensível. O presente trabalho tem como objetivo refletir sobre a compreensão de corpo encontrado nos pastoris norteriograndenses

Entre corpos reais e virtuais: reflexões da dança contemporânea para pensar o corpo na educação física

Esta pesquisa objetiva identifi car as novas confi gurações de corpo advindas da interconexão entre Dança e Tecnologia, bem como compreender de que maneiras essas confi - gurações se aproximam e contribuem para a compreensão de corpo na Educação Física. O recurso metodológico é a análise de imagens dos vídeos de dança: Digital Brazuca e Corpo Aberto. Os vídeos analisados apontam para um repertório de saberes, que podem ser problematizados na área, e contribuem para reconfi gurar a relação homem/ambiente. Nesse sentido, promovem a plasticidade e a polissemia de relações entre o carbono e o silício, e desenham outras formas de compressão do corpo que incluem a complexidade, a incerteza, a reversibilidade e a descoberta

Estudo comparativo da área ocupada pelos corpos pedunculados no cérebro de duas espécies de abelhas (Hymenoptera, Apoidea)

The present study compare the size of the corpora pedunculata (mushroom bodies) of Exomalopsis aureopilosa a quasi-social specie and Apis mellifera a eusocial specie of bees. The aim was to correlate the developmental degree of such structures with the behavior complexity. The results show that the female specimens of both species have the corpora pedunculata with same relative size. However the area occupied by the neurones cellular bodies (glomeruli) is greater in the workers of A. mellifera. In other way in E. aureopilosa the total size of the corpora pedunculata is larger in females, but the glomeruli area is relatively larger in the male.

Lipoperoxidação, perda de viabilidade celular e diminuição da liberação de IL-8 de neutrófilos humanos na presença de corpos cetônicos

Type-1 diabetes patients suffer from frequent episodes of acidosis caused by an increased fatty acid metabolism and consequently increased plasma level of acetoacetate (AcAc) and β-hydroxybutyrate (β-HOB). This article describes a study of the effects of pathological concentrations of AcAc and β-HOB on lipoperoxidation, cell viability and the release of the CXCL8 (IL-8) cytokine by activated neutrophils. Neutrophils from healthy donors were isolated by density gradient (Histopaque® 1077/1119) and incubated with the ketone bodies. Lipoperoxidation was determined as thiobarbituric acid reactive substances (TBARS). The cell viability was evaluated by the release of intracellular lactate dehydrogenase. The release of CXCL8 was measured by ELISA in a 24-h culture of opsonized zymosan-stimulated neutrophils. AcAc, but not β-HOB, provoked a dose-dependent increase in the neutrophil membrane lipoperoxidation (p<0.05; r =0.9915). In the cytotoxicity assay, a dose-dependent release of LDH was observed when the neutrophils were incubated with AcAc in concentrations up to 40 mM (p<0.05). β-HOB was devoid of effect. The release of CXCL8 was inhibited by AcAc and β-HOB in a dose-dependent manner. In conclusion, these results suggest that the accumulation of ketone bodies in diabetic patients could be involved in their usually increased susceptibility to infection.

Cem números da Revista CEPAL: mil olhares sobre o desenvolvimento da América Latina e do Caribe

Incluye Bibliografía

Estudo comparativo com diferentes números de pontes na neurorrafia término-lateral em ratos

Pós-graduação em Bases Gerais da Cirurgia - FMB

Tàpies e seus corpos: um olhar sexuado

Pós-graduação em Artes - IA

Efeitos do inseticida fipronil sobre os corpos pedunculados de operárias de Scaptotrigona postica (Hymenoptera, Apidae, Meliponini)

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

Estudo do escoamento ao redor de cilindros elípticos

Pós-graduação em Engenharia Mecânica - FEIS

Simulação numérica de escoamentos hipersônicos sobre corpos rombudos pelo método de elementos finitos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Estudo analítico/numérico do problema de ablação em corpos rombudos com simetria axial

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)