A DENSIDADE DOS NÚMEROS REAIS: CONCEPÇÕES DE PROFESSORES DA EDUCAÇÃO BÁSICA

Este artículo presenta el tema de la densidad de los números reales y discute las concepcionesde maestros de la enseñanza secundaria sobre esta propiedad. No describe solamente lasconcepciones, pero también las reacciones de los maestros frente a la proposición de dosprocedimientos para obtener un numero real entre otros dos: el procedimiento de la mediaaritmética de los números dados y un procedimiento inspirado en el método de ladiagonalización usado por Cantor para probar que el conjunto de los números reales entre ceroy uno, no es numerable. A partir del cuestionamiento sobre la posibilidad de comenzar losestudios ya en la enseñanza secundaria, que puedan contribuir para la comprensión de lapropiedad de densidad de los números reales, relata la disponibilidad manifestada por losparticipantes de la investigación en usar la intervención propuesta en sus clases, por juzgarlaadecuada y exequible.Palabras clave: números reales y irracionales, densidad de los números reales; representacióndecimal infinita; recta realResumoO artigo aborda o tema da densidade dos números reais e discute as concepções deprofessores do Ensino Médio sobre tal propriedade. Descreve não só as concepções, mastambém as reações dos professores frente à proposta de dois procedimentos para a obtenção deum número real entre dois outros: o procedimento da média aritmética dos números dados eum procedimento inspirado no método da diagonalização utilizado por Cantor para provar queo conjunto dos números reais entre zero e um, não é enumerável. A partir do questionamentosobre a possibilidade de se iniciar estudos, já na Educação Básica, que possam contribuir paraa compreensão da propriedade da densidade dos números reais, relata a disponibilidademanifestada por participantes da investigação em utilizar a intervenção proposta em suasaulas, por julgarem-na adequada e exeqüível.Palavras chave: números racionais e irracionais; densidade dos números reais; representaçãodecimal infinita; reta real.THE DENSITY OF REAL NUMBERS:CONCEPTIONS OF TEACHERS OF BASIC EDUCATIONAbstractThe paper discusses the density of real numbers and the conceptions of teachers of high schoolon this property. Describes not only the concepts but also the reactions of teachers against theproposed two procedures for obtaining a real number between two others numbers: theprocedure of the arithmetic mean of two supplied and a procedure based on the Cantor’sdiagonalization argument used to prove that the set of real numbers between zero and one,have no countable enumeration. From the question on the possibility to initiate studies, as inBasic Education, which may contribute to the understanding of the density property of realnumbers, reports the readiness expressed by participants in the research using the proposedintervention in their classes by judging if it is appropriate and feasible.Keywords: rational and irrational numbers; density of the real numbers; infinite decimalrepresentation; straight line which represents real numbers

Princípios Ágeis Aplicados à Reengenharia de Software

Abstract. Agile application development and Software Product Line (SPL) are techniques which, although having the common objective of improving the software productivity, have requirements seemingly contradictory that prevent them to be used together. This paper proposes a feature-based iterative reengineering approach for the modernization of legacy systems and the creation of a core of reusable artifacts to support the development of SPL. Agile principles and techniques are applied across the whole process that foresees continuous interactions with the customer, deliveries of tested executable and partially modernized versions in short and frequent intervals, with documentation in appropriate level and prepared for changes. Resumo. Desenvolvimento ágil de aplicações e Linhas de Produtos de Software (LPS) são técnicas que, embora tenham o objetivo comum de melhorar a produtividade de software, possuem requisitos aparentemente contraditórios, que dificultam seu uso conjunto. Este trabalho propõe uma abordagem de reengenharia iterativa, orientada a características par

New species of Chelonus (Microchelonus) Szépligeti, 1908 (Hymenoptera: Braconidae: Cheloninae) from Brazil

Chelonus (Microchelonus) murici sp. nov. (Hymenoptera: Braconidae: Cheloninae) is described in this work. It was reared from an unknown host in murici fruits, Byrsonima verbascifolia (L.) Rich. ex A. L. Juss. (Malpighiaceae), a species from the Brazilian savannah whose fruits are widely consumed by the population in northern Brazil. The adult of this new species is illustrated

Vascularized osteochondral graft from the medial femoral trochlea: anatomical study and clinical perspectives

PURPOSE: Few donor sites for vascularized reconstruction of convex joint surfaces have been described. We studied the feasibility of a convex vascularized osteochondral graft harvested from the medial femoral condyle and trochlea, on an anatomical and practical point of view. METHODS: An injection-corrosion technique was used on 16 fresh cadaver specimens, and completed by a modified Spalteholz clearing. The extra- and intraosseous vascularization of the medial femoral condyle was systematized and the luminal diameter of the arteries was microscopically measured. Radii of curvature of the medial trochlea and of the carpal bones were measured on arthro-CT-scanner reconstructed images. RESULTS: The periosteal vessels of the medial condyle are responsible for the whole peripheral intraosseous vascularization, without any watershed region. They are fed by the articular branch of the descending genicular artery and/or the superomedial genicular artery. Several constant vascular axes can be found, and may serve as a pedicle for a vascularized osteochondral graft from the medial femoral trochlea. The radii of curvature of this graft do fit those of the proximal carpal row. A simple surgical approach is suggested. CONCLUSIONS: A vascularized graft harvested on the medial femoral trochlea is a technically feasible procedure that could represent a new reconstructive tool for convex joint surfaces. Osteonecrosis of the proximal pole of the scaphoid or Kienböck's disease are among several situation