Construções euclidianas e o desfecho de problemas famosos da geometria

Construction techniques with ruler and the compasses, fundamental on Euclidean geometry, have been related to modern algebraic theories such as solving equations and extension of bodies from the works by Paolo Ruffini (1765-1822), Niels Henrik Abel (1802-1829) and Evariste Galois (1811-1832). This relation could provide an answer to some famous problems, from ancient Greece, such as doubling the cube, the trisection Angle, the Quadrature of the Circle and the construction of regular polygons, which remained unsolved for over two thousand years. Also important for our purposes are the notions of algebraic numbers, transcendental and the criteria for constructability, of those numbers. The objective of this study is to reconstruct relevant steps of geometric constructions with ruler (unmarked) and the compasses, from the elementary to the outcome buildings, in the nineteenth century, considering those mentioned problems.

Simulação computacional da extração líquido-líquido fracionada de enzimas para produção de biodiesel

Liquid-liquid extraction is utilized for purification of biomolecules by Aqueous Biphasic Systems (ABS), since this process does not damage the biotechnological potential of these compounds. In this work, using the free software Scilab®, the fractionated liquid-liquid extraction was studied aiming a lipase (target enzyme) partition in a water + PEG + DEX system. Lisozime was considered as contaminant. As computer simulations has been extensively used when a first estimation of technical feasibility of process is desired, this work demonstred that the system is viable for recovery the 80 % till 90 % the target enzyme, but should be noted that the trial aimed only the fractionation of the enzyme target of a contaminant, not its concentration, which should be done by another process.

Biblioteca de escalonamento de tarefas em grid computacional - LIBTS

The use of computational grid simulators is particularly important for studying the algorithms of task scheduling. Through the simulators it’s possible to assess and compare the performance of different algorithms in various scenarios. Despite the simulation tools provide basic features for simulation in distributed environments, they don’t offer internal policies of task scheduling, so that the implementation of the algorithms must be realized by the user himself. Therefore, this study aims to present the library of task scheduling LIBTS (LIBrary Tasks Scheduling) which is developed and adapted to the SimGrid simulator to provide the users with a tool to analyze the algorithms of task scheduling in the computational grid.

Aplicações do fluxo de Ricci à teoria da relatividade geral: estudo dos buracos negros

The flow of Ricci is an analytical tool, and a similar equation for heat geometry, a diffusive process which acts on a variety of metrics Riemannian and thus can be used in mathematics to understand the topology of varieties and also in the study geometric theories. Thus, the Ricci curvature plays an important role in the General Theory of Relativity, characterized as a geometric theory, which is the dominant term in the Einstein field equations. The present work has as main objectives to develop and apply Ricci flow techniques to general relativity, in this case, a three-dimensional asymptotically flat Riemannian metric as a set of initial data for Einstein equations and establish relations and comparisons between them.

Máximos e mínimos na geometria euclidiana: uma abordagem histórica

The goal of this work is to perform a historical approach of important results about maxima and minima, on Euclidean geometry, involving perimeters, areas and volumes. As a highlight, we can mention the Dido’s isoperimetric problem and the Papus’s problem about the wit of the bees. In this context, with a concern didactic, we tried to use, whenever possible, the geometry classical formulas to the calculus of areas. On the other hand, in the case of isoperimetric inequality the techniques of differential and integral calculus became more suitable for our purposes.

A geometria da Esponja de Menger

Neste trabalho estudaremos algumas propriedades geom´etricas do fractal “Esponja de Menger”, que é um objeto matemático construído através de um processo recursivo infinito que o torna auto-semelhante. Além disso, a dimens˜ao de um fractal n˜ao é necessariamente um número inteiro, diferentemente do que ocorre com os objetos da Geometria Euclidiana. Mais ainda, a Esponja possui área infinita e volume nulo, fatos que demonstraremos ao longo deste texto.

Modelagem computacional das túnicas cardíacas para processamento e controle de qualidade

This paper considers a study of the anatomical features of the cardiac system and a three-dimensional model of the different tunics that comprise the heart wall, for processing and quality control of radiological images. The structures are built by the layer overlapping method, where a layer can be understood as a slice of the three-dimensional object. The pericardium, myocardium and endocardium were represented with three-dimensional cylinders and hexagons. The spatial arrangement of the cardiac system is determined by an background image of a real model, which values are defined according to the shape of the region and on the anatomical patients characteristics. The results are significant, considering the anatomical structures details, as well as the representation of the thicknesses of the regions of the heart wall. The validation of the anatomical model was accomplished through comparisons with dimensions obtained from a real model and allows verifying that the model is appropriate. The degree of representation will allow the verification of the influence of radiological parameters, morphometric peculiarities and stage of the diseases on the quality of the images, as well as on the performance of the Computer-Aided Diagnosis (CAD).

Influência de diferentes superfícies de implantes unitários com geometria do tipo hexágono externo, Platform Switching e Cone-Morse em osso tipo III e IV: estudo pelo método dos elementos finitos tridimensionais

Pós-graduação em Odontologia - FOA

Desenvolvimento do sistema computacional CARTOMORPH para processamento de imagens de sensoriamento remoto

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

Um ambiente computacional para emular em rede aplicações interativas desenvolvidas para televisão digital

Pós-graduação em Televisão Digital: Informação e Conhecimento - FAAC

Lewis Carroll, a educação e o ensino de geometria na Inglaterra vitoriana

Research partly motivated by Lewis Carroll's Euclid and his modern rivals (1879) portuguese translation, this paper presents some hermeneutical remarks taken as necessary to understand the context in which such book was produced. The paper focuses particularly on education, in general, and on the teaching of mathematics and Geometry in victorian England.

O uso da Geometria do Táxi no ensino de Análise Combinatória

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Uma proposta para o 6ºano do EF: primeiras formas de geometria espacial-construindo conceitos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Situações didáticas no ensino de geometria com o aplicativo GeoGebra

Pós-graduação em Matemática - IBILCE