109 resultados para Euclidean isometry
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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
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This paper presents some outcomes from research based on classroom experiences. The main themes are the use of mirrors, kaleidoscopes, dynamic geometry software, and manipulative material considering their possibilities for the teaching and learning of Euclidean and non-Euclidean geometries.
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The soybean crop is considered a high expression around the world. In plant breeding programs, knowledge of genetic diversity is extremely important and in this context, are frequently used multivariate analyzes. Thus, the aim of the present study was to evaluate the genetic divergence between soybean crosses through multivariate techniques. In total, 16 crosses were evaluated, which were in the F2 generation of inbreeding. The evaluated characteristics were plant height at maturity, height of the first pod, number of branches per plant, number of pods per plant, number of nodes per plant, hundred seed weight, grain yield and oil content. For the analyzes was used Euclidean distance, methods of hierarchical clustering UPGMA and Ward and principal component analysis. Genetic distances estimated using Euclidean distance ranged from 1.24 to 8.13, with the smallest distance observed between crosses C1 and C4, and the greatest distance between the C2 crosses and C6. The methods UPGMA clustering and Ward met crossings in five different groups. The principal component analysis explained 86.2% of the variance contained in the original eight variables with three main components. The APM characters, NV, NR, NN, PG% and oil were the main contributors to genetic divergence among traits. Multivariate techniques were crucial to the analysis of genetic diversity, and the methods of Ward and UPGMA clustering and principal components have consistent results in this way, the simultaneous use of these tools in genetic analysis of crosses is indicated
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This research aims to understand how students of Early Childhood Education (considering the range of 2-3 years) build the space - geometric notions from the interaction established with the school routine. The venue was a municipal school Miners Tietê, within the State of São Paulo. The interest in this research took place from two reasons: the first because of course taken “Mathematics in Early Childhood Education” and the second stemmed from my professional work in a school for early childhood education. This research is initially composed by bibliographic studies concerning the topic and was grounded in a qualitative interpretive approach, aiming to investigate the psychological process of building space - geometric notions in children. The procedures used in the initial research to collect data were interviews using the method of clinical type and Piagetian tests. Thus allows us to understand the construction of the geometric space by children in their topological, projective and Euclidean relations
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Pós-graduação em Agronomia (Produção Vegetal) - FCAV
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Pós-graduação em Agronomia (Genética e Melhoramento de Plantas) - FCAV
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Pós-graduação em Matemática em Rede Nacional - IBILCE
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Pós-graduação em Matemática em Rede Nacional - IBILCE
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
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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.
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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.