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Abstract(s)
Este trabalho, foi elaborado como pré requisito para a obtenção do grau de mestre,
no âmbito do curso de mestrado em Matemática para Professores. Pretendemos
desenvolver o tema “Plano Projetivo e Construções com Régua” com o intuito último
de despertar o interesse de estudantes e professores da área da Matemática, no
sentido de promover esta subárea da Geometria com muita importância do ponto
de vista da história, investigação e aplicações da Matemática. Descrevemos a matem
ática do plano projetivo: pontos, retas, coordenadas homogéneas, transformações
projetivas, o Teorema Fundamental do Plano Projetivo, o princípio da dualidade,
os teoremas de Desargues, Pappus, Pascal e seus duais, formas bilineares e cónicas.
Apresentamos ainda a resolução de alguns problemas relacionados sobre construções
com régua não-graduada que envolvem aplicações dos teoremas estudados.
This work was elaborated as a prerequisite for obtaining the master's degree, within the framework of the master's degree in Mathematics for Teachers. We intend to develop the theme “Projective Plan and Constructions with Ruler” with the ultimate purpose of attracting the interest of students and teachers to this subarea of Geometry, which has a great importance from the point of view of history, in research and applications of Mathematics. We describe the mathematics of the projective plane: points, lines, homogeneous coordinates, projective transformations, the Fundamental Theorem of the Projective Plane, the principle of duality, the theorems of Desargues, Pappus, Pascal and their dual, bilinear and conic forms. We also present the resolution of some problems related to constructions with a non-graded rule that involve applications of the theorems previously studied.
This work was elaborated as a prerequisite for obtaining the master's degree, within the framework of the master's degree in Mathematics for Teachers. We intend to develop the theme “Projective Plan and Constructions with Ruler” with the ultimate purpose of attracting the interest of students and teachers to this subarea of Geometry, which has a great importance from the point of view of history, in research and applications of Mathematics. We describe the mathematics of the projective plane: points, lines, homogeneous coordinates, projective transformations, the Fundamental Theorem of the Projective Plane, the principle of duality, the theorems of Desargues, Pappus, Pascal and their dual, bilinear and conic forms. We also present the resolution of some problems related to constructions with a non-graded rule that involve applications of the theorems previously studied.
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Keywords
Cónicas Construções Com Régua Coordenadas Homogéneas Plano Projetivo Razão Cruzada Transforma- Ções Projetivas