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Curvas cónicas e superfícies geradas pelas curvas cónicas : os seus traçados geométricos e aplicações no design
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| 12.19 MB | Adobe PDF |
Authors
Abstract(s)
No âmbito do Design, é graficamente, sistematiza-se e aprofunda-se o conhecimento das curvas cónicas e, em especial, sobre as suas construções geométricas, contribuindo para o reconhecimento da importância do estudo destas curvas e das superfícies geradas a partir delas no ensino da geometria no Design. Utiliza-se um método expositivo de análise crítica do conhecimento existente, propondo-se ângulos de abordagem menos usuais. Procura-se, ainda, suprir o insuficiente conhecimento e divulgação científica das cónicas em Portugal, e em particular no Design, de três modos: pela sistematização do conhecimento existente, pela adaptação do conhecimento da geometria projetiva, com expressão na geometria plana e na geometria analítica, para a linguagem dos traçados geométricos em geometria plana e em geometria descritiva e, ainda, pela contribuição para a utilização mais generalizada, designadamente com os meios tecnológicos atuais.
Paralelamente, identificam-se potencialidades das curvas na capacidade de resolução de problemas de representação gráfica rigorosa, por designers e outros profissionais, designadamente os das áreas das artes visuais e da arquitetura, com reflexos no ensino e na prática profissional. Exemplificam-se utilizações dos traçados das curvas cónicas e das superfícies geradas com elas, no Design e em outras áreas, simplificando soluções e reafirmando a importância e atualidade da geometria plana e da geometria descritiva, tanto no processo de construção do conhecimento e no desenvolvimento do projeto, como nas aplicações práticas, enquanto suporte conceptual e representação gráfica.
Tendo em vista a simplificação da aplicação das cónicas e das superfícies geradas com elas em projetos de Design, resolveram-se alguns problemas com solução complexa, ou sem solução, na literatura consultada. Para tal, utilizámos métodos menos usuais, designadamente alguns derivados da geometria descritiva e, sobretudo, procurando integrar os conhecimentos mais recentes sobre as cónicas.
Tal abordagem permitiu ainda o aprofundamento de conhecimento com potencial interesse teórico em diversas áreas e o enunciar de algumas propriedades das cónicas que não se encontraram descritas na literatura, numa relação dialética entre teoria e prática, num contexto que contribui para a reafirmação da geometria descritiva, na sua capacidade de desenvolvimento do pensamento criativo.
Abstract : In context of Design, and graphically, this research aims to systematize and to deepen the knowledge about the conical curves, and especially on their geometrical constructions, contributing to the recognition of the importance of the study of theses curves and of the surfaces generated from them, mainly in the teaching of geometry in Design courses. An expositive methodology of critical analysis of literature is used, proposing less usual approaches. It also aims to compensate insufficient knowledge and scientific dissemination of conical curves in Portugal, particularly in Design, in three ways: systematizing the existent knowledge, adapting knowledge of projective geometry in plane and analytical geometry for the language of geometrical constructions in plane geometry and descriptive geometry and, still, contributing to a more generalized use involving recent technology. Parallel, the study identifies potentialities of the conical curves in solving problems of rigorous graphic representation for designers and other professionals, namely those from the areas of visual arts and of architecture, with reflexes in the teaching and in the professional practice. It gives examples of practical uses of graphic resolutions of conical curves and of their generated surfaces in Design and other areas, reassuring the importance and relevance of plane geometry and descriptive geometry, both in the construction of knowledge and in the development of the project and in practical applications, as a conceptual framework and graphic representation. Within the scope of simplifying the use of conics and surfaces generated with them in Design projects, are presented solutions for some problems with complex solutions, or without solution, in reviewed literature. The study approach contributes not only to deepen the theoretical frame in several areas but also enunciates some proprieties of conics not mentioned yet in literature, in a dialectical relationship between theory and practice, in a context that contributes to the reaffirmation of descriptive geometry and its capacity of development of creative thinking.
Abstract : In context of Design, and graphically, this research aims to systematize and to deepen the knowledge about the conical curves, and especially on their geometrical constructions, contributing to the recognition of the importance of the study of theses curves and of the surfaces generated from them, mainly in the teaching of geometry in Design courses. An expositive methodology of critical analysis of literature is used, proposing less usual approaches. It also aims to compensate insufficient knowledge and scientific dissemination of conical curves in Portugal, particularly in Design, in three ways: systematizing the existent knowledge, adapting knowledge of projective geometry in plane and analytical geometry for the language of geometrical constructions in plane geometry and descriptive geometry and, still, contributing to a more generalized use involving recent technology. Parallel, the study identifies potentialities of the conical curves in solving problems of rigorous graphic representation for designers and other professionals, namely those from the areas of visual arts and of architecture, with reflexes in the teaching and in the professional practice. It gives examples of practical uses of graphic resolutions of conical curves and of their generated surfaces in Design and other areas, reassuring the importance and relevance of plane geometry and descriptive geometry, both in the construction of knowledge and in the development of the project and in practical applications, as a conceptual framework and graphic representation. Within the scope of simplifying the use of conics and surfaces generated with them in Design projects, are presented solutions for some problems with complex solutions, or without solution, in reviewed literature. The study approach contributes not only to deepen the theoretical frame in several areas but also enunciates some proprieties of conics not mentioned yet in literature, in a dialectical relationship between theory and practice, in a context that contributes to the reaffirmation of descriptive geometry and its capacity of development of creative thinking.
Description
Keywords
Cónicas Curvas cónicas Superfícies Superfícies quádricas Design Conics Conical curves Surfaces Quadric surfaces