Pohlke theorem: demonstration and graphical solution
Fecha
2017Versión
Acceso abierto / Sarbide irekia
Tipo
Contribución a congreso / Biltzarrerako ekarpena
Versión
Versión aceptada / Onetsi den bertsioa
Impacto
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10.1007/978-3-319-45781-9_98
Resumen
It is known that the axonometric defined by Pohlke, is geometrically known as a means of representing the figures of space using a cylindrical projec-tion and proportions. His theorem says that the three unit vectors orthogonal axes of the basis in the space can be transformed into three arbitrary vectors with com-mon origin located in the frame plane. Another way of expressing this theorem is gi ...
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It is known that the axonometric defined by Pohlke, is geometrically known as a means of representing the figures of space using a cylindrical projec-tion and proportions. His theorem says that the three unit vectors orthogonal axes of the basis in the space can be transformed into three arbitrary vectors with com-mon origin located in the frame plane. Another way of expressing this theorem is given in three segments mismatched and incidents at one point in a plane, there is a trirectangular unitary thriedra in the space that can be transformed in these three segments. This paper presents a graphical procedure to demonstrate a solution of Pohlke¿s theorem. To do this, we start from previous work by the authors on the axonometric perspective. Graphic constructions that allow a single joint invariant description of relationships between an orthogonal axonometric oblique axono-metric system and systems associated thereby. At a same time of the geometric lo-cus generated by the diagonal magnitude positioned at any direction in the plane of the picture. This magnitude is the square root of the sum of the squares of the projection of the three segments representing axonometric on arbitrary magnitude. [--]
Materias
Axonometric system,
Descriptive geometry,
Pohlke theorem
Editor
Springer
Publicado en
Eynard, B.; Nigrelli, V.; Oliveri, S. M.; Peris-Fajarnes, G.; Rizzuti, S. (Eds.). Advances on Mechanics, Design Engineering and Manufacturing: proceedings of the International Joint Conference on Mechanics, Design Engineering & Advanced Manufacturing (JCM 2016). Berlín: Springer; 2017. p.981-988 978-3-319-45780-2
Departamento
Universidad Pública de Navarra. Departamento de Proyectos e Ingeniería Rural /
Nafarroako Unibertsitate Publikoa. Landa Ingeniaritza eta Proiektuak Saila