# Person: Gimena Ramos, Lázaro

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Gimena Ramos

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Lázaro

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Proyectos e Ingeniería Rural

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2342

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Publication Open Access Pohlke theorem: demonstration and graphical solution(Springer, 2017) Gimena Ramos, Faustino; Gimena Ramos, Lázaro; Goñi Garatea, Mikel; Gonzaga Vélez, Pedro; Proyectos e Ingeniería Rural; Landa Ingeniaritza eta ProiektuakShow more 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.Show more Publication Open Access Geometric locus associated with thriedra axonometric projections. Intrinsic curve associated with the ellipse generated(Springer, 2017) Gonzaga Vélez, Pedro; Gimena Ramos, Faustino; Gimena Ramos, Lázaro; Goñi Garatea, Mikel; Proyectos e Ingeniería Rural; Landa Ingeniaritza eta ProiektuakShow more In previous work on the axonometric perspective, the authors presented some graphic constructions that allowed a single and joint invariant description of the relations between an orthogonal axonometric system, its related orthogonal views, and oblique axonometric systems associated with it. Continuing this work and using only the items drawn on the frame plane, in this communication we start from the three segments, representing trirectangular unitary thriedra, joined in the origin and defining an axonometric perspective. Each is projected onto any direc-tion and the square root of the summa of the squares of these projections is deter-mined. We call this magnitude, orthoedro diagonal whose sides would be formed by the three projections axonometric unit segments. If the diagonal size is built from the origin of coordinates and onto the direction used, this describes a locus here called intrinsic curve associated with the ellipse. When the starting three segments represent an orthogonal axonometric perspective, the intrinsic curve as-sociated with the ellipse is a circle.Show more