Pohlke Theorem: Demonstration and Graphical Solution

Abstract

It is known that the axonometric defined by Pohlke, is geometrically known as a means of representing the figures of space using a cylindrical projection 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 common 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 axonometric system and systems associated thereby. At a same time of the geometric locus 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.