Pohlke's theorem

It was established 1853 by the German painter and teacher of descriptive geometry Karl Wilhelm Pohlke.

The first proof of the theorem was published 1864 by the German mathematician Hermann Amandus Schwarz, who was a student of Pohlke.

For a mapping of a unit cube, one has to apply an additional scaling either in the space or in the plane.

Because a parallel projection and a scaling preserves ratios one can map an arbitrary point

Pohlke's theorem can be stated in terms of linear algebra as: Pohlke's theorem is the justification for the following easy procedure to construct a scaled parallel projection of a 3-dimensional object using coordinates,:[2][3] In order to get undistorted pictures, one has to choose the images of the axes and the forshortenings carefully (see Axonometry).