Pohlke's Theorem

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Pohlke’s Theorem


the fundamental theorem of ax-onometry. First stated, without proof, by the German geometer K. Pohlke in 1860, it asserts that three coplanar line segments of arbitrary length that issue at arbitrary angles from a given point constitute the parallel projection of three equal and mutually perpendicular segments issuing from a point in space. It follows from the theorem that any three segments in the plane of projection that share a common endpoint can be taken as the projection of a set of three orthogonal coordinate axes with identical scales on the axes.

Pohlke’s theorem was generalized by the German mathematician H. Schwarz, who provided an elementary proof of it in 1864. The general theorem states that any nondegenerate complete quadrangle can be considered as a parallel projection of a tetrahedron of preassigned shape.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.