A Proposition of Rigid Studies Related To Area And To The Calculus Of Variations

摘要

The object of this note is to establish for bivoctors in m- space, and in particular for bivectors in 4-space or what amounts to the same for forces and couples in 3-space, the existence of an appropriate polyhedron with a plane boundary, provided that the given bisectors have a bivector as their resultant. This polyhedron is made up of faces obtained by a subdivision and translation from the triangles whose oriented areas represent the given bivectors, and by the addition if necessary of further triangles whose total area is arbitrarily small.