Page "Gaspard Monge" Paragraph 15

**" Sur la théorie des déblais et des remblais " ( Mém.

de l ’ acad.

de Paris, 1781 ), which is an elegant investigation of the problem with earthworks referred to in the title and establishes in connection with it his capital discovery of the curves of curvature of a surface.

Leonhard Euler, in his 1760 paper on curvature in the Berlin Memoirs for, had considered, not the normals of the surface, but the normals of the plane sections through a particular normal, so that the question of the intersection of successive normals of the surface had never presented itself to him.

Monge's paper gives the ordinary differential equation of the curves of curvature, and establishes the general theory in a very satisfactory manner ; the application to the interesting particular case of the ellipsoid was first made by him in a later paper in 1795.

( Monge's 1781 memoir is also the earliest known anticipation of Linear Programming type of problems, in particular of the transportation problem.

Related to that, the Monge soil-transport problem leads to a weak-topology definition of a distance between distributions rediscovered many times since by such as L. V. Kantorovich, P. Levy, L. N. Wasserstein, and others ; and bearing their names in various combinations in various contexts.