Editing Gaspard Monge (section)

== Work==
Between 1770 and 1790 Monge contributed various papers on mathematics and physics to the ''Memoirs of the Academy of Turin'', the ''Mémoires des savantes étrangers'' of the Academy of Paris, the ''Mémoires'' of the same Academy, and the ''[[Annales de chimie]]'', including "''Sur la théorie des déblais et des remblais''" ["On the theory of cut and fill"] (''Mém. de l’acad. de Paris'', 1781),<ref name=EB1911/> 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.<ref name=EB1911/> It is also noteworthy to mention that in his ''Mémoire sur quelques phénomènes de la vision'' Monge proposed an early implicit explanation of the [[color constancy]] phenomenon based on several known observations.

[[Leonhard Euler]], in his 1760 paper on curvature in the ''Berlin Memoirs'', 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.<ref name=EB1911/> 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.<ref name=EB1911/>

Monge's 1781 memoir is also the earliest known anticipation of [[Linear programming|linear optimization]] problems, in particular of the [[Transportation theory (mathematics)|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]], [[Paul Lévy (mathematician)|Paul Lévy]], [[Leonid Vaseršteĭn]], and others; and bearing their names in various combinations in various contexts.

Another of his papers in the volume for 1783 relates to the production of water by the combustion of [[hydrogen]]. Monge's results had been anticipated by [[Henry Cavendish]].<ref name=EB1911/> It was also in this time, from 1783 - 1784, that Monge worked with (Jean-François, Jean-Baptiste-Paul-Antoine, or Abbé Pierre-Romain) Clouet to liquefy [[sulfur dioxide]] by passing a stream of the gas through a U-tube sunken in a refrigerant mixture of ice and salt.<ref>Taton, Rene. “Some Details About The Chemist Clouet and Two of His Namesakes.” Review of the History of Sciences and Their Applications, vol. 5, no. 4, 1952, p. 359–67. {{JSTOR|23905084}}.</ref> This made them the first to liquefy a pure gas.<ref>{{cite web |last=Wisniak |first=Jaime |title=Louis Paul Cailletet—The liquefaction of the permanent gases |date=2003 |url=https://nopr.niscpr.res.in/bitstream/123456789/22723/1/IJCT%2010%282%29%20223-236.pdf }}</ref>

<!-- this section has no references
== Students ==

* [[Charles Julien Brianchon]]
* [[Jean-Victor Poncelet]]
*[[Antoine-François Lomet]]
*[[Barnabé Brisson (engineer)|Barnabé Brisson]]
*[[Théodore Olivier]]
*[[Sylvestre François Lacroix]]
*[[Charles de Tinseau d'Amondans]]
*[[Théodore Olivier]]
*[[Charles Dupin]]
*[[Edme-François Jomard]]
*[[François Arago]]
*[[Joseph Fourier]]
*[[Michel Ange Lancret]]
*Guy de Vernon
*Coulomb
*Carnot
-->