Gaspard Monge | |
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| Born | (1746-05-09)9 May 1746 |
| Died | 28 July 1818(1818-07-28) (aged 72) |
| Resting place | Père Lachaise Cemetery |
| Known for | Descriptive geometry Transportation theory |
| Scientific career | |
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| Notable students | Jean-Baptiste Biot[1] Charles Dupin Sylvestre François Lacroix Jean-Victor Poncelet[1] |
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Gaspard Monge, Comte dePéluse (French:[ɡaspaʁmɔ̃ʒkɔ̃tdəpelyz]; 9 May 1746[2] – 28 July 1818)[3] was a French mathematician, commonly presented as the inventor ofdescriptive geometry,[4][5] (the mathematical basis of)technical drawing, and the father ofdifferential geometry.[6]
He contributed alongside chemistBerthollet, chemist and physicianChaptal, andpolymathLaplace to the establishment ofArts et Métiers ParisTech.
During theFrench Revolution he served as the Minister of the Marine, and was involved in thereform of the French educational system, helping to found, with Lamblardie andLazare Carnot, theÉcole Polytechnique, France's most prestigious engineering school.
Monge was born atBeaune,Côte-d'Or, the son of a merchant. He was educated at the college of theOratorians atBeaune.[5] In 1762 he went to theCollège de la Trinité atLyon, where, one year after he had begun studying, he was made a teacher ofphysics[5] at the age of seventeen.[7]
After finishing his education in 1764 he returned to Beaune, where he made a large-scale plan of the town, inventing the methods of observation and constructing the necessary instruments; the plan was presented to the town, and is still preserved in their library.[5] An officer of engineers who saw it wrote to the commandant of theÉcole Royale du Génie atMézières, recommending Monge to him and he was given a job as adraftsman.[5]L. T. C. Rolt, an engineer and historian of technology,credited Monge with the birth of engineering drawing.[8] When in the Royal School, he became a member of aFreemasonry, initiated into″L’Union parfaite″ lodge.[9]
Those studying at the officer school were exclusively drawn from the aristocracy, so he was not allowed admission to the institution itself. His manual skill was highly regarded, but his mathematical skills were not made use of. Nevertheless, he worked on the development of his ideas in his spare time. At this time he came to contact withCharles Bossut, the professor of mathematics at the École Royale du Génie. "I was a thousand times tempted," he said long afterwards, "to tear up my drawings in disgust at the esteem in which they were held, as if I had been good for nothing better."[5]
After a year at the École Royale, Monge was asked to produce adéfilement plan for a fortification in such a way as to optimise its defensive arrangement. In military terminology,défilement is "the science of aligning the summits of fortifications in a vertical plane, so as to evade gunfire from a height outside the fortress".[10][11]
A fort should protect the defenders. That is, from any point on the terrain outside, there cannot be directline of sight into defending positions inside. This safe space is called thedefilade, and could be pictured as follows: Place a lamp at each location where the attacker may fire, then the shadow space cast by the walls is thedefilade. Thedéfilement is a kind ofdefilade, where the attackers may be raised above the ground. This would protect the defenders against artillery placed on raised platforms built during a siege.Defilade anddéfilement would avoidenfilade.
A particularly dangerous kind of artillery fire isenfilade fire. The top edge of a fort wall is a polygonal line. On each segment, defenders can move. If an attacker can place an artillery on a point along that straight segment, then the attacker can shoot directly along the line, and hit all the defenders on that line segment.
Computing thedéfilement is a complex problem, since to counter the development of artillery, European forts was becoming increasingly complicated in their geometry, as represented by thestar fort. The famous military engineerVauban proposed a slow and manual process to measure thedéfilement. Soldiers would be sent to strategically critical positions outside the fort. At each position, they would measure the shape of the polygonal line created by the upper edge of thecurtain wall. This creates a sequence of triangles that together create a polygonal dome in space. The space under the polygonal dome would then be thedéfilement of the walls, within which the defenders are safe from direct lines of sight.[12]
Other than the observational method, there was also an established method for doing this, which involved lengthy calculations that would take a week, but Monge devised a way of solving the problems by using drawings. At first his solution was not accepted, since it had only taken two days, but upon examination the value of the work was recognised, and Monge's exceptional abilities were recognised. The essence of Monge's method was to graphically construct visibility cones. For example, consider a hemisphereH, with a raised pointp aboveH, representing a point on the fortification wall. The visibility cone atp is a cone that is tangent toH and apexed atp. Continuing his researches, Monge began the subject descriptive geometry, which was kept as a French military secret for years.[5][13]
After Bossut left the École Royale du Génie, Monge took his place in January 1769, and in 1770 he was also appointed instructor in experimental physics.[7]
In 1777, Monge married Cathérine Huart, who owned aforge. This led Monge to develop an interest inmetallurgy. In 1780 he became a member of theFrench Academy of Sciences; his friendship with chemistC. L. Berthollet began at this time.[5] In 1783, after leaving Mézières, he was, on the death ofÉ. Bézout, appointed examiner of naval candidates.[5] Although pressed by the minister to prepare a complete course of mathematics, he declined to do so on the grounds that this would deprive Mme Bézout of her only income, that from the sale of thetextbooks written by her late husband.[5] In 1786 he wrote and published hisTraité élémentaire de la statique.[5]
TheFrench Revolution completely changed the course of Monge's career. He was a strong supporter of the Revolution, and in 1792, on the creation by theLegislative Assembly of an executive council, Monge accepted the office ofMinister of the Navy,[5] and held this office from 10 August 1792 to 10 April 1793, when he resigned.[7] When theCommittee of Public Safety made an appeal to the academics to assist in the defence of the republic, he applied himself wholly to these operations, and distinguished himself by his energy, writing theDescription Le l'art de Fabriquer Les canons andAvis aux ouvriers en fer sur la fabrication de l'acier.[5]
He took a very active part in the measures for the establishment of theEcole Normale (which existed only during the first four months of the year 1795), and of the school for public works, afterwards theÉcole Polytechnique, and was at each of them professor for descriptive geometry.[5]Géométrie descriptive. Leçons données aux écoles normales was published in 1799 from transcriptions of his lectures given in 1795. He later publishedApplication de l'analyse à la géométrie,[5] which enlarged on the Lectures.
From May 1796 to October 1797 Monge was inItaly with C.L. Berthollet and some artists to select the paintings and sculptures being levied from the Italians.[5] While there he became friendly withNapoleon. Upon his return to France, he was appointed as the Director of theÉcole Polytechnique, but early in 1798 he was sent toItaly on a mission that ended in the establishment of the short-livedRoman Republic.[5]
From there Monge joinedNapoleon's expedition to Egypt, taking part with Berthollet[5] in the scientific work of theInstitut d'Égypte and theEgyptian Institute of Sciences and Arts. They accompanied Napoleon toEgypt, and returned with him in 1799 to France.[5] Monge was appointed president of the Egyptian commission, and he resumed his connection with the École Polytechnique.[5] His later mathematical papers are published (1794–1816) in the Journal and the Correspondence of the École Polytechnique. On the formation of theSénat conservateur he was appointed a member of that body, with an ample provision and the title of count ofPelusium[5] (Comte de Péluse), and he became the Senate conservateur's president during 1806–7. Then on the fall of Napoleon he had all of his honours taken away, and he was even excluded from the list of members of the reconstituted Institute.[5]
Napoleon Bonaparte stated Monge was anatheist.[14][15] His remains were first interred in amausoleum inLe Père Lachaise Cemetery in Paris and later transferred to thePanthéon in Paris.
Astatue portraying him was erected in Beaune in 1849. Monge's name is one of the72 names inscribed on the base of the Eiffel Tower.
Since 4 November 1992 theMarine Nationale operate theMRISMonge, named after him.
Between 1770 and 1790 Monge contributed various papers on mathematics and physics to theMemoirs of the Academy of Turin, theMémoires des savantes étrangers of the Academy of Paris, theMémoires of the same Academy, and theAnnales 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),[5] 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.[5] It is also noteworthy to mention that in hisMémoire sur quelques phénomènes de la vision Monge proposed an early implicit explanation of thecolor constancy phenomenon based on several known observations.
Leonhard Euler, in his 1760 paper on curvature in theBerlin 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.[5] 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.[5]
Monge's 1781 memoir is also the earliest known anticipation oflinear optimization problems, in particular of theearth-mover's problem, a special case of theoptimal 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 asL. V. Kantorovich,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 ofhydrogen. Monge's results had been anticipated byHenry Cavendish.[5] 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 liquefysulfur dioxide by passing a stream of the gas through a U-tube sunken in a refrigerant mixture of ice and salt.[16] This made them the first to liquefy a pure gas.[17]
Yet, sailing to Egypt, he had lain on deck, asking his scientists whether the planets were inhabited, how old the Earth was, and whether it would perish by fire or by flood. Many, like his friend Gaspard Monge, the first man to liquefy a gas, were atheists.
Media related toGaspard Monge at Wikimedia Commons| Political offices | ||
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| Preceded by | Minister of the Navy and the Colonies 10 August 1792 – 10 April 1793 | Succeeded by |
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