Jean-Victor Poncelet | |
|---|---|
 | |
| Born | (1788-07-01)1 July 1788 |
| Died | 22 December 1867(1867-12-22) (aged 79) |
| Alma mater | École Polytechnique |
| Known for | Poncelet wheel Poncelet's porism Poncelet–Steiner theorem Trilinear polarity |
| Awards | Pour le Mérite (1863) ForMemRS (1842) |
| Scientific career | |
| Fields | Mathematics,engineering |
| Institutions | École d'application de l'artillerie ofMetz University of Paris École Polytechnique |
| Academic advisors | Gaspard Monge[1][2] |
| Signature | |
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Jean-Victor Poncelet (French pronunciation:[ʒɑ̃viktɔʁpɔ̃slɛ]; 1 July 1788 – 22 December 1867) was aFrenchengineer andmathematician who served most notably as the Commanding General of theÉcole Polytechnique. He is considered a reviver ofprojective geometry, and his workTraité des propriétés projectives des figures is considered the first definitive text on the subject sinceGérard Desargues' work on it in the 17th century. He later wrote an introduction to it:Applications d'analyse et de géométrie.[3]
As a mathematician, his most notable work was inprojective geometry, although an early collaboration withCharles Julien Brianchon provided a significant contribution toFeuerbach's theorem. He also made discoveries aboutprojective harmonic conjugates; relating these to the poles and polar lines associated withconic sections. He developed the concept of parallel lines meeting at apoint at infinity and defined thecircular points at infinity that are on every circle of the plane. These discoveries led to theprinciple of duality, and theprinciple of continuity and also aided in the development ofcomplex numbers.[3]
As a military engineer, he served inNapoleon's campaign against theRussian Empire in 1812, in which he was captured and held prisoner until 1814. Later, he served as aprofessor ofmechanics at the École d'application in his home town ofMetz, during which time he publishedIntroduction à la mécanique industrielle, a work he is famous for, and improved the design ofturbines andwater wheels. While a professor of applied mechanics, he also, independently fromCoriolis, pioneered the use ofwork in mechanics and thework-energy theorem, including coining the term "mechanical work".[4] In 1837, a tenured 'Chaire de mécanique physique et expérimentale' was specially created for him at the Sorbonne (theUniversity of Paris).[5] In 1848, he became the commanding general of hisalma mater, theÉcole Polytechnique.[3] He is honoured by having his name listed among notable French engineers and scientists displayed around the first stage of theEiffel tower.
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Poncelet was born inMetz, France, on 1 July 1788, theillegitimate then legitimated[6] son of Claude Poncelet, alawyer of the Parliament of Metz and wealthy landowner.[7] His mother, Anne-Marie Perrein, had a more modest background.[8] At a young age, he was sent to live with the Olier family atSaint-Avold.[9] He returned to Metz for his secondary education, atLycée Fabert.[7] After this, he attended theÉcole Polytechnique, a prestigious school inParis, from 1808 to 1810, though he fell behind in his studies in his third year due to poor health.[7] After graduation, he joined the Corps ofMilitaryEngineers. He attended the École d'application in his hometown during this time, and achieved the rank oflieutenant in theFrench Army the same year he graduated.[10]
Poncelet took part inNapoleon'sinvasion of Russia in 1812. His biographerDidion writes that he was part of the group which was cut from MarshalMichel Ney's army at theBattle of Krasnoi and was forced to capitulate to the Russians,[11] though other sources say that he was left for dead.[7] Upon capture, he was interrogated byGeneralMikhail Andreyevich Miloradovich, but he did not disclose any information.[12] The Russians held him as aprisoner of war and confined him atSaratov.[13] During his imprisonment, in the years 1812–1814, he wrote his most notable work,Traité des propriétés projectives des figures, which outlined the foundations of projective geometry, as well as some new results. Poncelet, however, could not publish it until after his release in 1814.[3]
In 1815, the year after his release, Poncelet was employed a military engineer at his hometown of Metz. In 1822, while at this position, he publishedTraité des propriétés projectives des figures. This was the first major work to discussprojective geometry since Desargues', thoughGaspard Monge had written a few minor works about it previously. It is considered the founding work of modern projective geometry.[10]Joseph Diaz Gergonne also wrote about this branch of geometry at approximately the same time, beginning in 1810. Poncelet published several papers about the subject inAnnales de Gergonne (officially known asAnnales de mathématiques pures et appliquées).[3] However, Poncelet and Gergonne ultimately engaged in a bitter priority dispute over the Principle of Duality.[10]
In 1825, he became the professor ofmechanics at the École d'Application in Metz, a position he held until 1835. During his tenure at this school, he improved the design ofturbines andwater wheels, deriving his work from the mechanics of theProvençal mill from southern France.[14] Although the turbine of his design was not constructed until 1838, he envisioned such a design twelve years previous to that.[3] In 1835, he left École d'Application, and in December 1837 became a tenured professor at Sorbonne (theUniversity of Paris), where a 'Chaire de mécanique physique et expérimentale' was specially created for him with the support ofLouis Jacques Thénard.[15]
In 1848, Poncelet became the Commanding General of hisalma mater, the École Polytechnique.[16] He held the position until 1850, when he retired.
During this time, he wroteApplications d'analyse et de géométrie, which served as an introduction to his earlier workTraité des propriétés projectives des figures. It was published in two volumes in 1862 and 1864.[17] He was elected a Foreign Honorary Member of theAmerican Academy of Arts and Sciences in 1865.[18]
Poncelet discovered the following theorem in 1822:Euclideancompass and straightedge constructions can be carried out using only astraightedge if a singlecircle and its center is given. Swiss mathematicianJakob Steiner proved this theorem in 1833, leading to the name of the theorem. The constructions that this theorem states are possible are known as Steiner constructions.[19]
Ingeometry,Poncelet's porism (sometimes referred to asPoncelet's closure theorem) states that whenever apolygon isinscribed in oneconic section andcircumscribes another one, the polygon must be part of an infinite family of polygons that are all inscribed in and circumscribe the same two conics.[20][21]
