Joseph Fourier 1

Joseph Fourier

Joseph Fourier

Jean Baptiste Joseph Fourier

Born 21 March 1768Auxerre, Burgundy, Kingdom of France (now in Yonne, France)

Died 16 May 1830 (aged 62)Paris, Kingdom of France

Residence France

Nationality French

Fields Mathematician, Physicist, and historian

Institutions École NormaleÉcole Polytechnique

Alma mater École Normale

Doctoral advisor Joseph-Louis Lagrange

Doctoral students Peter Gustav Lejeune DirichletGiovanni PlanaClaude-Louis Navier

Known for Fourier seriesFourier transformFourier's law of conduction

Jean Baptiste Joseph Fourier (21 March 1768 – 16 May 1830) was a French mathematician and physicist born inAuxerre and best known for initiating the investigation of Fourier series and their applications to problems of heattransfer and vibrations. The Fourier transform and Fourier's Law are also named in his honour. Fourier is alsogenerally credited with the discovery of the greenhouse effect.

BiographyFourier was born at Auxerre (now in the Yonne département of France), the son of a tailor. He was orphaned at agenine. Fourier was recommended to the Bishop of Auxerre, and through this introduction, he was educated by theBenedictine Order of the Convent of St. Mark. The commissions in the scientific corps of the army were reserved forthose of good birth, and being thus ineligible, he accepted a military lectureship on mathematics. He took aprominent part in his own district in promoting the French Revolution, serving on the local RevolutionaryCommittee. He was imprisoned briefly during the Terror but in 1795 was appointed to the École NormaleSupérieure, and subsequently succeeded Joseph-Louis Lagrange at the École Polytechnique.

Joseph Fourier 2

Fourier accompanied Napoleon Bonaparte on his Egyptian expedition in 1798, as scientific adviser, and wasappointed secretary of the Institut d'Égypte. Cut off from France by the English fleet, he organized the workshops onwhich the French army had to rely for their munitions of war. He also contributed several mathematical papers to theEgyptian Institute (also called the Cairo Institute) which Napoleon founded at Cairo, with a view of weakeningEnglish influence in the East. After the British victories and the capitulation of the French under General Menou in1801, Fourier returned to France.

1820 watercolor caricatures of French mathematicians Adrien-MarieLegendre (left) and Joseph Fourier (right) by French artist

Julien-Leopold Boilly, watercolor portrait numbers 29 and 30 ofAlbum de 73 Portraits-Charge Aquarelle’s des Membres de

I’Institute.[1]

In 1801, Napoleon appointed Fourier Prefect(Governor) of the Department of Isère in Grenoble,where he oversaw road construction and other projects.However, Fourier had previously returned home fromthe Napoleon expedition to Egypt to resume hisacademic post as professor at École Polytechniquewhen Napoleon decided otherwise in his remark

... the Prefect of the Department of Isère havingrecently died, I would like to express my confidence incitizen Fourier by appointing him to this place.

Hence being faithful to Napoleon, he took the office ofPrefect. It was while at Grenoble that he began toexperiment on the propagation of heat. He presentedhis paper On the Propagation of Heat in Solid Bodiesto the Paris Institute on December 21, 1807. He alsocontributed to the monumental Description del'Égypte.[2]

Fourier moved to England in 1816. Later, he returned to France, and in 1822 succeeded Jean Baptiste JosephDelambre as Permanent Secretary of the French Academy of Sciences. In 1830, he was elected a foreign member ofthe Royal Swedish Academy of Sciences.

In 1830, his diminished health began to take its toll:Fourier had already experienced, in Egypt and Grenoble, some attacks of aneurism of the heart. At Paris,it was impossible to be mistaken with respect to the primary cause of the frequent suffocations which heexperienced. A fall, however, which he sustained on the 4th of May 1830, while descending a flight ofstairs, aggravated the malady to an extent beyond what could have been ever feared.

Shortly after this event, he died in his bed on 16 May 1830.Fourier was buried in the Père Lachaise Cemetery in Paris, a tomb decorated with an Egyptian motif to reflect hisposition as secretary of the Cairo Institute, and his collation of Description de l'Égypte. His name is one of the 72names inscribed on the Eiffel Tower.

Joseph Fourier 3

Rosetta StoneIn 1801, Fourier returned from Egypt on the Napoleon expedition with many artifacts including an ink pressed copyof the Rosetta Stone. The original stone was discovered in 1799, and by 1802, a translation of the ancient Greek texthad already been popularly printed.Born in 1790 as the seventh son to an impoverished family, young Jean-Francois Champollion joined his elderbrother at Académie de Grenoble in 1801; Fourier became Prefect of Grenoble the same year. Champollion wasquickly recognized as a virtuoso and self-educated linguist. Fourier and Champollion met and Fourier introducedChampollion (then age 11) to an ink pressed copy of the Rosetta Stone. Champollion, amazed that none haddeciphered its meaning, dedicated himself to the translation of ancient Egyptian. In 1806, Champollion with thecontinued support of Fourier and his elder brother, Jacques, presented a paper on Coptic at Académie de Grenoblewith insight to ancient Egyptian. Furthermore in 1809, Champollion returned after 2 years in Paris to Académie deGrenoble after being helped by Fourier to gain exemption from military service. Ultimately, Fourier's first influentialencounter with Champollion and subsequent relationship largely supported Champollion's translation of ancientEgyptian from 1822 to 1824 when he finally gained widespread fame for his breakthrough publication.

The Analytic Theory of HeatIn 1822 Fourier published his work on heat flow in Théorie analytique de la chaleur (The Analytic Theory of Heat),in which he based his reasoning on Newton's law of cooling, namely, that the flow of heat between two adjacentmolecules is proportional to the extremely small difference of their temperatures. This book was translated,[3] witheditorial 'corrections',[4] into English 56 years later by Freeman (1878).[5] The book was also edited, with manyeditorial corrections, by Darboux and republished in French in 1888.

Sketch of Fourier, circa 1820.

There were three important contributions in this work, one purelymathematical, two essentially physical. In mathematics, Fourierclaimed that any function of a variable, whether continuous ordiscontinuous, can be expanded in a series of sines of multiples ofthe variable. Though this result is not correct, Fourier's observationthat some discontinuous functions are the sum of infinite serieswas a breakthrough. The question of determining when a Fourierseries converges has been fundamental for centuries. Joseph-LouisLagrange had given particular cases of this (false) theorem, andhad implied that the method was general, but he had not pursuedthe subject. Peter Gustav Lejeune Dirichlet was the first to give asatisfactory demonstration of it with some restrictive conditions.

One physical contribution in the book was the concept ofdimensional homogeneity in equations; i.e. an equation can beformally correct only if the dimensions match on either side of theequality; Fourier made important contributions to dimensionalanalysis.[6] The other physical contribution was Fourier's proposal of his partial differential equation for conductivediffusion of heat. This equation is now taught to every student of mathematical physics.

Joseph Fourier 4

Determinate equationsFourier left an unfinished work on determinate equations which was edited by Claude-Louis Navier and published in1831. This work contains much original matter — in particular, there is a demonstration of Fourier's theorem on theposition of the roots of an algebraic equation. Joseph-Louis Lagrange had shown how the roots of an algebraicequation might be separated by means of another equation whose roots were the squares of the differences of theroots of the original equation. François Budan, in 1807 and 1811, had enunciated the theorem generally known bythe name of Fourier, but the demonstration was not altogether satisfactory. Fourier's proof is the same as that usuallygiven in textbooks on the theory of equations. The final solution of the problem was given in 1829 by JacquesCharles François Sturm.

Discovery of the greenhouse effectIn the 1820s Fourier calculated that an object the size of the Earth, and at its distance from the Sun, should beconsiderably colder than the planet actually is if warmed by only the effects of incoming solar radiation. Heexamined various possible sources of the additional observed heat in articles published in 1824 and 1827. While heultimately suggested that interstellar radiation might be responsible for a large portion of the additional warmth,Fourier's consideration of the possibility that the Earth's atmosphere might act as an insulator of some kind is widelyrecognized as the first proposal of what is now known as the greenhouse effect.[7]

Bust of Fourier in Grenoble

In his articles, Fourier referred to an experiment by de Saussure,[8] wholined a vase with blackened cork. Into the cork, he inserted severalpanes of transparent glass, separated by intervals of air. Middaysunlight was allowed to enter at the top of the vase through the glasspanes. The temperature became more elevated in the more interiorcompartments of this device. Fourier concluded that gases in theatmosphere could form a stable barrier like the glass panes.[9] Thisconclusion may have contributed to the later use of the metaphor of the'greenhouse effect' to refer to the processes that determine atmospherictemperatures. Fourier noted that the actual mechanisms that determinethe temperatures of the atmosphere included convection, which wasnot present in de Saussure's experimental device.

Joseph Fourier 5

Fourier's grave, Père Lachaise Cemetery

Works

• Fourier, Joseph (1822). Théorie analytique de lachaleur [10]. Paris: Firmin Didot Père et Fils.

• Fourier, Joseph (1824). Annales de chimie et dephysique [11] 27. Paris: Annals of Chemistry andPhysics. pp. 236–281.

• Fourier, Joseph (1827). Mémoire sur la températuredu globe terrestre et des espaces planétaires [12] 7.Memoirs of the Royal Academy of Sciences of theInstitut de France. pp. 569–604.

• Fourier, Joseph (1827). Mémoire sur la distinctiondes racines imaginaires, et sur l'application des théorèmes d'analyse algébrique aux équations transcendantesqui dépendent de la théorie de la chaleur [13] 7. Memoirs of the Royal Academy of Sciences of the Institut deFrance. pp. 605–624.

• Fourier, Joseph (1827). Analyse des équations déterminées [14] 10. Firmin Didot frères. pp. 119–146.• Fourier, Joseph (1827). Remarques générales sur l'application du principe de l'analyse algébrique aux équations

transcendantes [15] 10. Paris: Memoirs of the Royal Academy of Sciences of the Institut de France. pp. 119–146.• Fourier, Joseph (1833). Mémoire d'analyse sur le mouvement de la chaleur dans les fluides [16] 12. Paris:

Memoirs of the Royal Academy of Sciences of the Institut de France. pp. 507–530.• Fourier, Joseph (1821). Rapport sur les tontines [17] 5. Paris: Memoirs of the Royal Academy of Sciences of the

Institut de France. pp. 26–43.

References[1] Boilly, Julien-Leopold. (1820). Album de 73 Portraits-Charge Aquarelle’s des Membres de I’Institute ( watercolor portrait (http:/ / translate.

google. com/ translate?js=y& prev=_t& hl=en& ie=UTF-8& layout=1& eotf=1& u=http:/ / www. photo. rmn. fr/ cf/ htm/ CSearchZ.aspx?E=2K1KTS6T7WAMK& SubE=2C6NU00YI4TE& sl=auto& tl=en) #29). Biliotheque de l’Institut de France.

[2] Nowlan, Robert. A Chronicle of Mathematical People ([www.robertnowlan.com/pdfs/Fourier,%20Joseph.pdf])[3] Freeman, A. (1878). The Analytical Theory of Heat, Cambridge University Press, Cambridge UK, cited by Truesdell, C.A. (1980), The

Tragicomical History of Thermodynamics, 1822–1854, Springer, New York, ISBN 0-387-90403-4, page 52.[4] Truesdell, C.A. (1980). The Tragicomical History of Thermodynamics, 1822–1854, Springer, New York, ISBN 0-387-90403-4, page 52.[5][5] Digital Image Processing by Rafeel Gonzalez and Richard E Woods ,Third Edition , Pg 200 , PHI Eastern Economy Edition.[6] Mason, Stephen F.: A History of the Sciences (Simon & Schuster, 1962), p. 169.[7] Weart, S. (2008). The Carbon Dioxide Greenhouse Effect (http:/ / www. aip. org/ history/ climate/ co2. htm). Retrieved on 27 May 2008[8][8] fr:Horace-Bénédict de Saussure[9] Translation by W M Connolley of: Fourier 1827: MEMOIRE sur les temperatures du globe terrestre et des espaces planetaires (http:/ / www.

wmconnolley. org. uk/ sci/ fourier_1827/ fourier_1827. html)[10] http:/ / books. google. com/ books?id=TDQJAAAAIAAJ[11] http:/ / books. google. com/ books?id=1Jg5AAAAcAAJ& dq=Annales+ de+ chimie+ et+ de+ physique+ volume+ 27&[12] http:/ / gallica. bnf. fr/ ark:/ 12148/ bpt6k32227. image. r=memoires+ de+ l%27academie+ des+ sciences. f808. langEN[13] http:/ / gallica. bnf. fr/ ark:/ 12148/ bpt6k32227/ f844. image. r=memoires+ de+ l'academie+ des+ sciences. langEN[14] http:/ / num-scd-ulp. u-strasbg. fr:8080/ 827/[15] http:/ / gallica. bnf. fr/ ark:/ 12148/ bpt6k32255. image. r=memoires+ de+ l%27academie+ des+ sciences. f346. langEN[16] http:/ / gallica. bnf. fr/ ark:/ 12148/ bpt6k3227s. image. r=memoires+ de+ l%27academie+ des+ sciences. f620. langEN[17] http:/ / gallica. bnf. fr/ ark:/ 12148/ bpt6k3220m. image. f568. pagination. langEN

Joseph Fourier 6

Further reading• Initial text from the public domain Rouse History of Mathematics• Fourier, Joseph. (1822). Theorie Analytique de la Chaleur. Firmin Didot (reissued by Cambridge University

Press, 2009; ISBN 978-1-108-00180-9)• Fourier, Joseph. (1878). The Analytical Theory of Heat. Cambridge University Press (reissued by Cambridge

University Press, 2009; ISBN 978-1-108-00178-6)• Fourier, J.-B.-J. (1824). Mémoires de l'Académie Royale des Sciences de l'Institut de France VII. 570–604 (http:/

/ www. academie-sciences. fr/ activite/ archive/ dossiers/ Fourier/ Fourier_pdf/ Mem1827_p569_604. pdf)(Mémoire sur Les Temperatures du Globe Terrestre et Des Espaces Planetaires – greenhouse effect essaypublished in 1827)

• The Project Gutenberg EBook of Biographies of Distinguished Scientific Men (http:/ / www. gutenberg. org/etext/ 16775) by François Arago

•• Fourier, J. Éloge historique de Sir William Herschel, prononcé dans la séance publique de l'Académie royale dessciences le 7 Juin, 1824. Historie de l'Académie Royale des Sciences de l'Institut de France, tome vi., année 1823,p. lxi.[Pg 227]

External links

Wikisource has the text of a 1906 New International Encyclopedia article about Joseph Fourier.

Wikiquote has quotations related to: Joseph Fourier

• O'Connor, John J.; Robertson, Edmund F., "Joseph Fourier" (http:/ / www-history. mcs. st-andrews. ac. uk/Biographies/ Fourier. html), MacTutor History of Mathematics archive, University of St Andrews.

• Fourier, J. B. J., 1824, Remarques Générales Sur Les Températures Du Globe Terrestre Et Des EspacesPlanétaires., in Annales de Chimie et de Physique, Vol. 27, pp. 136–167 – translation by Burgess (1837). (http:/ /fourier1824. geologist-1011. mobi)

• Fourier 1827: MEMOIRE sur les températures du globe terrestre et des espaces planétaires (http:/ / www.wmconnolley. org. uk/ sci/ fourier_1827/ fourier_1827. html)

• Université Joseph Fourier, Grenoble, France (http:/ / www. ujf-grenoble. fr)• Joseph Fourier and the Vuvuzela (http:/ / blog. mathsbank. co. uk/ 2010/ 06/ joseph-fourier-and-vuvuzela. html)

on MathsBank.co.uk (http:/ / mathsbank. co. uk)• Joseph Fourier (http:/ / www. genealogy. ams. org/ id. php?id=17981) at the Mathematics Genealogy Project• Joseph Fourier – Œuvres complètes, tome 2 (http:/ / portail. mathdoc. fr/ cgi-bin/ oetoc?id=OE_FOURIER__2)

Gallica-Math• Joseph Fourier, Théorie analytique de la chaleur (http:/ / books. google. de/ books?id=TDQJAAAAIAAJ&

pg=PA525) Google books

Article Sources and Contributors 7

Article Sources and ContributorsJoseph Fourier  Source: http://en.wikipedia.org/w/index.php?oldid=618154212  Contributors: 67th Tigers, Acather96, Akriasas, Akritas2, Alan U. Kennington, Alansohn, Anon user, Antandrus,Arjen Dijksman, Arthur Rubin, Avicennasis, Avjoska, AxelBoldt, BRG, Badseed, Bassbonerocks, Bcent1234, Bender235, Benjaminevans82, Bergsten, Bethpage89, Bob Burkhardt, Bostonbetty,Bunzil, CALR, CBDunkerson, CLC Editorial, CSWarren, CambridgeBayWeather, Cantiorix, Carcharoth, Causesobad, Charles Matthews, Chenopodiaceous, Chjoaygame, Courcelles,CousinJohn, Coyau, Cp111, Cubs Fan, D6, DARTH SIDIOUS 2, David Eppstein, David Le Page, David.Monniaux, DerHexer, Derek Ross, Dialectric, Discospinster, Djordjes, Docu, DoulosChristos, Dreadstar, Eliyak, Emerson7, Eoghanc, Eric-Wester, Erkcan, Ethically Yours, Eusebius, Expert12, Fallenfromthesky, Father Time89, Foolip, Gadfium, Gareth Owen, Garion96, Gauss,Giftlite, GirasoleDE, GoingBatty, Graham87, Guitarspecs, Gullanian, Harel, Hede2000, Hektor, HueSatLum, Islescape, J.delanoy, Jake Wartenberg, Jan1nad, Jaredwf, Jauhienij, Jer ome,Jiuguang Wang, Jmc, Joe Canuck, John, John of Reading, John254, Jojit fb, Jormundgard, Josce, Juansempere, Jumbuck, K.C. Tang, Kev 847, Kgrad, Khym Chanur, Knutux, Kraxler, La GrandeReverteur, Lee2008, Lenthe, Levalley, Libb Thims, Lockley, Looxix, Lukerobinson001, LutzL, Lzur, Mackensen, Majilis, MarkSweep, Martin451, MathMartin, Mav, MiLo28, Michael Hardy,Michur, Miguel Chong, Mikeh98245, Monegasque, Moreschi, Moskvax, Mottaku, Myasuda, Nbarth, Neddyseagoon, Nickpowerz, Nimetapoeg, Ninmacer20, Nk, Numbo3, OccultZone,Ohnoitsjamie, Olivier, Omnipaedista, Oracleofottawa, Ouzel Ring, PDH, Palica, Philippebcn, Pi, Plucas58, Poppy, Pufferfish101, Qutezuce, Qwertylurker, Raonisousa, Ravn, Resurgentinsurgent, Rich Farmbrough, Richard Harvey, Ricochet17, Rob Hooft, RoddyYoung, Rrburke, Rubicon, Ruud Koot, Salih, Sasank2102, Schlier22, Sean.hoyland, Short Brigade Harvester Boris,Sjakkalle, Smeira, Snoyes, Snurddnert, Some jerk on the Internet, SteelGray, Stevan White, Stonehead, Studerby, SuperGirl, SureFire, SusikMkr, Tbvdm, The Anome, The Red, TheCajun80,TheJJJunk, Thorwald, Titodutta, Tom Lougheed, Tomas e, Tomisti, Tommy2010, Towerman, Triona, Triwbe, Turgidson, Ulric1313, Vaughan Pratt, Vina, Vsmith, Waltor, WikHead, Wikiborg,Wile E. Heresiarch, William M. Connolley, Woohookitty, XJaM, Xchbla423, Yamamoto Ichiro, Yerpo, Yurivict, Zandetroit, Александър, 302 ,ساجد امجد ساجد anonymous edits

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