Joseph Fourier 1

Joseph Fourier

Joseph Fourier

Jean Baptiste Joseph Fourier

Born 21 March 1768Auxerre, Yonne, France

Died 16 May 1830 (aged 62)Paris, France

Residence France

Nationality French

Fields Mathematician, physicist, and historian

Institutions École NormaleÉcole Polytechnique

Alma mater École Normale

Doctoral advisor Joseph Lagrange

Doctoral students Gustav 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 bestknown for initiating the investigation of Fourier series and their applications to problems of heat transfer andvibrations. The Fourier transform and Fourier's Law are also named in his honour. Fourier is also generally creditedwith the discovery of the greenhouse effect.[1]

LifeFourier was born at Auxerre (now in the Yonne département of France), the son of a tailor. He was orphaned at ageeight. Fourier was recommended to the Bishop of Auxerre, and through this introduction, he was educated by theBenvenistes of the Convent of St. Mark. The commissions in the scientific corps of the army were reserved for thoseof good birth, and being thus ineligible, he accepted a military lectureship on mathematics. He took a prominent partin his own district in promoting the French Revolution, and was rewarded by an appointment in 1795 in the ÉcoleNormale Supérieure, and subsequently by a chair at the École Polytechnique.Fourier went with Napoleon Bonaparte on his Egyptian expedition in 1798, and was made governor of Lower Egypt and secretary of the Institut d'Égypte. Cut off from France by the English fleet, he organized the workshops on which the French army had to rely for their munitions of war. He also contributed several mathematical papers to the Egyptian Institute (also called the Cairo Institute) which Napoleon founded at Cairo, with a view of weakening

Joseph Fourier 2

English influence in the East. After the British victories and the capitulation of the French under General Menou in1801, Fourier returned to France, and was made prefect of Isère, and it was while there that he made his experimentson the propagation of heat.

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.[2]

In 1806 he quit the post of full professor at the ÉcolePolytechnique because Napoleon sent him to Grenoble.He was replaced by Siméon Denis Poisson.

Fourier moved to England in 1816. Later he returned toFrance, and in 1822 succeeded Jean Baptiste JosephDelambre as Permanent Secretary of the FrenchAcademy of Sciences. In 1830, he was elected a foreignmember of the Royal Swedish Academy of Sciences.

Fourier believed that keeping the body wrapped up inblankets was beneficial to the health. He died in 1830when in this state he tripped and fell down the stairs athis home.[3]

Fourier was buried in the Pere Lachaise Cemetery inParis, a tomb decorated with an Egyptian motif toreflect his position as secretary of the Cairo Institute,and his collation of the landmark Description del'Égypte. His name is one of the 72 names inscribed onthe Eiffel Tower.

Théorie analytique de la chaleur

In 1822 Fourier presented his work on heat flow in Théorie analytique de la chaleur (The Analytic Theory ofheat),[4] in which he based his reasoning on Newton's law of cooling, namely, that the flow of heat between twoadjacent molecules is proportional to the extremely small difference of their temperatures. This book wastranslated[5] , with editorial 'corrections'[6] into English 56 years later by Freeman (1878).[7] The book was alsoedited, with many editorial corrections, by Darboux and republished in French in 1888.[6]

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. Johann Dirichlet was the first to give a satisfactorydemonstration of it with some restrictive conditions. One physicalcontribution in the book was the concept of dimensionalhomogeneity in equations; i.e. an equation can only be formallycorrect if the dimensions match on either side of the equality.

Joseph Fourier 3

Fourier also developed dimensional analysis, the method of representing physical units, such as velocity andacceleration, by their fundamental dimensions of mass, time, and length, to obtain relations between them.[8] Theother physical contribution was Fourier's proposal of his partial differential equation for conductive diffusion of heat,which is now taught to every student of mathematical physics.

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 effect"In 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 only by the effects of incoming solar radiation. Heexamined various possible sources of the additional observed heat in articles published in 1824[9] and 1827.[10]

While he ultimately suggested that interstellar radiation might be responsible for a large portion of the additionalwarmth, Fourier's consideration of the possibility that the Earth's atmosphere might act as an insulator of some kindis widely recognized as the first proposal of what is now known as the greenhouse effect.[11]

Bust of Fourier in Grenoble

In his articles Fourier referred to an experiment by de Saussure[12] ,who lined 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.[13]. Fourier concluded that gases in theatmosphere could form a stable barrier like the glass panes. 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 4

Fourier's grave, Pere Lachaise

Works

• Fourier, Joseph (1822). Théorie analytique de lachaleur [14]. Paris: Firmin Didot Père et Fils.

• Fourier, Joseph (1824). Annales de chimie et dephysique [15]. 27. Paris: Annals of Chemistry andPhysics. pp. 236-281.

• Fourier, Joseph (1827). Mémoire sur la températuredu globe terrestre et des espaces planétaires [16]. 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 desthéorèmes d'analyse algébrique aux équationstranscendantes qui dépendent de la théorie de lachaleur [17]. 7. Memoirs of the Royal Academy ofSciences of the Institut de France. pp. 605-624.

• Fourier, Joseph (1827). Analyse des équationsdéterminées [18]. 10. Firmin Didot frères.pp. 119-146.

• Fourier, Joseph (1827). Remarques générales surl'application du principe de l'analyse algébrique aux équations transcendantes [19]. 10. Paris: Memoirs of theRoyal 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 [20]. 12. Paris:Memoirs of the Royal Academy of Sciences of the Institut de France. pp. 507-530.

• Fourier, Joseph (1821). Rapport sur les tontines [21]. 5. Paris: Memoirs of the Royal Academy of Sciences of theInstitut de France. pp. 26-43.

Notes and references[1] Cowie, J. (2007). Climate Change: Biological and Human Aspects. Cambridge University Press. p. 3. ISBN 978-0521696197.[2] 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.

[3] "Fourier, Joseph (1768-1830)" (http:/ / scienceworld. wolfram. com/ biography/ Fourier. html). Science World Wolfram. . Retrieved2009-05-06.

[4] Fourier, Joseph (1822). Théorie analytique de la chaleur (http:/ / books. google. com/ books?id=TDQJAAAAIAAJ). Paris: Firmin Didot Pèreet Fils. .

[5] Freeman, A. (1878). The Analytical Theory of Heat, Cambridge University Press, Cambridge UK, cited by Truesdell, C.A. (1980), TheTragicomical History of Thermodynamics, 1822-1854, Springer, New York, ISBN 0-387-90403-4, page 52.

[6] Truesdell, C.A. (1980). The Tragicomical History of Thermodynamics, 1822-1854, Springer, New York, ISBN 0-387-90403-4, page 52.[7] Digital Image Processing by Rafeel Gonzalez and Richard E Woods ,Third Edition , Pg 200 , PHI Eastern Economy Edition.[8] Mason, Stephen F.: A History of the Sciences (Simon & Schuster, 1962), p. 169.[9] Fourier J (1824). "Remarques Générales Sur Les Températures Du Globe Terrestre Et Des Espaces Planétaires". Annales de Chimie et de

Physique 27: 136–67.[10] Fourier J (1827). "Mémoire Sur Les Températures Du Globe Terrestre Et Des Espaces Planétaires" (http:/ / visualiseur. bnf. fr/

StatutConsulter?N=sorel1. bnf. fr-1295037014309& B=1& E=PDF& O=NUMM-3370). Mémoires de l'Académie Royale des Sciences 7:569–604. .

[11] Weart, S. (2008). The Carbon Dioxide Greenhouse Effect (http:/ / www. aip. org/ history/ climate/ co2. htm). Retrieved on 27 May 2008

Joseph Fourier 5

[12] fr:Horace-Bénédict de Saussure[13] http:/ / www. wmconnolley. org. uk/ sci/ fourier_1827/ fourier_1827. html#text[14] http:/ / books. google. com/ books?id=TDQJAAAAIAAJ[15] http:/ / books. google. com/ books?id=1Jg5AAAAcAAJ& dq=Annales+ de+ chimie+ et+ de+ physique+ volume+ 27&[16] http:/ / gallica. bnf. fr/ ark:/ 12148/ bpt6k32227. image. r=memoires+ de+ l%27academie+ des+ sciences. f808. langEN[17] http:/ / gallica. bnf. fr/ ark:/ 12148/ bpt6k32227/ f844. image. r=memoires+ de+ l'academie+ des+ sciences. langEN[18] http:/ / num-scd-ulp. u-strasbg. fr:8080/ 827/[19] http:/ / gallica. bnf. fr/ ark:/ 12148/ bpt6k32255. image. r=memoires+ de+ l%27academie+ des+ sciences. f346. langEN[20] http:/ / gallica. bnf. fr/ ark:/ 12148/ bpt6k3227s. image. r=memoires+ de+ l%27academie+ des+ sciences. f620. langEN[21] http:/ / gallica. bnf. fr/ ark:/ 12148/ bpt6k3220m. image. f568. pagination. langEN

• 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) (http:/ / fourier1824. geologist-1011. mobi)Remarques Générales Sur Les Températures

Du Globe Terrestre Et Des Espaces Planétaires., in Annales de Chimie et de Physique, Vol. 27, pp. 136–167.• Fourier, J.-B.-J. Mémoires de l'Académie Royale des Sciences de l'Institut de France VII. 570–604 (1827) (http:/ /

www. academie-sciences. fr/ membres/ in_memoriam/ Fourier/ Fourier_pdf/ Mem1827_p569_604. pdf)(greenhouse effect essay)

• 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• 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 Espaces

Planétaires., 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.

Article Sources and Contributors 6

Article Sources and ContributorsJoseph Fourier  Source: http://en.wikipedia.org/w/index.php?oldid=432343091  Contributors: 67th Tigers, Acather96, Akriasas, Alan U. Kennington, Alansohn, Anon user, Antandrus, ArjenDijksman, Arthur Rubin, Avicennasis, Avjoska, AxelBoldt, BRG, Badseed, Bassbonerocks, Bcent1234, Bender235, Benjaminevans82, Bergsten, Bethpage89, Bunzil, CALR, CBDunkerson, CLCEditorial, CSWarren, CambridgeBayWeather, Cantiorix, Carcharoth, Causesobad, Charles Matthews, Chjoaygame, Courcelles, CousinJohn, Cp111, Cubs Fan, D6, DARTH SIDIOUS 2,David.Monniaux, DerHexer, Derek Ross, Discospinster, Djordjes, Docu, Doulos Christos, Dreadstar, Eliyak, Eoghanc, Eric-Wester, Eusebius, Expert12, Fallenfromthesky, Father Time89,Gadfium, Gareth Owen, Garion96, Gauss, Giftlite, Graham87, Guitarspecs, Gullanian, Harel, Hede2000, Hektor, Islescape, J.delanoy, Jake Wartenberg, Jan1nad, Jaredwf, Jauhienij, JiuguangWang, Jmc, Joe Canuck, John, John of Reading, John254, Jojit fb, Josce, Juansempere, Jumbuck, K.C. Tang, Khym Chanur, Knutux, Kraxler, La Grande Reverteur, Lee2008, Lenthe, Levalley,Libb Thims, Lockley, Looxix, Lukerobinson001, LutzL, Lzur, Mackensen, MarkSweep, Martin451, MathMartin, Mav, MiLo28, Michael Hardy, Michur, Mikeh98245, Monegasque, Moreschi,Moskvax, Mottaku, Myasuda, Nbarth, Neddyseagoon, Nickpowerz, Nk, Numbo3, Ohnoitsjamie, Olivier, Oracleofottawa, Ouzel Ring, PDH, Palica, Pi, Plucas58, Poppy, Pufferfish101, Qutezuce,Qwertylurker, Raonisousa, Ravn, Resurgent insurgent, Rich Farmbrough, Ricochet17, Rob Hooft, RoddyYoung, Rrburke, Rubicon, Ruud Koot, Salih, Sasank2102, Schlier22, Short BrigadeHarvester Boris, Sjakkalle, Smeira, Snoyes, Snurddnert, SteelGray, Stonehead, Studerby, SuperGirl, SureFire, Tbvdm, The Anome, The Red, TheCajun80, Thorwald, Tom Lougheed, Tomas e,Tomisti, Tommy2010, Triona, Triwbe, Turgidson, Ulric1313, Vaughan Pratt, Vina, Vsmith, WikHead, Wikiborg, Wile E. Heresiarch, William M. Connolley, Woohookitty, XJamRastafire,Xchbla423, Yamamoto Ichiro, Yerpo, Yurivict, Zandetroit, Александър, 250 anonymous edits

Image Sources, Licenses and ContributorsFile:Fourier2.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Fourier2.jpg  License: Public domain  Contributors: Original uploader was User:Bunzil at en.wikipediaFile:Legendre and Fourier (1820).jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Legendre_and_Fourier_(1820).jpg  License: Public Domain  Contributors: Original uploader wasLibb Thims at en.wikipediaFile:Joseph Fourier (circa 1820).jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Joseph_Fourier_(circa_1820).jpg  License: Public Domain  Contributors: Original uploader wasLibb Thims at en.wikipediaFile:Grenoble - ancien évêché - Joseph Fourier.JPG  Source: http://en.wikipedia.org/w/index.php?title=File:Grenoble_-_ancien_évêché_-_Joseph_Fourier.JPG  License: Creative CommonsAttribution 3.0  Contributors: Eusebius, Jean-FrédéricImage:Perelachaise-p1000361.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Perelachaise-p1000361.jpg  License: unknown  Contributors: User:Rama

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