Joseph Fourier

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Joseph Fourier
Fourier2.jpg
Jean-Baptiste Joseph Fourier
Born(1768-03-21)21 March 1768
Died16 May 1830(1830-05-16) (aged 62)
ResidenceFrance
Nationality French
Alma mater École Normale Supérieure
Known for Fourier series
Fourier transform
Fourier's law of conduction
Fourier–Motzkin elimination
Scientific career
Fields Mathematician, physicist, historian
Institutions École Normale Supérieure
École Polytechnique
Academic advisors Joseph-Louis Lagrange
Notable students Peter Gustav Lejeune Dirichlet
Claude-Louis Navier
Giovanni Plana

Jean-Baptiste Joseph Fourier ( /ˈfʊri, -iər/ ; [1] French:  [fuʁje] ; 21 March 1768 – 16 May 1830) was a French mathematician and physicist born in Auxerre and best known for initiating the investigation of Fourier series and their applications to problems of heat transfer and vibrations. The Fourier transform and Fourier's law are also named in his honour. Fourier is also generally credited with the discovery of the greenhouse effect. [2]

The French are an ethnic group and nation who are identified with the country of France. This connection may be ethnic, legal, historical, or cultural.

Mathematician person with an extensive knowledge of mathematics

A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.

Physicist scientist who does research in physics

A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate causes of phenomena, and usually frame their understanding in mathematical terms. Physicists work across a wide range of research fields, spanning all length scales: from sub-atomic and particle physics, through biological physics, to cosmological length scales encompassing the universe as a whole. The field generally includes two types of physicists: experimental physicists who specialize in the observation of physical phenomena and the analysis of experiments, and theoretical physicists who specialize in mathematical modeling of physical systems to rationalize, explain and predict natural phenomena. Physicists can apply their knowledge towards solving practical problems or to developing new technologies.

Contents

Biography

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

Auxerre Prefecture and commune in Bourgogne-Franche-Comté, France

Auxerre is the capital of the Yonne department and the fourth-largest city in Burgundy. Auxerre's population today is about 39,000; the metropolitan area comprises roughly 92,000 inhabitants. Residents of Auxerre are referred to as Auxerrois.

Yonne Department of France

Yonne is a French department named after the river Yonne. It is one of the eight constituent departments of Bourgogne-Franche-Comté and is located in the northwest of the region, bordering Île-de-France. It was created in 1790 during the French Revolution. Its prefecture (capital) is Auxerre and its postcode number is 89.

Tailor person who makes, repairs, or alters clothing professionally, typically mens clothing

A tailor is a person who makes, repairs, or alters clothing professionally, especially suits and men's clothing.

Fourier accompanied Napoleon Bonaparte on his Egyptian expedition in 1798, as scientific adviser, and was appointed secretary of the Institut d'Égypte. Cut off from France by the British 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 British influence in the East. After the British victories and the capitulation of the French under General Menou in 1801, Fourier returned to France.

French campaign in Egypt and Syria military conflict

The French Campaign in Egypt and Syria (1798–1801) was Napoleon Bonaparte's campaign in the Ottoman territories of Egypt and Syria, proclaimed to defend French trade interests, weaken Britain's access to British India, and to establish scientific enterprise in the region. It was the primary purpose of the Mediterranean campaign of 1798, a series of naval engagements that included the capture of Malta.

Institut dÉgypte

The Institut d’Égypte or Egyptian Scientific Institute is a learned society in Cairo specializing in Egyptology. It was established in 1798 by Napoleon Bonaparte to carry out research during his Egyptian campaign and is the oldest scientific institute in Egypt. The building in which it was housed was burnt down, with the loss of many documents, during the Arab Spring unrest of 2011. It reopened in December 2012.

Cairo Capital city in Egypt

Cairo is the capital of Egypt. The city's metropolitan area is one of the largest in Africa, the largest in the Middle East, and the 15th-largest in the world, and is associated with ancient Egypt, as the famous Giza pyramid complex and the ancient city of Memphis are located in its geographical area. Located near the Nile Delta, modern Cairo was founded in 969 CE by the Fatimid dynasty, but the land composing the present-day city was the site of ancient national capitals whose remnants remain visible in parts of Old Cairo. Cairo has long been a centre of the region's political and cultural life, and is titled "the city of a thousand minarets" for its preponderance of Islamic architecture. Cairo is considered a World City with a "Beta +" classification according to GaWC.

1820 watercolor caricatures of French mathematicians Adrien-Marie Legendre (left) and Joseph Fourier (right) by French artist Julien-Leopold Boilly, watercolor portrait numbers 29 and 30 of Album de 73 Portraits-Charge Aquarelle's des Membres de I'Institute. Legendre and Fourier (1820).jpg
1820 watercolor caricatures of French mathematicians Adrien-Marie Legendre (left) and Joseph Fourier (right) by French artist Julien-Leopold Boilly, watercolor portrait numbers 29 and 30 of Album de 73 Portraits-Charge Aquarelle’s des Membres de I’Institute.

In 1801, [4] 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 from the Napoleon expedition to Egypt to resume his academic post as professor at École Polytechnique when Napoleon decided otherwise in his remark

Napoleon 18th/19th-century French monarch, military and political leader

Napoléon Bonaparte was a French statesman and military leader who rose to prominence during the French Revolution and led several successful campaigns during the French Revolutionary Wars. He was Emperor of the French as Napoleon I from 1804 until 1814 and again briefly in 1815 during the Hundred Days. Napoleon dominated European and global affairs for more than a decade while leading France against a series of coalitions in the Napoleonic Wars. He won most of these wars and the vast majority of his battles, building a large empire that ruled over much of continental Europe before its final collapse in 1815. He is considered one of the greatest commanders in history, and his wars and campaigns are studied at military schools worldwide. Napoleon's political and cultural legacy has endured as one of the most celebrated and controversial leaders in human history.

Prefect (France) French states representative in a department or region

A prefect in France is the State's representative in a department or region. Sub-prefects are responsible for the subdivisions of departments, arrondissements. The office of a prefect is known as a prefecture and that of a sub-prefect as a subprefecture.

Isère Department of France

Isère is a department in the Auvergne-Rhône-Alpes region in eastern France named after the river Isère.

... the Prefect of the Department of Isère having recently died, I would like to express my confidence in citizen Fourier by appointing him to this place. [4]

Hence being faithful to Napoleon, he took the office of Prefect. [4] It was while at Grenoble that he began to experiment on the propagation of heat. He presented his paper On the Propagation of Heat in Solid Bodies to the Paris Institute on December 21, 1807. He also contributed to the monumental Description de l'Égypte . [5]

<i>Description de lÉgypte</i> 19th century book series

The Description de l'Égypte was a series of publications, appearing first in 1809 and continuing until the final volume appeared in 1829, which aimed to comprehensively catalog all known aspects of ancient and modern Egypt as well as its natural history. It is the collaborative work of about 160 civilian scholars and scientists, known popularly as the savants, who accompanied Napoleon's expedition to Egypt in 1798 to 1801 as part of the French Revolutionary Wars, as well as about 2000 artists and technicians, including 400 engravers, who would later compile it into a full work.

In 1822, Fourier succeeded Jean Baptiste Joseph Delambre as Permanent Secretary of the French Academy of Sciences. In 1830, he was elected a foreign member of the 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 he experienced. A fall, however, which he sustained on the 4th of May 1830, while descending a flight of stairs, aggravated the malady to an extent beyond what could have been ever feared. [6]

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 his position as secretary of the Cairo Institute, and his collation of Description de l'Égypte. His name is one of the 72 names inscribed on the Eiffel Tower.

A bronze statue was erected in Auxerre in 1849, but it was melted down for armaments during World War II. [7] Joseph Fourier University in Grenoble is named after him.

The Analytic Theory of Heat

Sketch of Fourier, circa 1820. Joseph Fourier (circa 1820).jpg
Sketch of Fourier, circa 1820.

In 1822 Fourier published his work on heat flow in Théorie analytique de la chaleur (The Analytical Theory of Heat), [8] in which he based his reasoning on Newton's law of cooling, namely, that the flow of heat between two adjacent molecules is proportional to the extremely small difference of their temperatures. This book was translated, [9] with editorial 'corrections', [10] into English 56 years later by Freeman (1878). [11] The book was also edited, with many editorial corrections, by Darboux and republished in French in 1888. [10]

There were three important contributions in this work, one purely mathematical, two essentially physical. In mathematics, Fourier claimed that any function of a variable, whether continuous or discontinuous, can be expanded in a series of sines of multiples of the variable. Though this result is not correct without additional conditions, Fourier's observation that some discontinuous functions are the sum of infinite series was a breakthrough. The question of determining when a Fourier series converges has been fundamental for centuries. Joseph-Louis Lagrange had given particular cases of this (false) theorem, and had implied that the method was general, but he had not pursued the subject. Peter Gustav Lejeune Dirichlet was the first to give a satisfactory demonstration of it with some restrictive conditions. This work provides the foundation for what is today known as the Fourier transform.

One important physical contribution in the book was the concept of dimensional homogeneity in equations; i.e. an equation can be formally correct only if the dimensions match on either side of the equality; Fourier made important contributions to dimensional analysis. [12] The other physical contribution was Fourier's proposal of his partial differential equation for conductive diffusion of heat. This equation is now taught to every student of mathematical physics.

Real roots of polynomials

Bust of Fourier in Grenoble Grenoble - ancien eveche - Joseph Fourier.JPG
Bust of Fourier in Grenoble

Fourier left an unfinished work on determining and locating real roots of polynomials, which was edited by Claude-Louis Navier and published in 1831. This work contains much original matter—in particular, Fourier's theorem on polynomial real roots, published in 1820. [13] François Budan, in 1807 and 1811, had published independently his theorem (also known by the name of Fourier), which is very close to Fourier's theorem (each theorem is a corollary of the other). Fourier's proof [13] is the one that was usually given, during 19th century, in textbooks on the theory of equations. [14] A complete solution of the problem was given in 1829 by Jacques Charles François Sturm.

Discovery of the greenhouse effect

Fourier's grave, Pere Lachaise Cemetery Pere-Lachaise - Division 18 - Joseph Fourier 03.jpg
Fourier's grave, Père Lachaise Cemetery

In the 1820s Fourier calculated that an object the size of the Earth, and at its distance from the Sun, should be considerably colder than the planet actually is if warmed by only the effects of incoming solar radiation. He examined various possible sources of the additional observed heat in articles published in 1824 [15] and 1827. [16] While he ultimately 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 widely recognized as the first proposal of what is now known as the greenhouse effect, [17] although Fourier never called it that. [18] [19]

In his articles, Fourier referred to an experiment by de Saussure, who lined a vase with blackened cork. Into the cork, he inserted several panes of transparent glass, separated by intervals of air. Midday sunlight was allowed to enter at the top of the vase through the glass panes. The temperature became more elevated in the more interior compartments of this device. Fourier concluded that gases in the atmosphere could form a stable barrier like the glass panes. [20] This conclusion may have contributed to the later use of the metaphor of the "greenhouse effect" to refer to the processes that determine atmospheric temperatures. [21] Fourier noted that the actual mechanisms that determine the temperatures of the atmosphere included convection, which was not present in de Saussure's experimental device.

Works

See also

Related Research Articles

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References

  1. "Fourier". Dictionary.com Unabridged. Random House.
  2. Cowie, J. (2007). Climate Change: Biological and Human Aspects. Cambridge University Press. p. 3. ISBN   978-0-521-69619-7.
  3. Boilly, Julien-Leopold. (1820). Album de 73 Portraits-Charge Aquarelle’s des Membres de I’Institute (watercolor portrait #29). Biliotheque de l’Institut de France.
  4. 1 2 3 "Jean-Baptiste Fourier" . Retrieved 4 April 2012.
  5. Nowlan, Robert. A Chronicle of Mathematical People (PDF).
  6. Arago, François (1857). Biographies of Distinguished Scientific Men.
  7. A subscription has been launched to erect a new one.
  8. Fourier, Joseph (1822). Théorie analytique de la chaleur (in French). Paris: Firmin Didot Père et Fils. OCLC   2688081.
  9. 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.
  10. 1 2 Truesdell, C.A. (1980). The Tragicomical History of Thermodynamics, 1822–1854, Springer, New York, ISBN   0-387-90403-4, page 52.
  11. Gonzalez, Rafael; Woods, Richard E. (2010). Digital Image Processing (Third ed.). Upper Saddle River: Pearson Prentice Hall. p. 200. ISBN   978-0-13-234563-7.
  12. Mason, Stephen F.: A History of the Sciences (Simon & Schuster, 1962), p. 169.
  13. 1 2 Fourier, Jean Baptiste Joseph (1820). "Sur l'usage du théorème de Descartes dans la recherche des limites des racines". Bulletin des Sciences, Par la Société Philomatique de Paris: 156–165.
  14. These questions were no more considered as important from the end of 19th century to the second half of 20th century, where they reappeared for the need of computer algebra.
  15. Fourier J (1824). "Remarques Générales Sur Les Températures Du Globe Terrestre Et Des Espaces Planétaires". Annales de Chimie et de Physique . 27: 136–67.
  16. Fourier J (1827). "Mémoire Sur Les Températures Du Globe Terrestre Et Des Espaces Planétaires". Mémoires de l'Académie Royale des Sciences. 7: 569–604.
  17. Weart, S. (2008). The Carbon Dioxide Greenhouse Effect . Retrieved on 27 May 2008
  18. Fleming J R (1999). "Joseph Fourier, the "greenhouse effect", and the quest for a universal theory of terrestrial temperatures". Endeavour. 23 (2): 72–75. doi:10.1016/s0160-9327(99)01210-7.
  19. Baum, Sr., Rudy M. (2016). "Future Calculations: The first climate change believer". Distillations. 2 (2): 38–39. Retrieved 22 March 2018.
  20. Translation by W M Connolley of: Fourier 1827: MEMOIRE sur les temperatures du globe terrestre et des espaces planetaires
  21. Osman, Jheni (2011), 100 Ideas that Changed the World, Random House, p. 65, ISBN   9781446417485, [Fourier] didn't call his discovery the greenhouse effect but future scientists named it that after an experiment by [de Saussure] which influenced Fourier's work.
  22. Coppel, William A. (1969). "J.B. Fourier – on the occasion of his two hundredth birthday". Amer. Math. Monthly. 76 (5): 468–483. doi:10.2307/2316953. JSTOR   2316953.

Further reading