Joseph Fourier

Joseph Fourier

Overview
Jean Baptiste Joseph Fourier (21 March 1768 – 16 May 1830) was a French
French people
The French are a nation that share a common French culture and speak the French language as a mother tongue. Historically, the French population are descended from peoples of Celtic, Latin and Germanic origin, and are today a mixture of several ethnic groups...

 mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

 and physicist
Physicist
A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...

 best known for initiating the investigation of Fourier series
Fourier series
In mathematics, a Fourier series decomposes periodic functions or periodic signals into the sum of a set of simple oscillating functions, namely sines and cosines...

 and their applications to problems of heat transfer
Heat transfer
Heat transfer is a discipline of thermal engineering that concerns the exchange of thermal energy from one physical system to another. Heat transfer is classified into various mechanisms, such as heat conduction, convection, thermal radiation, and phase-change transfer...

 and vibrations. The Fourier transform
Fourier transform
In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...

 and Fourier's Law are also named in his honour. Fourier is also generally credited with the discovery of the greenhouse effect
Greenhouse effect
The greenhouse effect is a process by which thermal radiation from a planetary surface is absorbed by atmospheric greenhouse gases, and is re-radiated in all directions. Since part of this re-radiation is back towards the surface, energy is transferred to the surface and the lower atmosphere...

.

Fourier was born at Auxerre
Auxerre
Auxerre is a commune in the Bourgogne region in north-central France, between Paris and Dijon. It is the capital of the Yonne department.Auxerre's population today is about 45,000...

 (now in the Yonne
Yonne
Yonne is a French department named after the Yonne River. It is one of the four constituent departments of Burgundy in eastern France and its prefecture is Auxerre. Its official number is 89....

 département of France), the son of a tailor
Tailor
A tailor is a person who makes, repairs, or alters clothing professionally, especially suits and men's clothing.Although the term dates to the thirteenth century, tailor took on its modern sense in the late eighteenth century, and now refers to makers of men's and women's suits, coats, trousers,...

.
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Unanswered Questions
Quotations

Primary causes are unknown to us; but are subject to simple and constant laws, which may be discovered by observation, the study of them being the object of natural philosophy. Heat, like gravity, penetrates every substance of the universe, its rays occupy all parts of space. The object of our work is to set forth the mathematical laws which this element obeys. The theory of heat will hereafter form one of the most important branches of general physics.

Ch. 1, p. 1

Profound study of nature is the most fertile source of mathematical discoveries.

Ch. 1, p. 7
Encyclopedia
Jean Baptiste Joseph Fourier (21 March 1768 – 16 May 1830) was a French
French people
The French are a nation that share a common French culture and speak the French language as a mother tongue. Historically, the French population are descended from peoples of Celtic, Latin and Germanic origin, and are today a mixture of several ethnic groups...

 mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

 and physicist
Physicist
A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...

 best known for initiating the investigation of Fourier series
Fourier series
In mathematics, a Fourier series decomposes periodic functions or periodic signals into the sum of a set of simple oscillating functions, namely sines and cosines...

 and their applications to problems of heat transfer
Heat transfer
Heat transfer is a discipline of thermal engineering that concerns the exchange of thermal energy from one physical system to another. Heat transfer is classified into various mechanisms, such as heat conduction, convection, thermal radiation, and phase-change transfer...

 and vibrations. The Fourier transform
Fourier transform
In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...

 and Fourier's Law are also named in his honour. Fourier is also generally credited with the discovery of the greenhouse effect
Greenhouse effect
The greenhouse effect is a process by which thermal radiation from a planetary surface is absorbed by atmospheric greenhouse gases, and is re-radiated in all directions. Since part of this re-radiation is back towards the surface, energy is transferred to the surface and the lower atmosphere...

.

Life


Fourier was born at Auxerre
Auxerre
Auxerre is a commune in the Bourgogne region in north-central France, between Paris and Dijon. It is the capital of the Yonne department.Auxerre's population today is about 45,000...

 (now in the Yonne
Yonne
Yonne is a French department named after the Yonne River. It is one of the four constituent departments of Burgundy in eastern France and its prefecture is Auxerre. Its official number is 89....

 département of France), the son of a tailor
Tailor
A tailor is a person who makes, repairs, or alters clothing professionally, especially suits and men's clothing.Although the term dates to the thirteenth century, tailor took on its modern sense in the late eighteenth century, and now refers to makers of men's and women's suits, coats, trousers,...

. He was orphaned at age eight. Fourier was recommended to the Bishop of Auxerre, and through this introduction, he was educated by the Benveniste
Benveniste
Benveniste, also Benvenisti, Benvenista, Benvenisto is the surname of an old, rich, and scholarly family of Narbonne, France, several branches of which were found all over Spain and the Provence, France, as well as at various places in the Orient. It is also borne by families in Bulgaria, Serbia,...

s 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
French Revolution
The French Revolution , sometimes distinguished as the 'Great French Revolution' , was a period of radical social and political upheaval in France and Europe. The absolute monarchy that had ruled France for centuries collapsed in three years...

, and was rewarded by an appointment in 1795 in the École Normale Supérieure
École Normale Supérieure
The École normale supérieure is one of the most prestigious French grandes écoles...

, and subsequently by a chair at the École Polytechnique
École Polytechnique
The École Polytechnique is a state-run institution of higher education and research in Palaiseau, Essonne, France, near Paris. Polytechnique is renowned for its four year undergraduate/graduate Master's program...

.

Fourier went with Napoleon Bonaparte on his Egyptian expedition in 1798, and was made governor of Lower Egypt
Lower Egypt
Lower Egypt is the northern-most section of Egypt. It refers to the fertile Nile Delta region, which stretches from the area between El-Aiyat and Zawyet Dahshur, south of modern-day Cairo, and the Mediterranean Sea....

  and secretary of the Institut d'Égypte
Institut d'Égypte
The Institut d’Égypte was a learned academy formed by Napoleon Bonaparte to carry out research during his Egyptian campaign.-Early work:It first met on 24 August 1798, with Gaspard Monge as president, Bonaparte himself as vice-president and Joseph Fourier and Costaz as secretaries...

. 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
Cairo
Cairo , is the capital of Egypt and the largest city in the Arab world and Africa, and the 16th largest metropolitan area in the world. Nicknamed "The City of a Thousand Minarets" for its preponderance of Islamic architecture, Cairo has long been a centre of the region's political and cultural life...

, with a view of weakening English influence in the East. After the British victories and the capitulation of the French under General Menou in 1801, Fourier returned to France, and was made prefect of Isère
Isère
Isère is a department in the Rhône-Alpes region in the east of France named after the river Isère.- History :Isère is one of the original 83 departments created during the French Revolution on March 4, 1790. It was created from part of the former province of Dauphiné...

, and it was while there that he made his experiments on the propagation of heat.
In 1806 he quit the post of full professor at the École Polytechnique because Napoleon sent him to Grenoble
Grenoble
Grenoble is a city in southeastern France, at the foot of the French Alps where the river Drac joins the Isère. Located in the Rhône-Alpes region, Grenoble is the capital of the department of Isère...

. He was replaced by Siméon Denis Poisson
Siméon Denis Poisson
Siméon Denis Poisson , was a French mathematician, geometer, and physicist. He however, was the final leading opponent of the wave theory of light as a member of the elite l'Académie française, but was proven wrong by Augustin-Jean Fresnel.-Biography:...

.

Fourier moved to England in 1816. Later he returned to France, and in 1822 succeeded Jean Baptiste Joseph Delambre as Permanent Secretary of the French Academy of Sciences
French Academy of Sciences
The French Academy of Sciences is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research...

. In 1830, he was elected a foreign member of the Royal Swedish Academy of Sciences
Royal Swedish Academy of Sciences
The Royal Swedish Academy of Sciences or Kungliga Vetenskapsakademien is one of the Royal Academies of Sweden. The Academy is an independent, non-governmental scientific organization which acts to promote the sciences, primarily the natural sciences and mathematics.The Academy was founded on 2...

.

Fourier believed that keeping the body wrapped up in blankets was beneficial to the health. He died in 1830 when in this state he tripped and fell down the stairs at his home.

Fourier was buried in the Pere Lachaise Cemetery
Père Lachaise Cemetery
Père Lachaise Cemetery is the largest cemetery in the city of Paris, France , though there are larger cemeteries in the city's suburbs.Père Lachaise is in the 20th arrondissement, and is reputed to be the world's most-visited cemetery, attracting hundreds of thousands of visitors annually to the...

 in Paris, a tomb decorated with an Egyptian motif to reflect his position as secretary of the Cairo Institute, and his collation of the landmark Description de l'Égypte
Description de l'Egypte
Description de l'Égypte is the title of several books.* Description de l'Égypte - Description de l'Égypte ou Recueil des observations et des recherches qui ont été faites en Égypte pendant l'expédition de l'armée française Pub; First Edition , L'Imprimerie Imperiale, 1809-1813; l'Imprimerie...

. His name is one of the 72 names inscribed on the Eiffel Tower
The 72 names on the Eiffel Tower
On the Eiffel Tower, seventy-two names of French scientists, engineers and some other notable people are engraved in recognition of their contributions. This is according to the design by Gustave Eiffel. The engravings are found on the sides of the tower under the first balcony...

.

Théorie analytique de la chaleur


In 1822 Fourier presented 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 adjacent molecules is proportional to the extremely small difference of their temperatures. This book was translated, with editorial 'corrections', into English 56 years later by Freeman (1878). The book was also edited, with many editorial corrections, by Darboux
Jean Gaston Darboux
Jean-Gaston Darboux was a French mathematician.-Life:Darboux made several important contributions to geometry and mathematical analysis . He was a biographer of Henri Poincaré and he edited the Selected Works of Joseph Fourier.Darboux received his Ph.D...

 and republished in French in 1888.
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
Sine wave
The sine wave or sinusoid is a mathematical function that describes a smooth repetitive oscillation. It occurs often in pure mathematics, as well as physics, signal processing, electrical engineering and many other fields...

 of multiples of the variable. Though this result is not correct, 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
Joseph Louis Lagrange
Joseph-Louis Lagrange , born Giuseppe Lodovico Lagrangia, was a mathematician and astronomer, who was born in Turin, Piedmont, lived part of his life in Prussia and part in France, making significant contributions to all fields of analysis, to number theory, and to classical and celestial mechanics...

 had given particular cases of this (false) theorem, and had implied that the method was general, but he had not pursued the subject. Johann Dirichlet
Johann Peter Gustav Lejeune Dirichlet
Johann Peter Gustav Lejeune Dirichlet was a German mathematician with deep contributions to number theory , as well as to the theory of Fourier series and other topics in mathematical analysis; he is credited with being one of the first mathematicians to give the modern formal definition of a...

 was the first to give a satisfactory demonstration of it with some restrictive conditions.

One 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 also developed dimensional analysis
Dimensional analysis
In physics and all science, dimensional analysis is a tool to find or check relations among physical quantities by using their dimensions. The dimension of a physical quantity is the combination of the basic physical dimensions which describe it; for example, speed has the dimension length per...

, the method of representing physical units, such as velocity and acceleration, by their fundamental dimensions of mass, time, and length, to obtain relations between them. The other physical contribution was Fourier's proposal of his partial differential equation
Heat equation
The heat equation is an important partial differential equation which describes the distribution of heat in a given region over time...

 for conductive diffusion of heat. This equation is now taught to every student of mathematical physics.

Determinate equations


Fourier left an unfinished work on determinate equations which was edited by Claude-Louis Navier
Claude-Louis Navier
Claude-Louis Navier born Claude Louis Marie Henri Navier , was a French engineer and physicist who specialized in mechanics.The Navier–Stokes equations are named after him and George Gabriel Stokes....

 and published in 1831. This work contains much original matter — in particular, there is a demonstration of Fourier's theorem on the position of the roots of an algebraic equation. Joseph Louis Lagrange
Joseph Louis Lagrange
Joseph-Louis Lagrange , born Giuseppe Lodovico Lagrangia, was a mathematician and astronomer, who was born in Turin, Piedmont, lived part of his life in Prussia and part in France, making significant contributions to all fields of analysis, to number theory, and to classical and celestial mechanics...

 had shown how the roots of an algebraic equation might be separated by means of another equation whose roots were the squares of the differences of the roots of the original equation. François Budan
François Budan de Boislaurent
Ferdinand François Désiré Budan de Boislaurent was a French mathematician, best known for enunciating the Fourier transform in 1807 and 1811, although his demonstration was not altogether accurate, and, although being published before Joseph Fourier's explanation, was discovered...

, in 1807 and 1811, had enunciated the theorem generally known by the name of Fourier, but the demonstration was not altogether satisfactory. Fourier's proof is the same as that usually given in textbooks on the theory of equations. The final solution of the problem was given in 1829 by Jacques Charles 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 be considerably colder than the planet actually is if warmed only by the effects of incoming solar radiation. He examined various possible sources of the additional observed heat in articles published in 1824 and 1827. 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
Greenhouse effect
The greenhouse effect is a process by which thermal radiation from a planetary surface is absorbed by atmospheric greenhouse gases, and is re-radiated in all directions. Since part of this re-radiation is back towards the surface, energy is transferred to the surface and the lower atmosphere...

.
In his articles Fourier referred to an experiment by de Saussure
Horace-Bénédict de Saussure
200px|thumb|Portrait of Horace-Bénédict de Saussure Horace-Bénédict de Saussure was a Genevan aristocrat, physicist and Alpine traveller, often considered the founder of alpinism, and considered to be the first person to build a successful solar oven.-Life and work:Saussure was born in Conches,...

, 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.http://www.wmconnolley.org.uk/sci/fourier_1827/fourier_1827.html#text. Fourier concluded that gases in the atmosphere could form a stable barrier like the glass panes. 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. 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.

See also


  • Fourier analysis
  • Fourier number
    Fourier number
    In physics and engineering, the Fourier number or Fourier modulus, named after Joseph Fourier, is a dimensionless number that characterizes heat conduction. Conceptually, it is the ratio of the heat conduction rate to the rate of thermal energy storage. Together with the Biot number, it...

  • Fourier–Deligne transform
    Fourier–Deligne transform
    In algebraic geometry, the Fourier–Deligne transform, or ℓ-adic Fourier transform, or geometric Fourier transform, is an operation on objects of the derived category of ℓ-adic sheaves over the affine line. It was introduced by Pierre Deligne on November 29th, 1976 in a letter to David Kazhdan as...

  • Fourier's Law
    Heat conduction
    In heat transfer, conduction is a mode of transfer of energy within and between bodies of matter, due to a temperature gradient. Conduction means collisional and diffusive transfer of kinetic energy of particles of ponderable matter . Conduction takes place in all forms of ponderable matter, viz....

  • Heat equation
    Heat equation
    The heat equation is an important partial differential equation which describes the distribution of heat in a given region over time...


External links