Definitions

# Fourier

[foor-ee-ey, -ee-er; for 1, 2 also Fr. foo ryey]
Fourier, Charles, 1772-1837, French social philosopher. From a bourgeois family, he condemned existing institutions and evolved a kind of utopian socialism. In Théorie des quatre mouvements (1808) and later works he developed his idea that the natural passions of man would, if properly channeled, result in social harmony. To achieve this goal, many of the artificial restraints of civilization were to be destroyed. The social organization for such development was to be based on the "phalanx," an economic unit composed of 1,620 people. Members would live in the phalanstère (or phalanstery), a community building, and work would be divided among people according to their natural inclinations. Fourier was not ready to discard capitalism completely; basically his ideal was an agricultural society, systematically arranged. His writings anticipated the 20th-century social problems resulting from mechanization and industrialization. Fourierism obtained a number of converts in France, and several newspapers spread the doctrines, but followers failed to establish any lasting colony there. After Fourier's death his principal disciple, Victor Prosper Considérant, tried to found a colony in Texas. Albert Brisbane and Horace Greeley were the principal figures in the sudden and wide development of colonies in the United States. Brook Farm was for a time Fourierist. The most successful of the communities was the North American Phalanx at Red Bank, N.J.

See studies by N. V. Riasanovsky (1969), D. Zeldin (1969), and J. F. Beecher (1987).

Fourier, Jean Baptiste Joseph, Baron, 1768-1830, French mathematician and physicist. He was noted for his researches on heat and on numerical equations. He originated Fourier's theorem on vibratory motion and the Fourier series, which provided a method for representing discontinuous functions by a trigonometric series. Fourier was professor (1795-98) at the École polytechnique, Paris; accompanied Napoleon I to Egypt; and was prefect of Isère (1802-15). In 1808 he was made a baron. He wrote Théorie analytique de la chaleur (1822; tr. 1878, repr. 1955). His scientific writings were collected in two volumes (1888-90).

Charles Fourier, engraving by Samuel Sartain after a painting by Jean-François Gigoux

(born April 7, 1772, Besançon, France—died Oct. 10, 1837, Paris) French social theorist. He advocated a reconstruction of society based on communal associations of producers known as phalanges (phalanxes). His system became known as Fourierism. He felt that phalanges would distribute wealth more equitably than would capitalism and that they would contribute both to a cooperative lifestyle and to individual self-fulfillment. After inheriting his mother's estate in 1812, he devoted himself to writing and refining his theories. Cooperative settlements based on Fourierism were started in France and the U.S., including Brook Farm.

Fourier (French pronunciation fuʁie) may refer to:

• Charles Fourier (1772–1837), a French utopian socialist thinker
• Joseph Fourier (1768–1830), a French mathematician and physicist
• Mathematics, physics, and engineering terms named in his honor for his work on the concepts underlying them:
• Mathematics tools:
• The Fourier series, a weighted sum of sinusoids having a common period, the result of Fourier analysis of a periodic function
• Fourier analysis, the description of functions as sums of sinusoids
• The Fourier transform, the type of linear canonical transform that is the generalization of the Fourier series
• The Fourier operator, the kernel of the Fredholm integral of the first kind that defines the continuous Fourier transform
• Fourier inversion theorem, any one of several theorems by which Fourier inversion recovers a function from its Fourier transform
• List of Fourier-related transforms, a list of linear transformations of functions related to Fourier analysis
• Short-time Fourier transform or short-term Fourier transform (STFT), a Fourier transform during a short term of time, used in the area of signal analysis
• Fractional Fourier transform (FRFT), a linear transformation generalizing the Fourier transform, used in the area of harmonic analysis
• Discrete-time Fourier transform (DTFT), the reverse of the Fourier series, a special case of the Z-transform around the unit circle in the complex plane
• Discrete Fourier transform (DFT), occasionally called the finite Fourier transform, the Fourier transform of a discrete periodic sequence (yielding discrete periodic frequencies), which can also be thought of as the DTFT of a finite-length sequence evaluated at discrete frequencies
• Fast Fourier transform (FFT), a fast algorithm for computing a Discrete Fourier transform
• Generalized Fourier series, generalizations of Fourier series that are special cases of decompositions over an orthonormal basis of an inner product space
• Physics and engineering:
• The Fourier number ($mathit\left\{Fo\right\}$) (also known as the Fourier modulus), a ratio $alpha t/d^2$ of the rate of heat conduction $alpha t$ to the rate of thermal energy storage $d^2$
• Fourier transform spectroscopy, a measurement technique whereby spectra are collected based on measurements of the temporal coherence of a radiative source, using time-domain measurements of the electromagnetic radiation or other type of radiation, including several methods such as the continuous wave Michelson or Fourier transform spectrometer and the pulsed Fourier transform spectrograph
• Peter Fourier (1565–1640), a French saint in the Roman Catholic Church and priest of Mattaincourt

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