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Alexis Claude de Clairaut
Alexis Claude de Clairaut
Born	7 May 1713
Died	17 May 1765
Nationality	French
Fields	mathematics
Known for	Clairaut's equation

Alexis Claude de Clairaut (or Clairault) (3 May 1713 – 17 May 1765) was a prominent French mathematician, astronomer, geophysicist, and intellectual.

Biography[link]

Childhood[link]

Clairaut was born in Paris, France, where his father taught mathematics. He was a prodigy — at the age of twelve he wrote a memoir on four geometrical curves and under his father's tutelage he made such rapid progress in the subject that in his thirteenth year he read before the Académie française an account of the properties of four curves which he had discovered. When only sixteen he finished a treatise on tortuous curves, Recherches sur les courbes a double courbure, which, on its publication in 1731, procured his admission into the French Academy of Sciences, although he was below the legal age as he was only eighteen.

The shape of the Earth[link]

In 1736, together with Pierre Louis Maupertuis, he took part in the expedition to Lapland, which was undertaken for the purpose of estimating a degree of the meridian arc.^[1] After his return he published his treatise Théorie de la figure de la terre (1743). In this work he promulgated the theorem, known as Clairaut's theorem, which connects the gravity at points on the surface of a rotating ellipsoid with the compression and the centrifugal force at the equator. This hydrostatic model of the shape of the Earth was founded on a paper by Colin Maclaurin, which had shown that a mass of homogeneous fluid set in rotation about a line through its centre of mass would, under the mutual attraction of its particles, take the form of an ellipsoid. Under the assumption that the Earth was composed of concentric ellipsoidal shells of uniform density, Clairaut's theorem could be applied to it, and allowed the ellipticity of the Earth to be calculated from surface measurements of gravity. In 1849 Stokes showed that Clairaut's result was true whatever the interior constitution or density of the Earth, provided the surface was a spheroid of equilibrium of small ellipticity.

Focus on astronomical motion[link]

He obtained an ingenious approximate solution of the problem of the three bodies; in 1750 he gained the prize of the St Petersburg Academy for his essay Théorie de la lune; and in 1759 he calculated the perihelion of Halley's comet.

The Théorie de la lune is strictly Newtonian in character. This contains the explanation of the motion of the apsis which had previously puzzled astronomers, and which Clairaut had at first deemed so inexplicable that he was on the point of publishing a new hypothesis as to the law of attraction when it occurred to him to carry the approximation to the third order, and he thereupon found that the result was in accordance with the observations. This was followed in 1754 by some lunar tables, which he computed using a form of the discrete Fourier transform.^[2] Clairaut subsequently wrote various papers on the orbit of the Moon, and on the motion of comets as affected by the perturbation of the planets, particularly on the path of Halley's comet.

Personal life and death[link]

His growing popularity in society hindered his scientific work: "He was focused," says Bossut, "with dining and with evenings, coupled with a lively taste for women, and seeking to make his pleasures into his day to day work, he lost rest, health, and finally life at the age of fifty-two."

He was elected a Fellow of the Royal Society of London in November, 1737.^[3]

Clairaut died in Paris in 1765.

See also[link]

• Symmetry of second derivatives
• Clairaut's theorem
• Clairaut's equation
• Clairaut's relation
• Human computer

Notes[link]

1. ^ O'Connor and, J. J.; E. F. Robertson (October 1998). "Alexis Clairaut". MacTutor History of Mathematics Archive. School of Mathematics and Statistics, University of St Andrews, Scotland. http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Clairaut.html. Retrieved 2009-03-12. 
2. ^ Terras, Audrey (1999). Fourier analysis on finite groups and applications. Cambridge University Press. ISBN 978-0-521-45718-7. http://books.google.com/?id=-B2TA669dJMC , p. 30
3. ^ "Library and Archive Catalogue". Royal Society. http://www2.royalsociety.org/DServe/dserve.exe?dsqIni=Dserve.ini&dsqApp=Archive&dsqCmd=Show.tcl&dsqDb=Persons&dsqPos=0&dsqSearch=%28Surname%3D%27clairaut%27%29. Retrieved 22 December 2010. 

References[link]

• Grier, David Alan, When Computers Were Human, Princeton University Press, 2005. ISBN 0-691-09157-9.
• Casey, J., "Clairaut's Hydrostatics: A Study in Contrast," American Journal of Physics, Vol. 60, 1992, pp. 549–554.

External links[link]

• Chronologie de la vie de Clairaut (1713-1765)
• O'Connor, John J.; Robertson, Edmund F., "Alexis Clairaut", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Clairaut.html .
• W.W. Rouse Ball A Short Account of the History of Mathematics

Alexis (Ancient Greek: Ἄλεξις, c.394 BC – c.288 BC) was a Greek comic poet of the Middle Comedy period. He was born at Thurii (in present day Calabria, Italy) in Magna Graecia and taken early to Athens,^[1] where he became a citizen, being enrolled in the deme Oion (Οἶον) and the tribe Leontides.^[2][3] It is thought he lived to the age of 106 and died on the stage while being crowned. According to the Suda, a 10th century encyclopedia, Alexis was the paternal uncle of the dramatist Menander and wrote 245 comedies, of which only fragments now survive, including some 130 preserved titles.

Life[link]

It was said he had a son, called Stephanus, who also wrote comedies.^[4] He appears to have been rather addicted to the pleasures of the table, according to Athenaeus.^[3][5]

He won his first Lenaean victory in the 350s BC, most likely, where he was sixth after Eubulus, and fourth after Antiphanes. While being a Middle Comic poet, Alexis was contemporary with several leading figures of New Comedy, such as Philippides, Philemon, Diphilus, and even Menander. There is also some evidence that, during his old age, he wrote plays in the style of New Comedy.

Plutarch says that he lived to the age of 106 and 5 months, and that he died on the stage while being crowned victor.^[6] He was certainly alive after 345 BC, for Aeschines mentions him as alive in that year. He was also living at least as late as 288 BC,^[3] from which his birth date is calculated. According to the Suda he wrote 245 comedies, of which only fragments including some 130 titles survive. His plays include Meropis, Ankylion, Olympiodoros, Parasitos (exhibited in 360 BC, in which he ridiculed Plato), Agonis (in which he ridiculed Misgolas), and the Adelphoi and the Stratiotes, in which he satirized Demosthenes, and acted shortly after 343 BC. Also Hippeis (316 BC)^{[citation needed]} (in which he referred to the decree of Sophocles against the philosophers), Pyraunos (312 BC), Pharmakopole (306 BC)^{[citation needed]}, Hypobolimaios (306 BC), and Ankylion.^[3]

Because he wrote a lot of plays, the same passages often appear in more than 3 plays. It was said that he also borrowed from Eubulus and many other playwrights in some of his plays.^[7] According to Carytius of Pergamum, Alexis was the first to use the part of the parasite.^[8] Alexis was known in Roman times; Aulus Gellius noted that Alexis' poetry was used by Roman comedians, including Turpilius and possibly Plautus.

Surviving titles and fragments[link]

Only fragments of any of the plays have survived - about 340 in all, totaling about 1,000 lines. They attest to the wit and refinement of the author, which Athenaeus praises.^[9] The surviving fragments also show that Alexis invented a great deal of words, mostly compound words, that he used normal words in an unusual way, and made strange and unusual forms of common words. The main sources of the fragments of Alexis are Stobaeus and Athenaeus.

The following 139 titles of Alexis's plays have been preserved:

References[link]

Editions of Fragments[link]

• Augustus Meineke. Poetarum Graecorum comicorum fragmenta, (1855).
• Theodor Kock. Comicorum Atticorum fragmenta, i. (1880).
• Colin Austin and Rudolf Kassel. Poetae Comici Graeci. vol. 1.

References[link]

Wikisource has the text of the 1911 Encyclopædia Britannica article Alexis.

• Arnott, W. Geoffrey. Alexis: The Fragments. A Commentary. Cambridge: Cambridge University Press, 1996.
•  This article incorporates text from a publication now in the public domain: Chisholm, Hugh, ed. (1911). Encyclopædia Britannica (11th ed.). Cambridge University Press.