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	Clairaut (crater) - Wikipedia, the free encyclopedia
		Clairaut is a lunar crater that is located in the rugged southern highlands of the Moon's near side.
		'Clairaut E' is attached to the exterior of the northwest rim.
		The inner wall of Clairaut has been softened by impacts until now it forms a simple slope down to the relatively flat floor, at least where the floor has not been marked by impacts.
	en.wikipedia.org /wiki/Clairaut_(crater) (232 words)

	Alexis Claude Clairaut (Site not responding. Last check: 2007-10-31)
		Clairaut also became friends with König and, for many years, the two continued a useful scientific collaboration by correspondence.
		Clairaut decided to apply his knowledge of the three-body problem to compute the orbit of Halley's comet and predict the exact date of its return.
		Clairaut wrote some important memoirs on the topic, studying the theory as well as conducting optical experiments.
	www.stetson.edu /~efriedma/periodictable/html/Cl.html (638 words)

	Clairaut biography
		Although we have already noted that Clairaut was the only one of twenty children of his parents to reach adulthood, he did have a younger brother who, at the age of 14, read a mathematics paper to the Academy in 1730.
		However, by the spring of 1748, Clairaut realised that the difference between the observed motion of the moon's apogee and the one predicted by the theory was due to errors coming from the approximations that were being made rather than from the inverse square law of gravitational attraction.
		Clairaut decided to apply his knowledge of the three-body problem to compute the orbit of Halley's comet and so predict the exact date of its return.
	www-groups.dcs.st-and.ac.uk /~history/Biographies/Clairaut.html (2004 words)

	Alexis Claude Clairaut http://www
		Clairaut was one of the participating scientist who helped obtain and measure the meridian degree of the earth’s surface.
		In 1752, Clairaut published his "Theory of the Moon" which is considered by many to be completely Newton in character.
		See also: Clairaut's equation This page is based on public domain text taken from 'A Short Account of the History of Mathematics' (4th edition, 1908) by W. Rouse Ball.
	www.southernct.edu /~pinciuv/mat530pr5.html (594 words)

	BookRags: Alexis-Claude Clairaut Biography
		Clairaut surpassed even Isaac Newton in his analysis of the effects of gravity and centrifugal force on a rotating body such as Earth, now known as Clairaut's theorem.
		Clairaut's book, Théorie de la figure de la terre, which he published in 1743, was said to be responsible to a great degree for the acceptance of Isaac Newton's gravitational theories.
		The book was the result of Clairaut's journey to Lapland in 1736, where he assisted Pierre Louis Moreau de Maupertuis, director of the exploration, in measuring the curvature of the Earth inside the arctic circle.
	www.bookrags.com /biography/alexis-claude-clairaut-wom (526 words)

	Alexis Claude Clairaut (1713 - 1765) (Site not responding. Last check: 2007-10-31)
		Alexis Claude Clairaut was born at Paris on May 13, 1713, and died there on May 17, 1765.
		In 1741 Clairaut went on a scientific expedition to measure the length of a meridian degree on the earth's surface, and on his return in 1743 he published his
		This is founded on a paper by Maclaurin, wherein it had been shewn 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 a spheroid.
	www.maths.tcd.ie /pub/HistMath/People/Clairaut/RouseBall/RB_Clairaut.html (427 words)

	Biografía matemáticos:Alexis Claude Clairaut (Bibliografía)
		The problem of the Earth's shape from Newton to Clairaut : the rise of mathematical science in eighteenth-century Paris and the fall of 'normal' science.
		Clairaut et le retour de la 'comete de Halley' en 1759, L'Astronomie 100 (1986), 397-408.
		Clairaut's calculations of the eighteenth-century return of Halley's comet, J. Hist.
	www.divulgamat.net /weborriak/Historia/MateOspetsuak/ClairautBiblio.asp (201 words)

	The Problem of the Earth's Shape from Newton to Clairaut - Cambridge University Press
		The evolution of Parisian mechanics proved not to be the replacement of a Cartesian paradigm by a Newtonian one, a replacement that might be expected from Thomas Kuhn's formulations about scientific revolutions, but a complex process instead involving many areas of research and contributions of different kinds from the entire scientific world.
		Clairaut's mature theory of the Earth's shape (1741-1743): first substantial connections between the revival of mathematics in Paris and progress in mechanics there; 10.
		Epilogue: Fontaine's and Clairaut's advances in the partial differential calculus revisited, or the virtues of interrelated developments in mathematics and science, and the fall of 'normal' science; Notes to chapters; Biography.
	www.cambridge.org /catalogue/print.asp?isbn=0521385415&print=y (421 words)

	[No title]
		Clairaut was a leading French mathematician (geometer) who expressed his mathematical abilities in early childhood.
		He was a mathematical genius who already at the age of twelve had been called to visit the Academy of Sciences in Paris.
		Clairaut was one of the scientists who accompanied Maupertuis to Lapland to collect data that was used to determine the shape of the earth.
	www.southernct.edu /~pinciuv/mat360pr5.html (312 words)

	The research notebook of a beleaguered hack. » Struik: A Concise History of Mathematics: The Eighteenth Century
		Alexis Claude Clairaut, a contemporary of Maupertuis, made a first attempt to deal with the analytical and differential geometry of space curves.
		Clairaut also made contributions to the theory of line integrals and differential equations.
		Clairaut’s name is preserved in Clairaut’s equation and Clairaut’s theorem.
	bentham.k2.t.u-tokyo.ac.jp /notebook/?p=92 (1581 words)

	Alexis-Claude Clairaut (Site not responding. Last check: 2007-10-31)
		Alexis Clairaut was a member of the French Academie des Sciences.
		Alexis-Claude Clairaut was one of the most renown mathematicians and physicists of the 18th century.
		Emilie's translation of Newton's Principia included an explanation of Clairaut's additions to Newton's work on the refraction of light (1739) and on the shape of the earth (1740).
	www.visitvoltaire.com /e_alexis-claude_clairaut.htm (271 words)

	Clairaut, Alexis Claude - HighBeam Encyclopedia (Site not responding. Last check: 2007-10-31)
		CLAIRAUT, ALEXIS CLAUDE [Clairaut, Alexis Claude], 1713-65, French mathematician.
		He is noted for his work on differential equations and on curves and for formulating Clairaut's theorem dealing with geodesic lines on the surface of an ellipsoid.
		Find newspaper and magazine articles plus images and maps related to "Clairaut, Alexis Claude" at HighBeam.
	www.encyclopedia.com /html/c/clairaut.asp (112 words)

	Alexis Claude Clairaut - The degree measurements by de Maupertuis (Site not responding. Last check: 2007-10-31)
		Alexis Claude Clairaut - The degree measurements by de Maupertuis
		Alexis Clairaut was born in 1713 and died in 1765.
		Clairaut proposition postulates in a simple way the dependency of the
	www4.rovaniemi.fi /lapinkavijat/maupertuis/clairaut_eng.html (84 words)

	CLAIRAUT, ALEXIS CLAUDE (1713 - 1765) (Site not responding. Last check: 2007-10-31)
		This is the first edition of Clairaut's first publication, a treatise on tortuous curves, with six folding engraved plates, written when he was only sixteen.
		The Académie des Sciences was so impressed by this mathematical prodigy that it suspended its rules of admission to elect him to the Académie at the age of eighteen.
		Much of Clairaut's later research was on the effect of gravity and centrifugal force on rotating bodies, going beyond Isaac Newton whose monumental Principia he assisted in translating.
	www.scs.uiuc.edu /~mainzv/exhibitmath/bkgd/clairaut-bkgd.htm (94 words)

	Clairaut's theorem - Wikipedia, the free encyclopedia
		In mathematical analysis, Clairaut's theorem states that if
		This theorem is named after the French mathematician Alexis Clairaut.
		A byproduct of this theorem is Clairaut's constant (alternatively known as "Clairaut's formula" and "Clairaut's parameter"), which relates the latitude,
	en.wikipedia.org /wiki/Clairaut's_theorem (116 words)

	Clairaut
		http://publish.uwo.ca/~jbell/chap7.pdf) Clairaut was elected to the Royal Society of London, the Academy of Berlin, the Academy of St. Petersburg and the Academies of Bologna and
		One of the areas of mathematics that Clairaut contributed to was geometry.
		Clairaut also showed that the area of a rectangle is the product of the measures of the length and the width and then a triangle is half of its base and height since a triangle is half of a rectangle.
	home.southernct.edu /~merckj1/MAT360Project.html (714 words)

	The Problem of the Earth's Shape from Newton to Clairaut - Cambridge University Press (Site not responding. Last check: 2007-10-31)
		His central thesis is that Newton's own publications contributed only a small part of the work done on the shape of the earth.
		The evolution of Parisian physics, then, proved to be not merely the replacement of one paradigm with another, as might be expected from Thomas Kuhn's formulations about scientific revolutions, but a long, complicated process involving many areas of research and contributions from the entire scientific world.
		Alexis-Claude Clairaut's first theories of the Earth's shape; 7.
	www.cambridge.org /us/catalogue/catalogue.asp?isbn=0521385415 (332 words)

	Lalande, Joseph Jérôme Le Français de (1732-1807)
		She and her collaborator released their findings in September 1757, in the nick of time, since by Christmas of that year the first sightings of the comet began.
		Their work was published in a paper by Clairaut, who, initially, gave full credit to Mme Lepaute’s efforts.
		Later, sadly, Clairaut retracted his statements and took full credit for himself.
	www.daviddarling.info /encyclopedia/L/LalandeJ.html (483 words)

	Rudy Rucker's KappaTau Space Curve Paper (Site not responding. Last check: 2007-10-31)
		Historically, space curves were first discussed by the mathematician Alexis-Claude Clairaut in a paper called "Recherche sur les Courbes a Double Courbure," published in 1731 when Clairaut was eighteen [1].
		Clairaut is said to have been an attractive, engaging man; he was a popular figure in eighteenth-century Paris society.
		In speaking of "double curvature," Clairaut meant that a path through three-dimensional space can warp itself in two independent ways; he thought of a curve in terms of its shadow projections onto, say, the floor and a wall.
	www.mathcs.sjsu.edu /faculty/rucker/kaptaudoc/ktpaper.htm (3028 words)

	Euler's Correspondence with Alexis Claude Clairaut
		A precocious youth, Alexis Clairaut was admitted to the French Academy of Sciences at the age of sixteen -- below the legal age for admittance.
		He is perhaps best known for his work on the three-body problem; his determination of the shape of the Earth (confirming Newton's declaration that it would be flattened at the poles); and his settling an apparent difference between observations of the apogees of the moon and theoretical predictions of the same.
		He wrote Clairaut to ask for assistance, but was apparently sufficiently unsatisfied with Clairaut's answer.
	math.dartmouth.edu /~euler/correspondence/correspondents/Clairaut.html (204 words)

	The New Atlantis - The Age of Female Computers - David Skinner
		But it was the French mathematician Alexis-Claude Clairaut, along with Lalande and Lepaute, who first computed the date of the comet’s perihelion with any precision in 1757, predicting it would occur in the spring of the following year.
		Lalande and Lepaute focused on the orbits and gravitational pulls of Jupiter and Saturn (the three-body problem), while Clairaut focused on the comet’s orbit.
		“With the perspective of modern astronomy,” Grier writes, “we know that Clairaut did not account for the influences of Uranus and Neptune, two large planets that were unknown in 1757.” Still, the result of their number-crunching was a tenfold improvement in accuracy over Halley’s prediction, if still not perfect.
	www.thenewatlantis.com /archive/12/skinner.htm (2564 words)

	Clairaut (Site not responding. Last check: 2007-10-31)
		ODE with the option Method->Clairaut attempts to solve a first-order differential equation considered as a Clairaut equation.
		The command form is Clairaut[f,const][t], where const is a symbol representing the constant of integration.
		In addition, Clairaut attempts to eliminate the parameter s (using Mathematica's Eliminate command) to produce the singular solution.
	www.maths.man.ac.uk /~kd/ode/3x/ref/odeappix/node5.htm (126 words)

	The Problem of the Earth's Shape from Newton to Clairaut: The Rise of Mathematical Science in Eighteenth-Century Paris ...
		The Problem of the Earth's Shape from Newton to Clairaut: The Rise of Mathematical Science in Eighteenth-Century Paris and the Fall of 'Normal' Science
		Until far into the 18th century man has wondered about the shape of the earth and different theories resulted in different shapes.
		Clairaut was the genius who applied hydrodynamical ideas in order to explain why the world has a larder diameter at the equator than at the poles.
	www.gettextbooks.com /isbn_0521385415.html (339 words)

	ESA - Space Science - 7 May
		It included precise measurements of the spacecraft's roll angle in space, subtle image distortions, and an investigation into the effects of stray light, which contaminate the science images.
		1713: On 7 May 1713, Alexis Claude Clairaut was born.
		He determined the first reasonable value for the mass of Venus, an improved value for the mass of the Moon, and predicted the timing of the return of Comet Halley.
	www.esa.int /esaSC/SEMY8O77ESD_index_0.html (463 words)

	History of Science and Technology: 18th-century Astronomy (Site not responding. Last check: 2007-10-31)
		1743 Clairaut, Theory of the shape of the earth, shows that Newton's theory is correct
		1747 Clairaut, Theory of the moon, announces that Newton's theory cannot account for the motions of the moon
		1749 Clairaut reverses himself and announces that Newton's theory does account for the motions of the moon
	www.public.asu.edu /~warrenve/s18_ast.html (277 words)

	Symbolic (Includes simple_11_6_02.html items from Mathematica)
		He introduced beta and gamma functions, and integrating factors for differential equations.
		He studied continuum mechanics, lunar theory with Clairaut, the three body problem, elasticity, acoustics, the wave theory of light, hydraulics, and music.
		He laid the foundation of analytical mechanics, especially in his Theory of the Motions of Rigid Bodies (1765).
	www.cs.ucla.edu /~klinger/pami/simple_11_06_02.html (226 words)

	Thomas Simpson (1710 - 1761) (Site not responding. Last check: 2007-10-31)
		In this last memoir Simpson obtained a differential equation for the motion of the apse of the lunar orbit similar to that arrived at by Clairaut, but instead of solving it by successive approximations, he deduced a general solution by indeterminate coefficients.
		The result agrees with that given by Clairaut.
		Simpson solved this problem in 1747, two years later than the publication of Clairaut's memoir, but the solution was discovered independently of Clairaut's researches, of which Simpson first heard in 1748.
	www.maths.tcd.ie /pub/HistMath/People/Simpson/RouseBall/RB_Simpson.html (458 words)

	Calculus III (Math 2415) - Partial Derivatives - Higher Order Partial Derivatives (Site not responding. Last check: 2007-10-31)
		Notice as well that for both of these we differentiate once with respect to y and twice with respect to x. There is also another third order partial derivative in which we can do this,
		To this point we’ve only looked at functions of two variables, but everything that we’ve done to this point will work regardless of the number of variables that we’ve got in the function and there are natural extensions to Clairaut’s theorem to all of these cases as well. For instance,
		In general, we can extend Clairaut’s theorem to any function and mixed partial derivatives. The only requirement is that in each derivative we differentiate with respect to each variable the same number of times. In other words, provided we meet the continuity condition, the following will be equal
	tutorial.math.lamar.edu /AllBrowsers/2415/HighOrderPartialDerivs.asp (728 words)

	[No title]
		Part III might be used as an introduction to Lagrange and Clairaut type differential equations (if they are covered in the course).
		TI92 Plus scripts for solving Lagrange and Clairaut types of differential equations are given in the Appendix.
		Appendix — Solving Lagrange and Clairaut Differential Equations Figure 9 — TI92 Plus script — Solving Lagrange differential equation Figure 10 - TI92 Plus script — Solving Clairaut differential equation Lagrange Differential Equation: EMBED Equation.3 , EMBED Equation.3 and EMBED Equation.3 are differentiable functions.
	archives.math.utk.edu /ICTCM/EP-16/C5/MSWord/paper.doc (2171 words)

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