Alexis Claude Clairaut

Alexis Claude Clairaut , born with Paris the May 13rd 1713 and died in Paris the May 17th 1765, is a Mathématicien French.

Biography

He is the second of a phratry of 21. His/her father, Jean-Baptiste Clairaut (1680 - 1766), taught mathematics. He is informed by him in this matter, learning how to read in the Éléments of Euclide . He shows himself of a precocity such as at the twelve years age he writes a report on four geometrical curves. At thirteen years, it reads in front of the Academy of Science a report of the properties of four curves which it had discovered. At sixteen years only, it finishes a treaty entitled Recherches on the tortuous curves which, during its publication in 1731, involve its admission with the Academy of Science whereas it did not have the lawful age.

In 1731, it obtains a demonstration of the remarkable fact due to Newton that all the third order curves are projections of five particular parabolas. He becomes member of the Royal Society on October 27th 1737.

In 1736, with Pierre Louis Moreau de Maupertuis, it takes part in forwarding in Lapland whose object is to estimate the length of a degree of Méridien. On its return, it publishes a treaty Théorie of the figure of the ground (1743), where it shows the theorem, known under the name of “theorem of Clairaut”, which connects geometrical flatness F to the surface of a Ellipsoïde in rotation with a kinetic quantity (the factor of geodynamic form J ₂) and with a dynamic quantity Q , representing the report/ratio of the centrifugal force to gravity with the equator. This work is founded on an article of Colin Maclaurin, which had shown that a homogeneous mass of fluid in regular rotation around a line passing by its Center of gravity, under the mutual attraction of its particles, took the form of a Sphéroïde. This work of Clairaut treats heterogeneous spheroids and contains the proof of its formula for the effect of acceleration of gravity in a point of the place of latitude L.

It obtains a clever approximate solution with the problem of the three bodies. Impressed by the power of the geometry in the writings of Newton and Maclaurin, the analysis is given up by Clairaut, and its following work, a Théorie of the moon (1752), is strictly of Newtonian nature. It contains the explanation of the movement of the Apside which had previously embarrassed the astronomers, and which Clairaut had initially regarded as so unexplainable that it was about to publish a new assumption on the law of attraction. It has then the idea to make an approximation with the third order, which enables him to note that the result was in conformity with the observations. This one is followed in 1754 of some lunar tables and, in 1759, it calculates the Périhélie Halley's Comet. It also finds the solutions singular of certain equations first order and natures higher.

The Astéroïde (9592) Clairaut was baptized in its honor.

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References and notes

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