Clairaut's theorem

Lagrange
Alexis Clairaut was a French mathematician who worked to confirm the Newton-Huygens belief that the Earth was flattened at the poles.
Alexis Claude Clairaut was a French mathematician, astronomer, and geophysicist.

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The Four Curves of Alexis Clairaut

Introduction

Alexis Clairaut was born 7 May 1713 in Paris, to father Jean-Baptiste and mother Catherine (née Petit). His father was a mathematician and teacher. Alexis was a veritable prodigy. His studies started early and were primarily domestic. He learned the alphabet from the diagrams in Euclid's Elements (though, to be fair, this may have been intended tongue-in-cheek, as in, He was studying mathematics so early that he was reading Euclid at the same time he was learning the alphabet!). At age four, he could read and write well. By nine, he had studied Application de l'algèbre à la géométrie by Guisnée, under the guidance of his father. At ten, he began studying Traité analytique des sections coniques and Analyse des infiniment petits, both by L'Hôpital. For further details about Clairaut's life and work, see [5,4,2]. In 1726, at the age of just twelve and a half, he presented his research on four families of algebraic curves to the Royal Academy of Sciences in Paris. This work was later published in 1734 in volume 4 of the

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Clairaut, Alexis Claude

Alexis Claude Clairaut: A Mathematical Genius Illuminates the Skies

Alexis Claude Clairaut, born in 1713, was a prodigious talent whose contributions to the field of astronomy left an indelible mark on our understanding of the cosmos. A child prodigy, he published his first significant mathematical work at the tender age of 12. This precocity, combined with his unwavering dedication to the study of celestial mechanics, propelled him to become one of the most influential astronomers of his time.

Clairaut's early work focused on the complex motion of the Moon, a celestial body whose orbit had long puzzled astronomers. He skillfully applied the laws of gravity and calculus to develop a more accurate mathematical model of the Moon's movement, offering invaluable insights into the intricate dance between Earth and its natural satellite. This groundbreaking research earned him recognition within the scientific community and cemented his reputation as a rising star in the field.

However, Clairaut's most famous achievement lay in his prediction of the perihelio

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Alexis Clairaut

French mathematician, astronomer, and geophysicist (1713–1765)

Alexis Claude Clairaut (; French:[alɛksiklodklɛʁo]; 13 May 1713 – 17 May 1765) was a French mathematician, astronomer, and geophysicist. He was a prominent Newtonian whose work helped to establish the validity of the principles and results that Sir Isaac Newton had outlined in the Principia of 1687. Clairaut was one of the key figures in the expedition to Lapland that helped to confirm Newton's theory for the figure of the Earth. In that context, Clairaut worked out a mathematical result now known as "Clairaut's theorem". He also tackled the gravitational three-body problem, being the first to obtain a satisfactory result for the apsidal precession of the Moon's orbit. In mathematics he is also credited with Clairaut's equation and Clairaut's relation.

Biography

Childhood and early life

Clairaut was born in Paris, France, to Jean-Baptiste and Catherine Petit Clairaut. The couple had 20 children, however only a few of them survived childbirth.^[2] His father t