**1.**

Adrien-Marie Legendre was a French mathematician who made numerous contributions to mathematics.

Adrien-Marie Legendre was a French mathematician who made numerous contributions to mathematics.

Adrien-Marie Legendre received his education at the College Mazarin in Paris, and defended his thesis in physics and mathematics in 1770.

Adrien-Marie Legendre taught at the Ecole Militaire in Paris from 1775 to 1780 and at the Ecole Normale from 1795.

Adrien-Marie Legendre assisted with the Anglo-French Survey to calculate the precise distance between the Paris Observatory and the Royal Greenwich Observatory by means of trigonometry.

Adrien-Marie Legendre lost his private fortune in 1793 during the French Revolution.

In 1795, Adrien-Marie Legendre became one of six members of the mathematics section of the reconstituted Academie des Sciences, renamed the Institut National des Sciences et des Arts.

Later, in 1803, Napoleon reorganized the Institut National, and Adrien-Marie Legendre became a member of the Geometry section.

From 1799 to 1812, Adrien-Marie Legendre served as mathematics examiner for graduating artillery students at the Ecole Militaire and from 1799 to 1815 he served as permanent mathematics examiner for the Ecole Polytechnique.

Adrien-Marie Legendre's pension was partially reinstated with the change in government in 1828.

Adrien-Marie Legendre died in Paris on 9 January 1833, after a long and painful illness, and Adrien-Marie Legendre's widow carefully preserved his belongings to memorialize him.

Adrien-Marie Legendre's name is one of the 72 names inscribed on the Eiffel Tower.

Adrien-Marie Legendre developed, and first communicated to his contemporaries before Gauss, the least squares method which has broad application in linear regression, signal processing, statistics, and curve fitting; this was published in 1806 as an appendix to his book on the paths of comets.

In number theory, he conjectured the quadratic reciprocity law, subsequently proved by Gauss; in connection to this, the Adrien-Marie Legendre symbol is named after him.

Adrien-Marie Legendre did pioneering work on the distribution of primes, and on the application of analysis to number theory.

Adrien-Marie Legendre did an impressive amount of work on elliptic functions, including the classification of elliptic integrals, but it took Abel's stroke of genius to study the inverses of Jacobi's functions and solve the problem completely.

Adrien-Marie Legendre is known for the Legendre transformation, which is used to go from the Lagrangian to the Hamiltonian formulation of classical mechanics.

Adrien-Marie Legendre is the namesake of the Legendre polynomials, solutions to Legendre's differential equation, which occur frequently in physics and engineering applications, such as electrostatics.

Adrien-Marie Legendre is best known as the author of Elements de geometrie, which was published in 1794 and was the leading elementary text on the topic for around 100 years.

The error arose from the fact that the sketch was labelled simply "Adrien-Marie Legendre" and appeared in a book along with contemporary mathematicians such as Lagrange.

The only known portrait of Adrien-Marie Legendre, rediscovered in 2008, is found in the 1820 book Album de 73 portraits-charge aquarelles des membres de I'Institut, a book of caricatures of seventy-three members of the Institut de France in Paris by the French artist Julien-Leopold Boilly as shown below:.