The French mathematician Adrien-Marie Legendre (1752–1833) taught at the French military academy with Pierre-Simon de Laplace, starting in 1775. In 1782 he won a prize for the best research project on the speed, path, and flight dynamics of cannon-balls moving through the air. Elected to the French Academy of Sciences the next year, he combined his research on abstract mathematics with important work on celestial mechanics. In 1794, Legendre wrote a geometry textbook that was the definitive work in the field for nearly a century. In 1806, he published *Nouvelles methods pour la determination des orbits des cometes* (“New Methods for the Determination of the Orbits of Comets”). Here he introduced a technique for finding the equation of a mathematical curve using imperfect data. Legendre is best known today for his work on elliptical functions and for inventing a class of functions called Legendre polynomials, which are valuable tools for studying harmonic vibrations and for finding mathematical curves that fit large series of data points.