Continued fractions have an history as long as the history of mathematics. I will begin by several short histories showing where continued fractions appear. Then, I review some mathematical problems involving them such as the golden ratio, the GCD, the square root, and Diophantine equations. The contributions of Indian mathematicians of the 12th century, Italian scholars from the Renaissance, and British scientists of the 17th century will be discussed. Then, comes the golden age with three outstanding mathematicians: Euler, Lambert and Lagrange, and the birth of Padé approximants. In the 19th century almost all mathematicians in the world knew continued fractions. I will discuss the work of Galois, and those of Liouville, Hermite, Lindemann on transcendental numbers, and I will end with Cantor, Stieltjes, and Hilbert.
Univ. of Sciences and Technologies of Lille, France
Este colóquio é organizado pelo Centro de Matemática da Universidade de Coimbra e pelo Departamento de Matemática da Universidade de Coimbra.