Continued fractions, Pell-Fermat equation and Fibonacci trick

The theory of ratios before Eudoxus of Cnidus led to the creation of an iterative algorithm for approximations of irrational square roots. From this algorithm, a method of solving the Pell-Fermat equation for some non-square numbers was formed. This iterative procedure was also used to obtain the golden ratio approximations. It caused Leonardo of Pisa (Fibonacci) to invent his curious problem about rabbits. After the lecture, a new book by Cassini Publishing House “Histoire du calcul graphique” will be announced.