| Abstract: | In this article, we will show that the Pythagorean approximationsof  coincide with those achieved in the 16th century by means of continued fractions. Assumingthis fact and the known relation that connects the Fibonaccisequence with the golden section, we shall establish a procedureto obtain sequences of rational numbers converging to differentalgebraic irrationals. We will see how approximations to someirrational numbers, using known facts from the history of mathematics,may perhaps help to acquire a better comprehension of the realnumbers and their properties at further mathematics level. |
