ABSTRACT
In this chapter authors are concerned with the subject of Diophantine approximation. Diophantine approximation is mainly concerned with the approximation of real numbers by rational numbers (hence, the term “Diophantine”). The author will discuss two different ways of doing this: by way of Farey fractions and by way of continued fractions. Farey fractions are a sequence of rationals that can be used in approximation problems and exist irrespective of the real numbers we are trying to approximate. Continued fractions can be looked on as an algorithm for producing a series of rationals that can be used as a sequence of progressively better approximations for a given real number.
