N. M. Beskin

The booklet describes various theories to which a deep study of the problem of dividing a line segment in a given ratio leads. Considering this elementary problem and those related to it, the reader will make a short travel over some branches of mathematics, come into contact with affine and projective geometry and the theory of groups, though in most cases without mentioning these names.
The book is intended for pupils of the senior forms; in its main parts it can be easily grasped by pupils of the seventh and eighth forms.… (mehr)

The book invites high-school students to make a short journey into a branch of arithmetic that deals with the approximation of real numbers by rational ones and get acquainted with the world of continued fractions. The theory of continued fractions is a part of classical mathematics that is widely used for evaluating functions. While there is an extensive literature on the theory, this is a fascinating presentation of its basic concepts and facts that will be useful for anyone interested in mathematics.… (mehr)