The present book is not addressed to a well defined group of readers. The first chapter is based on a lecture given to a special mathematics class of the sixth grade. The material of the second chapter belongs to elementary algebra; that of the third, fourth and fifth chapters may be studied by students of the twelfth grade. The subject of the sixth and seventh chapters may be accessible to selected high school seniors, but might just as well be read by college seniors. Knowledge of elementary Euclidean geometry is presupposed, and some familiarity with the basic notions of physics will be helpful.

It is hoped that this book will also be useful to teachers as a source of material and points of view not covered in the regular curriculum. The main viewpoints and guiding ideas in this book are explained in the introduction.

In order not to interrupt the unity of the presentation, many details have been skipped; the filling in of such details may perhaps serve in lieu of exercises.

The subject of this book is dominated by a definite theme strung along a somewhat meandering thread. Naturally, the author would be happy if there were at least one reader who would follow this thread from beginning to end.