Olds C.D. Continued Fractions

169 p. - Random House "New Mathematical Library" series - 3rd edition - 1963.This book is one of a series written by professional mathematicians in order to make some important mathematical ideas interesting and understandable to a large audience of high school students and laymen.Prefrace.
Expansion of Rational Functions.Definitions and notation.
Expansion of rational functions.
Expansion of rational functions (general discussion).
Convergents and their properties.
Differences of Convergents.
Some Historical Comments.
Diophantine Equations.The method used extensively by Euler.
The indeterminate equation ax - by = +-1.
The general solution of ax - by = c, (a, b) = 1.
The general solution of ax + by = c, (a, b) = 1.
The general solution of Ax +- By = +-C, (a, b) = 1.
Sailors, coconuts, and Monkeys.
Expansion of Irrational Numbers.Preliminary examples.
Convergents.
Additional theorems on convergents.
Some notations of a limit.
Infinite continued fractions.
Approximation theorems.
Geometrical interpretation of continued fractions.
Solution of the Equation x^2 = ax +1.
Fibonnaci numbers.
A method for calculation logarithms.
Periodic Continued Fractions.Purely periodic continued fractions.
Quadratic irrationals.
Reduced quadratic irrationals.
Converse of theorem 4.1.
Lagrange's theorem.
The continued fraction for sqrt(N).
Pell's equation, x^2 - Ny^2 = +-1.
How to obtain solutions of Pell's equation.
Epilogue.Statement of the problem.
Hurwitz' theorem.Appendix I Proof that x^2 - e y^2 = -1 Has no integral solutions.
Aooendix II Some Miscellaneous Expansions.
Solutions to Problems.