目录
 前辅文
 I. RATIONALS AND IRRATIONALS
  1. The preponderance of irrationals
  2. Countability
  3. Dense sets
  4. Decimal expansions
 II. SIMPLE IRATIONALITIES
  1. Introduction
  2. The trigonometric functions and π
  3. The hyperbolic, exponential, and logarithmic functions
 III. CERTAIN ALGEBRAIC NUMBERS
  1. Introduction
  2. Further background material
  3. The factorization of xn-1
  4. Certain trigonometric values
  5. Extension to the tangent
 IV.THE APPROXIMATION or IRRATIONALS BY RATIONALS
  1. The problem
  2. A generalization
  3. Linearly dependent sets
 v. CONTINTED FEACTIONS
  1. The Euclidean algorithm
  2. Uniqueness
  3. Infinite continued fractions
  4. Infinite continued fraction expansions
  5. The convergents as approximations
  6. Periodic continued fractions
 VI. FURTHER DIOPHANTINE APPROXIMATIONS
  1. A basic result
  2. Best possible approximations
  3. Uniform distributions
  4. A proof by Fourier analysis
 VII. ALGEBRAIC AND TRANSCENDENTAL NUMBERS
  1. Closure properties of algebraic numbers
  2. A property of algebraic integers
  3. Transcendental numbers
  4. The order of approximation
 VIII. NORMAL NUMBERS
  1. Definition of a normal number
  2. The measure of the set of normal numbers
  3. Equivalent definitions
  4. A normal number exhibited
 IX. THE GENERALIZED LINDEMANN THEOREM
  1. Statement of the theorem
  2. Preliminaries
  3. Proof of the theorem
  4. Applications of the theorem
  5. Squaring the circle
 X. THE GELFOND-SCHNEIDER THEOREM
  1. Hilbert's seventh problem
  2. Background material
  3. Two lemmas
  4. Proof of the Gelfond-Schneider theorem
 LIST OF NOTATION
 GLOSSARY
 REFERENCE Books
 INDEX or TOPICS
 INDEX or NAMES
 前辅文
 I. RATIONALS AND IRRATIONALS
  1. The preponderance of irrationals
  2. Countability
  3. Dense sets
  4. Decimal expansions
 II. SIMPLE IRATIONALITIES
  1. Introduction
  2. The trigonometric functions and π
  3. The hyperbolic, exponential, and logarithmic functions
 III. CERTAIN ALGEBRAIC NUMBERS
  1. Introduction
  2. Further background material
  3. The factorization of xn-1
  4. Certain trigonometric values
  5. Extension to the tangent
 IV.THE APPROXIMATION or IRRATIONALS BY RATIONALS
  1. The problem
  2. A generalization
  3. Linearly dependent sets
 v. CONTINTED FEACTIONS
  1. The Euclidean algorithm
  2. Uniqueness
  3. Infinite continued fractions
  4. Infinite continued fraction expansions
  5. The convergents as approximations
  6. Periodic continued fractions
 VI. FURTHER DIOPHANTINE APPROXIMATIONS
  1. A basic result
  2. Best possible approximations
  3. Uniform distributions
  4. A proof by Fourier analysis
 VII. ALGEBRAIC AND TRANSCENDENTAL NUMBERS
  1. Closure properties of algebraic numbers
  2. A property of algebraic integers
  3. Transcendental numbers
  4. The order of approximation
 VIII. NORMAL NUMBERS
  1. Definition of a normal number
  2. The measure of the set of normal numbers
  3. Equivalent definitions
  4. A normal number exhibited
 IX. THE GENERALIZED LINDEMANN THEOREM
  1. Statement of the theorem
  2. Preliminaries
  3. Proof of the theorem
  4. Applications of the theorem
  5. Squaring the circle
 X. THE GELFOND-SCHNEIDER THEOREM
  1. Hilbert's seventh problem
  2. Background material
  3. Two lemmas
  4. Proof of the Gelfond-Schneider theorem
 LIST OF NOTATION
 GLOSSARY
 REFERENCE Books
 INDEX or TOPICS
 INDEX or NAMES