eBook ISBN:  9780883859261 
Product Code:  NML/9.E 
List Price:  $50.00 
MAA Member Price:  $37.50 
AMS Member Price:  $37.50 
eBook ISBN:  9780883859261 
Product Code:  NML/9.E 
List Price:  $50.00 
MAA Member Price:  $37.50 
AMS Member Price:  $37.50 

Book DetailsAnneli Lax New Mathematical LibraryVolume: 9; 1963; 162 pp
Continued fractions were studied by the great mathematicians of the seventeenth and eighteenth centuries and are a subject of active investigation today. Fractions of this form provide much insight into many mathematical problems—particularly into the nature of numbers—and the theory of continued fractions is a powerful tool in number theory and other mathematical disciplines.
The author presents an easygoing discussion of simple continued fractions, beginning with an account of how rational fractions can be expanded into continued fractions. Gradually, the reader is introduced to such topics as the application of continued fractions to the solution of Diophantine equations and the expansion of irrational numbers into infinite continued fractions.

Table of Contents

Chapters

Chapter 1. Expansion of Rational Fractions

Chapter 2. Diophantine Equations

Chapter 3. Expansion of Irrational Numbers

Chapter 4. Periodic Continued Fractions

Chapter 5. Epilogue

Appendix I. Proof That $x^2  3y^2 = 1$ Has No Integral Solutions

Appendix II. Some Miscellaneous Expansions


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Continued fractions were studied by the great mathematicians of the seventeenth and eighteenth centuries and are a subject of active investigation today. Fractions of this form provide much insight into many mathematical problems—particularly into the nature of numbers—and the theory of continued fractions is a powerful tool in number theory and other mathematical disciplines.
The author presents an easygoing discussion of simple continued fractions, beginning with an account of how rational fractions can be expanded into continued fractions. Gradually, the reader is introduced to such topics as the application of continued fractions to the solution of Diophantine equations and the expansion of irrational numbers into infinite continued fractions.

Chapters

Chapter 1. Expansion of Rational Fractions

Chapter 2. Diophantine Equations

Chapter 3. Expansion of Irrational Numbers

Chapter 4. Periodic Continued Fractions

Chapter 5. Epilogue

Appendix I. Proof That $x^2  3y^2 = 1$ Has No Integral Solutions

Appendix II. Some Miscellaneous Expansions