Continued Fractions

C. D. Olds

doi:10.5948/UPO9780883859261

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 of this book presents an easy-going 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.

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Continued Fractions

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Contents

Frontmatter
pp i-vi

Contents
pp vii-viii

CONTINUED FRACTIONS
pp 1-2

Preface
pp 3-4

Chapter 1 - Expansion of Rational Fractions
pp 5-30

Chapter 2 - Diophantine Equations
pp 31-50

Chapter 3 - Expansion of Irrational Numbers
pp 51-87

Chapter 4 - Periodic Continued Fractions
pp 88-122

Chapter 5 - Epilogue
pp 123-130

Appendix I - Proof That x2 – 3y2 = –1 Has No Integral Solutions
pp 131-133

Appendix II - Some Miscellaneous Expansions
pp 134-139

Solutions to Problems
pp 140-158

References
pp 159-160

Index
pp 161-162

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Continued Fractions

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