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Continued Fractions /
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 #x97; particularly into the nature of numbers #x97; and the theory of...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2012.
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| Colección: | Anneli Lax new mathematical library.
|
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Olds, C. D. | |
| 245 | 1 | 0 | |a Continued Fractions / |c C.D. Olds. |
| 260 | |a Cambridge : |b Cambridge University Press, |c 2012. | ||
| 300 | |a 1 online resource | ||
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| 490 | 1 | |a Anneli Lax New Mathematical Library ; |v v. 9 | |
| 500 | |a Title from publishers bibliographic system (viewed on 30 Jan 2012). | ||
| 505 | 0 | |a Front Cover -- Continued Fractions -- Copyright Page -- Contents -- Preface -- Chapter 1. Expansion of Rational Fractions -- 1.1 Introduction -- 1.2 Definitions and Notation -- 1.3 Expansion of Rational Fractions -- 1.4 Expansion of Rational Fractions (General Discussion) -- 1.5 Convergents and Their Properties -- 1.6 Differences of Convergents -- 1.7 Some Historical Comments -- Chapter 2. Diophantine Equations -- 2.1 Introduction -- 2.2 The Method Used Extensively by Euler -- 2.3 The Indeterminate Equation ax � by = ±1 | |
| 505 | 8 | |a 2.4 The General Solution of ax -- by = c, (a, b) = 12.5 The General Solution of ax + by = c, (a, b) = 1 -- 2.6 The General Solution of Ax ± By = ±C -- 2.7 Sailors, Coconuts, and Monkeys -- Chapter 3. Expansion of Irrational Numbers -- 3.1 Introduction -- 3.2 Preliminary Examples -- 3.3 Convergents -- 3.4 Additional Theorems on Convergents -- 3.5 Some Notions of a Limit -- 3.6 Infinite Continued Fractions -- 3.7 Approximation Theorems -- 3.8 Geometrical Interpretation of Continued Fractions -- 3.9 Solution of the Equation x2 = ax + 1 -- 3.10 Fibonacci Numbers | |
| 505 | 8 | |a 3.11 A Method for Calculating LogarithmsChapter 4. Periodic Continued Fractions -- 4.1 Introduction -- 4.2 Purely Periodic Continued Fractions -- 4.3 Quadratic Irrationals -- 4.4 Reduced Quadratic Irrationals -- 4.5 Converse of Theorem 4.1 -- 4.6 Lagrange�s Theorem -- 4.7 The Continued Fraction for N -- 4.8 Pell�s Equation, x2 � Ny2 = ±1 -- 4.9 How to Obtain Other Solutions of Pell�s Equation -- Chapter 5. Epilogue -- 5.1 Introduction -- 5.2 Statement of the Problem -- 5.3 Hurwitz� Theorem -- 5.4 Conclusion | |
| 505 | 8 | |a Appendix I. Proof That x2 -- 3y2 = � 1 Has No Integral SolutionsAppendix II. Some Miscellaneous Expansions -- Solutions to Problems -- References -- Index | |
| 520 | |a 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 #x97; particularly into the nature of numbers #x97; 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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| 650 | 0 | |a Continued fractions. | |
| 650 | 6 | |a Fractions continues. | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Intermediate. |2 bisacsh | |
| 650 | 7 | |a Continued fractions |2 fast | |
| 776 | 0 | 8 | |i Print version: |a Olds, Carl D. |t Continued Fractions. |d Washington : Mathematical Association of America, ©2014 |z 9780883856093 |
| 830 | 0 | |a Anneli Lax new mathematical library. | |
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