Continued Fractions /
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| Author / Creator: | Olds, C. D. |
|---|---|
| Imprint: | Cambridge : Cambridge University Press, 2012. |
| Description: | 1 online resource |
| Language: | English |
| Series: | Anneli Lax New Mathematical Library ; v. 9 Anneli Lax new mathematical library. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11124522 |
MARC
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| 245 | 1 | 0 | |a Continued Fractions / |c C.D. Olds. |
| 260 | |a Cambridge : |b Cambridge University Press, |c 2012. | ||
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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 | |
| 650 | 0 | |a Continued fractions. |0 http://id.loc.gov/authorities/subjects/sh85051149 | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Intermediate. |2 bisacsh | |
| 650 | 7 | |a Continued fractions. |2 fast |0 (OCoLC)fst00876703 | |
| 655 | 0 | |a Electronic books. | |
| 655 | 4 | |a Electronic books. | |
| 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. |0 http://id.loc.gov/authorities/names/n2002012009 | |
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