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005			20240729125049.0
006			m o d |
007			cr cnu||||||||
008			240724s1963 xx o ||||0 eng d
020			_a9780883859261 _q(electronic bk.)
020			_z9780883856093
035			_a(MiAaPQ)EBC3330383
035			_a(Au-PeEL)EBL3330383
035			_a(CaPaEBR)ebr10729354
035			_a(OCoLC)929120429
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA295 -- .O43 1963eb
082	0		_a513.26
100	1		_aOlds, Carl D.
245	1	0	_aContinued Fractions.
250			_a1st ed.
264		1	_aWashington : _bAmerican Mathematical Society, _c1963.
264		4	_c©1963.
300			_a1 online resource (171 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aAnneli Lax New Mathematical Library ; _vv.9
505	0		_aFront 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 -- 2.4 The General Solution of ax - by = c, (a, b) = 1 -- 2.5 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 -- 3.11 A Method for Calculating Logarithms -- Chapter 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 -- Appendix I. Proof That x2 - 3y2 = - 1 Has No Integral Solutions -- Appendix II. Some Miscellaneous Expansions -- Solutions to Problems -- References -- Index.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aContinued fractions.
650		0	_aSeries.
655		4	_aElectronic books.
776	0	8	_iPrint version: _aOlds, Carl D. _tContinued Fractions _dWashington : American Mathematical Society,c1963 _z9780883856093
797	2		_aProQuest (Firm)
830		0	_aAnneli Lax New Mathematical Library
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3330383 _zClick to View
999			_c79837 _d79837