Revision #963 → #1566 · back to history
addedSimple continued fraction5622ec92e70f
addedCoefficients/terms of a continued fraction1e1bbcba7cbd
addedRational has two finite continued fraction expressions79392b36a20b
addedIrrationality of infinite continued fraction valueaeb327eaa0e2
addedUnique infinite continued fraction for irrationals12ca0b5a3efe
addedContinued fraction of 415/93253fba883f19
addedBracket notation for continued fractionsaca7da6f06d7
addedContinued fractions of √19, e, π, φ, γ482e602b0755
addedFinite iff rational21127a528f5f
addedTwo representations of a rational1f46021bfce3
addedUniqueness for irrationals5d59a3364b8c
addedEventually periodic iff quadratic irrational520034a4a0b8
addedCanonical form of a continued fraction10ce6d4d6f8a
addedFinite, infinite, periodic continued fractionda6c85587cb9
addedRecursive definition of terms30d23e516b0f
addedLimit definition of infinite simple continued fraction88e836a1cf93
addedRecursive definition of continued fraction representation99bf320cfc74
addedAlgorithm for continued fraction representatione5149dd9b90f
addedReciprocal shift propertyd824be7096b1
addedReciprocal with integer leading term6a0fcc317b96
addedLast term equal for number and reciprocalb21ef7878500
addedFinite continued fractions represent rationals (two ways)069c671c183b
addedInfinite continued fraction iff irrational334ed78b1fe3
addedConvergents01bfd6efa6c1
addedGaussian bracket recurrence for convergentse1b50b7676c3
addedEven/odd convergents bound the value05558f6c0a37
addedBabylonian method approximants appear as convergents7c01e0498bf7
addedBaire space homeomorphismab3867ba0feb
addedMinkowski question-mark mapping1d1dbafca92d
addedGauss–Kuzmin distribution30ab81ca1824
addedTheorem 1 (value of continued fraction)859ae760871c
addedTheorem 2 (convergent formula)5bc879f9d320
addedTheorem 3 (convergent identity)3ac0b22258cb
addedCorollary 1: convergents in lowest termsc1de0dbeaa6d
addedCorollary 2: difference of successive convergentsf183106299a6
addedCorollary 3: alternating series forme3617362ed60
addedCorollary 4: unimodular matrix57fe6eda6d1d
addedCorollary 5: odd/even term monotonicitya111c997b058
addedCorollary 6: denominator recurrence and growth08143b711f00
addedTheorem 4 (convergents get closer)792d6dfb77e5
addedCorollary 1 to Theorem 4: even convergents increaseb72662d27e10
addedCorollary 2 to Theorem 4: odd convergents decreased989e3a9c66c
addedTheorem 52acac9a36f42
addedCorollary 1 to Theorem 5: best approximation property6cb9810146d8
addedCorollary 2 to Theorem 5: large term gives close approximation14319e923dca
addedTheorem 6 (open intervals basis)ee7b19736a8c
addedCorollary to Theorem 6: Baire space homeomorphisma06b19ddda88
addedSemiconvergent18b2a927b7df
addedMonotonic sequence of semiconvergents70eef053fb98
addedBest rational approximation is a semiconvergente681cb0c1533
addedBest rational approximation0961f80e5a70
addedBest approximations of 0.843757167857736dd
addedHalf rule for semiconvergent admissibility9345904dd4fb
addedConvergents are best approximations in strong sense10f2685dd088
addedBest rational within an interval8d1440fadac4
addedBest rational extension to rational endpointsb6a8d76e30b3
addedBest rational rounding to 3.1416e18671a6f7cb
addedInterval characterization for a convergentf4dbf5cfc564
addedConvergent interval for 355/11340bc2f378dad
addedLegendre's theorem on continued fractions8f0beaa715cf
addedComparison of continued fractionsb43b9c4be808
addedComparison when one expansion is shorter18401d6ac035
addedConvergents of πce285cd73047
addedConvergent error bound for π788d20f7cc1c
addedNon-simple continued fractioncd5bd072442d
addedRegular non-simple continued fractions for π890863d81026
addedPeriodic expansions = quadratic irrationals410906b7b11b
addedSymmetric period of √n0c96766efd6d
addedHurwitz's theoremf8ed294f15b5
addedGolden ratio extremal approximation propertya1cf8cbb8ff9
addedContinued fraction pattern for e4b8fd6d821ee
addedBessel function continued fractionfbcda15487d9
addedArithmetic average of coefficients diverges8daf9a6f9048
addedKhinchin's theoremaa34007de053
addedLévy's theorem3ded69bfe64b
addedLochs' theoremab6efa6ef2d8
addedPell's equation and convergents7d0915f44e8a
addedGauss map (backwards shift)c0a081620fd8
addedGauss–Kuzmin–Wirsing operator8186d16103a7