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Everything about Simple continued fraction
Number represented as a0+1/(a1+1/...)
A simple or regular continued fraction is a continued fraction with numerators all equal to one, and denominators built from a sequence of integer numbers. The sequence can be finite or infinite, resulting in a finite continued fraction like or an infinite continued fraction like Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Simple continued fractionA 5-minute orientation
- Skim a recent paper: Error approximation for backwards and simple continued fractionsInfluential work since 2022
- Pick up a classic book: Signals and SystemsThe most-reprinted book on the subject
- Read the landmark paper: Continued-Fraction Description of Collective Motion in Simple FluidsCited 17 times
- Go sideways: Decimal representationA closely related topic
- Go sideways: Stern–Brocot treeA closely related topic
📖 Definitions
Noun A continued fraction were all of the numerators are 1.
🗂️ The subject at a glance
- Motivation and notation
- Formulation
- Calculating continued fraction representations
- Reciprocals
- Finite continued fractions
- Infinite continued fractions and convergents
- Semiconvergents
- Best rational approximations
- Comparison
- Continued fraction expansion of π and its convergents
- Non-simple continued fraction
- Other continued fraction expansions
🏆 Landmark papers (most cited)
Continued-Fraction Description of Collective Motion in Simple Fluids
Length of period simple continued fraction expansion of √d
The Simple Continued Fraction Expansion ofe
An upper bound for the period of the simple continued fraction for √D
Simple continued fraction solutions for diophantine equations
A Short Proof of the Simple Continued Fraction Expansion of 𝑒
A simple algorithm for expanding a power series as a continued fraction
A Short Proof of the Simple Continued Fraction Expansion of e
🆕 Influential since 2022
📚 Books worth reading
Signals and SystemsAlan V. Oppenheim, Alan S. Willsky · 1983
Exploratory data analysisJohn Wilder Tukey · 1970
Introduction to Probability and StatisticsJ. Susan Milton, Jesse C. Arnold · 1990
The Conspirators HierarchyJohn Coleman · 1992
Treaty Occupationay ToxicologySuelen Queiroz · 2010
First steps in random walksJ. Klafter · 2011- 📕Exploring Continued FractionsAndrew J. Simoson · 2019
- 📕Logistikēlogia, or Arithmetick surveighed and reviewedSamuel Jeake · 1696
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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- Continued fraction b0+a1b1+a2b2+a3b3+⋱ A continued fraction is a mathematical expression written as a fraction whose denominator contains a sum involving another fraction…
- Markov constant In number theory, specifically in Diophantine approximation theory, the Markov constant M(α) of an irrational number α is the factor for which Dirichlet's…
- Irrationality measure In mathematics, an irrationality measure of a real number x is a measure of how closely it can be approximated by a rational number. If a function f(t…
- Liouville number In number theory, a Liouville number is a real number x with the property that, for every positive integer n, there exists a pair of integers (p,q) with…
- Square root of 2 The square root of 2 (approximately 1.4142) is the positive real number that, when multiplied by itself or squared, equals the number 2. It may be written…
- Convergence problem In the analytic theory of continued fractions, the convergence problem is the determination of conditions on the partial numerators ai and partial denominators…