Statements (32)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
Simple continued fraction
|
| gptkbp:application |
gptkb:Diophantine_approximation
Best rational approximations Analysis of quadratic irrationals Solving Pell's equation |
| gptkbp:component |
Convergent
Partial quotient |
| gptkbp:defines |
A continued fraction in which all partial numerators are 1 and all partial denominators are positive integers
|
| gptkbp:field |
gptkb:Mathematics
gptkb:Number_theory Analysis |
| https://www.w3.org/2000/01/rdf-schema#label |
Regular continued fraction
|
| gptkbp:notation |
[a0; a1, a2, a3, ...]
|
| gptkbp:numberInSeries |
Sequence of partial quotients
|
| gptkbp:originatedIn |
Work of John Wallis
Work of Joseph-Louis Lagrange Work of Leonhard Euler |
| gptkbp:property |
The expansion is infinite for irrational numbers
Quadratic irrationals have periodic regular continued fraction expansions Every real number can be represented as a regular continued fraction The expansion is finite if and only if the number is rational |
| gptkbp:relatedTo |
gptkb:Euclidean_algorithm
gptkb:Generalized_continued_fraction Simple continued fraction Periodic continued fraction |
| gptkbp:supportsAlgorithm |
Continued fraction algorithm
|
| gptkbp:usedIn |
Mathematical proofs
Cryptography Computing square roots |
| gptkbp:bfsParent |
gptkb:Continued_Fractions
|
| gptkbp:bfsLayer |
7
|