Convergents

Convergents[list]
gives a list of the convergents corresponding to the continued fraction terms list.

Convergents[x,n]
gives the first n convergents for a number x.

Convergents[x]
gives if possible all convergents leading to the number x.

DetailsDetails

  • The convergents of the continued fraction are the rationals .
  • For exact numbers, Convergents[x] can be used if x is rational or a quadratic irrational.
  • If x is a quadratic irrational or a representation of a quadratic irrational as a continued fraction, the final list element returned by Convergents[x] is the quadratic irrational represented by x.
  • For inexact numbers, Convergents[x] generates a list of all convergents that can be obtained given the precision of x.
  • Convergents[x,n] will return n convergents if possible. If x represents a rational or an inexact number, fewer than n terms may be returned.

ExamplesExamplesopen allclose all

Basic Examples  (3)Basic Examples  (3)

Generate the first 10 convergents to the golden ratio:

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Generate convergents from the continued fraction terms for GoldenRatio:

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Introduced in 2007
(6.0)