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- Pell_number abstract "In mathematics, the Pell numbers are an infinite sequence of integers, known since ancient times, that comprise the denominators of the closest rational approximations to the square root of 2. This sequence of approximations begins 1/1, 3/2, 7/5, 17/12, and 41/29, so the sequence of Pell numbers begins with 1, 2, 5, 12, and 29. The numerators of the same sequence of approximations are half the companion Pell numbers or Pell-Lucas numbers; these numbers form a second infinite sequence that begins with 2, 6, 14, 34, and 82.Both the Pell numbers and the companion Pell numbers may be calculated by means of a recurrence relation similar to that for the Fibonacci numbers, and both sequences of numbers grow exponentially, proportionally to powers of the silver ratio 1 + √2. As well as being used to approximate the square root of two, Pell numbers can be used to find square triangular numbers, to construct integer approximations to the right isosceles triangle, and to solve certain combinatorial enumeration problems.As with Pell's equation, the name of the Pell numbers stems from Leonhard Euler's mistaken attribution of the equation and the numbers derived from it to John Pell. The Pell-Lucas numbers are also named after Édouard Lucas, who studied sequences defined by recurrences of this type; the Pell and companion Pell numbers are Lucas sequences.".
- Pell_number thumbnail Pell_octagons.svg?width=300.
- Pell_number wikiPageExternalLink filep.pdf.
- Pell_number wikiPageExternalLink sellers4.pdf.
- Pell_number wikiPageExternalLink diazbar.pdf.
- Pell_number wikiPageID "1355482".
- Pell_number wikiPageRevisionID "605790635".
- Pell_number hasPhotoCollection Pell_number.
- Pell_number title "Pell Number".
- Pell_number urlname "PellNumber".
- Pell_number subject Category:Integer_sequences.
- Pell_number subject Category:Recurrence_relations.
- Pell_number type Abstraction100002137.
- Pell_number type Arrangement107938773.
- Pell_number type Group100031264.
- Pell_number type IntegerSequences.
- Pell_number type Ordering108456993.
- Pell_number type Sequence108459252.
- Pell_number type Series108457976.
- Pell_number comment "In mathematics, the Pell numbers are an infinite sequence of integers, known since ancient times, that comprise the denominators of the closest rational approximations to the square root of 2. This sequence of approximations begins 1/1, 3/2, 7/5, 17/12, and 41/29, so the sequence of Pell numbers begins with 1, 2, 5, 12, and 29.".
- Pell_number label "Liczby Pella".
- Pell_number label "Nombre de Pell".
- Pell_number label "Pell number".
- Pell_number label "Pell-Folge".
- Pell_number label "Pellgetal".
- Pell_number label "Число Пелля".
- Pell_number label "ペル数".
- Pell_number label "佩尔数".
- Pell_number sameAs Pell-Folge.
- Pell_number sameAs Αριθμοί_του_Πελ.
- Pell_number sameAs Nombre_de_Pell.
- Pell_number sameAs ペル数.
- Pell_number sameAs Pellgetal.
- Pell_number sameAs Liczby_Pella.
- Pell_number sameAs m.04w8mj.
- Pell_number sameAs Q1386491.
- Pell_number sameAs Q1386491.
- Pell_number sameAs Pell_number.
- Pell_number wasDerivedFrom Pell_number?oldid=605790635.
- Pell_number depiction Pell_octagons.svg.
- Pell_number isPrimaryTopicOf Pell_number.