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In mathematics, a Beatty sequence (or homogeneous Beatty sequence) is the sequence of integers found by taking the floor of the positive multiples of a positive irrational number. Beatty sequences are named after Samuel Beatty, who wrote about them in 1926. Rayleigh's theorem, named after Lord Rayleigh, states that the complement of a Beatty sequence, consisting of the positive integers that are not in the sequence, is itself a Beatty sequence generated by a different irrational number. Beatty sequences can also be used to generate Sturmian words.

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rdfs:label	Seqüències de Beatty (ca) Beatty sequence (en) Teorema de Beatty (es) Théorème de Beatty (fr) ビーティ数列 (ja) Последовательность Битти (ru) 贝亚蒂定理 (zh)
rdfs:comment	En matemàtiques una seqüència de Beatty, , és una seqüència d'enters generada per la part entera dels múltiples d'un nombre irracional. És a dir: la seqüència generada pel nombre irracional seria: , on el símbol significa que només es considera la part entera del producte. Reben el seu nom pel matemàtic canadenc Samuel Beatty qui el 1926 va demostrar que si i són dos irracionals positius tals que , aleshores i son una partició de . (ca) In mathematics, a Beatty sequence (or homogeneous Beatty sequence) is the sequence of integers found by taking the floor of the positive multiples of a positive irrational number. Beatty sequences are named after Samuel Beatty, who wrote about them in 1926. Rayleigh's theorem, named after Lord Rayleigh, states that the complement of a Beatty sequence, consisting of the positive integers that are not in the sequence, is itself a Beatty sequence generated by a different irrational number. Beatty sequences can also be used to generate Sturmian words. (en) En matemática, el teorema de Beatty señala la condición necesaria y suficiente para que dos sucesiones pseudo-aritméticas sean una partición de . Fue publicado en 1926 por el matemático canadiense , profesor de la Universidad de Toronto. Otra demostración de este teorema se publicó en 1927 por A.Ostrowski (Basilea) y A. C. Aitken (Chicago). (es) Le théorème de Beatty est un théorème d'arithmétique publié en 1926 par le mathématicien canadien Samuel Beatty (mais déjà mentionné par Lord Rayleigh en 1894) qui donne une condition nécessaire et suffisante sur deux réels pour que les deux suites associées partitionnent ℕ*. (fr) 数学におけるビーティ列（ビーティれつ、英: Beatty sequence, homogeneous Beatty sequence）は正の無理数の整数倍の床関数をとることによって得られる整数列である。ビーティ列の名称は、1926年にそれらについて著したに因む。レイリー卿に名を因むレイリーの定理は、ビーティ列の補集合（数列に現れない正整数からなる集合）がそれ自身別の無理数で生成されるビーティ列となることを述べる。ビーティ列はの生成にも用いられる。 (ja) В математике однородная последовательность Битти — последовательность целых чисел, найденных путём взятия целой части («пола») положительных кратных положительных иррациональных чисел. Последовательности Битти названы в честь Сэмюэля Битти, написавшего о них в 1926 году. Последовательности Битти также могут быть использованы для генерации . (ru) 在数论中，贝亚蒂定理（英文：Beatty sequence）指：若使得。定義集（贝亚蒂列），则P 和 Q 构成正整数集的一个分划：，。即是說：若兩個正無理數的倒數之和是1，則任何正整數都可剛好以一種形式表示為不大於其中一個無理數的正整數倍的最大整數。此定理由Sam Beatty在1926年發現。 (zh)
dct:subject	Combinatorics on words Articles containing proofs Theorems in number theory Integer sequences Diophantine approximation
Wikipage page ID	9487872 (xsd:integer)
Wikipage revision ID	1111371912 (xsd:integer)
Link from a Wikipage to another Wikipage	5 (number) 6 (number) 8 (number) Multiple (mathematics) 20 (number) Combinatorics on words John William Strutt, 3rd Baron Rayleigh 10 (number) 11 (number) 12 (number) 13 (number) 14 (number) 15 (number) 17 (number) 16 (number) Articles containing proofs Theorems in number theory Complement (set theory) Mathematics 18 (number) Alexander Bogomolny Golden ratio 1 Irrational number 21 (number) 23 (number) 4 7 22 (number) 24 (number) 25 (number) 26 (number) 27 (number) 28 (number) 29 (number) 31 (number) 34 (number) 36 (number) 39 (number) 41 (number) 44 (number) 47 (number) Integer sequences Cut-the-knot Floor and ceiling functions Partition of a set 19 (number) 9 J. V. Uspensky Lambek–Moser theorem The American Mathematical Monthly Difference operator 2 3 Diophantine approximation Square root of 2 Integer Canadian Mathematical Bulletin Rational number Real numbers Sequence Set (mathematics) Samuel Beatty (mathematician) Wythoff's game Wythoff array

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