Word Pronunciation & Dictionary

farey sequence

Word Rarity Very rare

Frequency: Zipf frequency 1.22 in modern English

Syllables: farey se-quence
IPA

30

Scrabble Score

13

Letters

2

Syllables

10

Unique Chars

Meaning

noun

For a given positive integer n, the sequence of completely reduced fractions between 0 and 1 which, when in lowest terms, have denominators less than or equal to n, arranged in order of increasing size.

Example Sentences

"Students should then see the number of fractions N, in the Farey sequence is equal to #92;phi(2)#43;#92;phi(3)#43;#92;phi(4)#43;#92;dots#43;#92;phi(n), where #92;phi(n) is the number of positive integers less than or equal to n that are relatively prime to n."
"2007, Jakub Pawlewicz, Order Statistics in the Farey Sequences in Sublinear Time, Lars Arge, Michael Hoffmann, Emo Welzl (editors), Algorithms - ESA 2007: 15th Annual European Symposium, Proceedings, Springer, LNCS 4698, page 218, The Farey sequence of order n (denoted ℱₙ) is the increasing sequence of all irreducible fractions from interval [0,1] with denominators less than or equal to n. The Farey sequences have numerous interesting properties and they are well known in the number theory and in the combinatorics."
"Riemann sums have also important connections with various problems from number theory, among them the Riemann Hypothesis, through their link with Farey sequences."

Etymology

Named after British geologist John Farey Sr., whose letter about the sequences was published in the Philosophical Magazine in 1816.

Inflected Forms

Farey sequences (plural)

Phrases

Farey neighbour Farey pair

Frequently Paired Words

Farey neighbour Farey pair

Questions

What does farey sequence mean?: For a given positive integer n, the sequence of completely reduced fractions between 0 and 1 which, when in lowest terms, have denominators less than or equal to n, arranged in order of increasing size.
Where does farey sequence come from?: Named after British geologist John Farey Sr., whose letter about the sequences was published in the Philosophical Magazine in 1816.

How to pronounce farey sequence

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