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- Stern–Brocot_tree abstract "In number theory, the Stern–Brocot tree is an infinite complete binary tree in which the vertices correspond one-for-one to the positive rational numbers, whose values are ordered from the left to the right as in a search tree.The Stern–Brocot tree was discovered independently by Moritz Stern (1858) and Achille Brocot (1861). Stern was a German number theorist; Brocot was a French clockmaker who used the Stern–Brocot tree to design systems of gears with a gear ratio close to some desired value by finding a ratio of smooth numbers near that value.The root of the Stern–Brocot tree corresponds to the number 1. The parent-child relation between numbers in the Stern–Brocot tree may be defined in terms of continued fractions or mediants, and a path in the tree from the root to any other number q provides a sequence of approximations to q with smaller denominators than q. Because the tree contains each positive rational number exactly once, a breadth first search of the tree provides a method of listing all positive rationals that is closely related to Farey sequences.".
- Stern–Brocot_tree thumbnail SternBrocotTree.svg?width=300.
- Stern–Brocot_tree wikiPageExternalLink stern_brocot.html.
- Stern–Brocot_tree wikiPageExternalLink Stern.shtml.
- Stern–Brocot_tree wikiPageExternalLink GDZPPN002150301.
- Stern–Brocot_tree wikiPageExternalLink watch?v=CiO8iAYC6xI.
- Stern–Brocot_tree wikiPageExternalLink watch?v=DpwUVExX27E.
- Stern–Brocot_tree wikiPageID "2546511".
- Stern–Brocot_tree wikiPageLength "14482".
- Stern–Brocot_tree wikiPageOutDegree "38".
- Stern–Brocot_tree wikiPageRevisionID "696994676".
- Stern–Brocot_tree wikiPageWikiLink American_Mathematical_Society.
- Stern–Brocot_tree wikiPageWikiLink Bijection.
- Stern–Brocot_tree wikiPageWikiLink Binary_search_algorithm.
- Stern–Brocot_tree wikiPageWikiLink Binary_search_tree.
- Stern–Brocot_tree wikiPageWikiLink Binary_tree.
- Stern–Brocot_tree wikiPageWikiLink Bit-reversal_permutation.
- Stern–Brocot_tree wikiPageWikiLink Brady_Haran.
- Stern–Brocot_tree wikiPageWikiLink Breadth-first_search.
- Stern–Brocot_tree wikiPageWikiLink Calkin–Wilf_tree.
- Stern–Brocot_tree wikiPageWikiLink Cartesian_tree.
- Stern–Brocot_tree wikiPageWikiLink Category:Continued_fractions.
- Stern–Brocot_tree wikiPageWikiLink Category:Number_theory.
- Stern–Brocot_tree wikiPageWikiLink Category:Trees_(data_structures).
- Stern–Brocot_tree wikiPageWikiLink Clockmaker.
- Stern–Brocot_tree wikiPageWikiLink Continued_fraction.
- Stern–Brocot_tree wikiPageWikiLink Crelles_Journal.
- Stern–Brocot_tree wikiPageWikiLink Cut-the-Knot.
- Stern–Brocot_tree wikiPageWikiLink Diophantine_approximation.
- Stern–Brocot_tree wikiPageWikiLink Farey_sequence.
- Stern–Brocot_tree wikiPageWikiLink Floating_point.
- Stern–Brocot_tree wikiPageWikiLink Fraction_(mathematics).
- Stern–Brocot_tree wikiPageWikiLink Gear_train.
- Stern–Brocot_tree wikiPageWikiLink Lowest_common_ancestor.
- Stern–Brocot_tree wikiPageWikiLink Mediant_(mathematics).
- Stern–Brocot_tree wikiPageWikiLink Minkowskis_question_mark_function.
- Stern–Brocot_tree wikiPageWikiLink Number_theory.
- Stern–Brocot_tree wikiPageWikiLink On-Line_Encyclopedia_of_Integer_Sequences.
- Stern–Brocot_tree wikiPageWikiLink Rational_number.
- Stern–Brocot_tree wikiPageWikiLink Search_tree.
- Stern–Brocot_tree wikiPageWikiLink Sign_(mathematics).
- Stern–Brocot_tree wikiPageWikiLink Smooth_number.
- Stern–Brocot_tree wikiPageWikiLink Tree_(graph_theory).
- Stern–Brocot_tree wikiPageWikiLink Vertex_(graph_theory).
- Stern–Brocot_tree wikiPageWikiLink File:SternBrocotTree.svg.
- Stern–Brocot_tree wikiPageWikiLinkText "Stern–Brocot tree".
- Stern–Brocot_tree authorlink "Achille Brocot".
- Stern–Brocot_tree authorlink "Moritz Stern".
- Stern–Brocot_tree first "Achille".
- Stern–Brocot_tree first "Moritz".
- Stern–Brocot_tree last "Brocot".
- Stern–Brocot_tree last "Stern".
- Stern–Brocot_tree title "Stern–Brocot Tree".
- Stern–Brocot_tree title "Stern–Brocot tree".
- Stern–Brocot_tree urlname "Stern-BrocotTree".
- Stern–Brocot_tree urlname "SternBrocotTree".
- Stern–Brocot_tree wikiPageUsesTemplate Template:=.
- Stern–Brocot_tree wikiPageUsesTemplate Template:Citation.
- Stern–Brocot_tree wikiPageUsesTemplate Template:Fraction.
- Stern–Brocot_tree wikiPageUsesTemplate Template:Harvs.
- Stern–Brocot_tree wikiPageUsesTemplate Template:MathWorld.
- Stern–Brocot_tree wikiPageUsesTemplate Template:PlanetMath.
- Stern–Brocot_tree wikiPageUsesTemplate Template:Reflist.
- Stern–Brocot_tree year "1858".
- Stern–Brocot_tree year "1861".
- Stern–Brocot_tree subject Category:Continued_fractions.
- Stern–Brocot_tree subject Category:Number_theory.
- Stern–Brocot_tree subject Category:Trees_(data_structures).
- Stern–Brocot_tree hypernym Tree.
- Stern–Brocot_tree type Plant.
- Stern–Brocot_tree type Field.
- Stern–Brocot_tree type Redirect.
- Stern–Brocot_tree type Structure.
- Stern–Brocot_tree type Technique.
- Stern–Brocot_tree comment "In number theory, the Stern–Brocot tree is an infinite complete binary tree in which the vertices correspond one-for-one to the positive rational numbers, whose values are ordered from the left to the right as in a search tree.The Stern–Brocot tree was discovered independently by Moritz Stern (1858) and Achille Brocot (1861).".
- Stern–Brocot_tree label "Stern–Brocot tree".
- Stern–Brocot_tree sameAs Q599079.
- Stern–Brocot_tree sameAs شجرة_ستيرن-بروكوت.
- Stern–Brocot_tree sameAs Arbre_de_Stern-Brocot.
- Stern–Brocot_tree sameAs Stern-Brocot-Baum.
- Stern–Brocot_tree sameAs Arbre_de_Stern-Brocot.
- Stern–Brocot_tree sameAs Drzewo_Sterna-Brocota.
- Stern–Brocot_tree sameAs m.07m7p6.
- Stern–Brocot_tree sameAs Дерево_Штерна_—_Броко.
- Stern–Brocot_tree sameAs ต้นไม้ชแตร์น–บรอโก.
- Stern–Brocot_tree sameAs Q599079.
- Stern–Brocot_tree wasDerivedFrom Stern–Brocot_tree?oldid=696994676.
- Stern–Brocot_tree depiction SternBrocotTree.svg.
- Stern–Brocot_tree isPrimaryTopicOf Stern–Brocot_tree.