Stern Brocot Tree
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High Quality Content by WIKIPEDIA articles! In number theory, the Stern Brocot tree is a tree in which the vertices correspond 1-for-1 to the positive rational numbers. 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…mehr

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High Quality Content by WIKIPEDIA articles! In number theory, the Stern Brocot tree is a tree in which the vertices correspond 1-for-1 to the positive rational numbers. 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.