Stern–Brocot Rational Tree
Find every positive rational through integer mediants and a unique left–right path.
Free theory articleFind every positive rational through integer mediants and a unique left–right path.
Concept & interpretation
The Stern–Brocot tree is a beautiful mathematical structure that enumerates all positive rational numbers in lowest terms. It generates these fractions by continuously forming the mediant of adjacent bounds, starting with 0/1 and 1/0.
experiment
Explore different rational targets and trace their location in the Stern-Brocot Tree.
- Set the Target dropdown to "5/7". Note the sequence of mediants evaluated as the search goes Left, Right, Right, Left.
- Adjust the Depth limit. If you lower it below the number of steps required to reach the target, the search stops early, and "Found" displays "No".
Try it out here: https://riano.app/module/stern-brocot-rationals