Fractions and the Stern-Brocot Tree - Real Numbers and Limits Math Foundations

Explore the fascinating world of fractions and the Stern-Brocot tree in this 36-minute mathematics lecture. Discover the remarkable representation of fractions using a binary tree, developed around 1860 by a German mathematician and French clockmaker. Learn about the mediant operation used to generate the tree and its pleasant properties, including one discovered by Canadian musical theorist Pierre Lamothe. Investigate the connections between the Stern-Brocot tree, Ford circles, and Farey sequences, revealing the deep structure of rational numbers. Follow the step-by-step construction of the tree, examine its properties, and understand the notion of fraction simplicity. Gain insights into this important mathematical concept that bridges number theory, geometry, and mathematical history.

Intro to the Stern-Brocot tree
How to build the Stern-Brocot tree
New elements added to previous sequence
Constructing the Stern-Brocot tree
Properties of the Stern-Brocot tree
Definition for the next few properties
Notion of simplicity of a fraction
Last property
Ford circles and the Stern-Brocot tree
Another look at Stern-Brocot tree