The Stern-Brocot Tree, Matrices and Wedges - Real Numbers and Limits Math Foundations

Explore the Stern-Brocot tree's matrix and geometrical representations in this 34-minute mathematics video. Delve into 2x2 matrices, determinants, and basic operations before examining a novel planar representation of the tree using visible integral points in the positive quadrant. Discover the role of the pseudo-fraction 1/0 in tree generation and learn about the theory of wedges, which combines matrix and geometrical forms to create a unique tesselation of the visible positive quadrant. Gain insights into moving smoothly down the tree and understand the relationship between matrices, fractions, and geometrical structures in this advanced exploration of number theory and linear algebra.

Intro to the Stern-Brocot tree
2x2 matrices
The Stern-Brocot tree diagram
Generating the matrix form of the Stern-Brocot tree
Stern-Brocot tree from the matrix form
Matrix is either Identity matrix or a product of Ls and Rs
Sequence of L's and R's for a rational number
Determinants
Wedges
Matrix form to geometrical form