Medians, Midlines, Centroids and Circumcenters - Universal Hyperbolic Geometry

Explore the fundamental concepts of triangle geometry within the framework of universal hyperbolic geometry in this 34-minute video lecture. Delve into the algebraic setting of rational numbers as you learn about medians, midlines, centroids, and circumcenters. Discover how midpoints of triangle sides behave differently in hyperbolic geometry, and examine the relationships between 6 medians and their dual lines. Investigate the fascinating connections between 4 centroids and 4 circumcenters, culminating in the z-point theorem. Gain insights into the Euler line, construction techniques, and the remarkable harmonic range formed by key triangle points on the ortho-axis.

Introduction
Euler line
Midlines of a side
# of midpoints of a triangle; duals of midpoints
Meets of medians theorem
construction of meets of midlines circumcenters
Centroid circumcenter correspondence theorem
Z-point ortho-axis theorem