Visualizing Quadrance with Circles - Universal Hyperbolic Geometry - NJ Wildberger

Explore the fundamental concept of quadrance between points in universal hyperbolic geometry through a detailed examination of circles in this 35-minute video lecture. Discover how circles, defined as conics in terms of quadrance, can appear as ellipses, parabolas, or hyperbolas in two-dimensional representations. Investigate three different families of circles with distinct centers, gaining a comprehensive understanding of this crucial geometric concept. Learn how quadrance replaces the traditional notion of distance in universal hyperbolic geometry, and visualize its applications through carefully illustrated examples.

Introduction visualizing quadrance
Circles
; conics introduced
Pictures of circles centered at [1:0:0]
Pictures of circles centered at c=[1:0:2]
Pictures of circles centered at c=[2:0:1]