Universal Hyperbolic Geometry - NJ Wildberger

Discover a revolutionary approach to hyperbolic geometry in this introductory video lecture. Explore the concept of 'Universal Hyperbolic Geometry,' which simplifies and extends the subject beyond traditional boundaries. Learn how this method works over general fields, goes beyond the usual disk in the Beltrami Klein model, and unifies hyperbolic, elliptic, and other geometries. Understand the key differences from standard textbooks and university courses, including the avoidance of real numbers, axioms, and transcendental functions. Delve into a high school algebra-based approach that combines projective geometry with a distinguished conic—the unit circle in the plane. Gain insights into the connection between this approach and Einstein's special theory of relativity. Presented by N J Wildberger, the originator of Rational Trigonometry, this 23-minute video sets the stage for a comprehensive exploration of Universal Hyperbolic Geometry.