How Chromogeometry Transcends Klein's Erlangen Program for Planar Geometries - N J Wildberger

Explore a groundbreaking lecture on chromogeometry, a revolutionary approach that unifies Euclidean and relativistic geometries to transform our understanding of planar geometry. Delve into the foundations of Rational Trigonometry and discover three fundamental planar metrical geometries. Examine the generalization of concepts like Euler lines, orthocenters, and circumcenters, culminating in the innovative Omega triangle. Investigate a novel perspective on conic sections, including the introduction of ellipse diagonals and chromogeometric aspects of ellipses and parabolas. Gain insights into the power of rational thinking in mathematics, challenging traditional notions of infinite sums and real numbers. Follow along as the lecture progresses through topics such as quadrance, spread, Pythagoras theorems in different geometries, colored altitudes, Euler lines, and chromatic parabolas. Witness how this new approach to geometry transcends Klein's Erlangen Program and opens doors to exciting mathematical discoveries.