How Chromogeometry transcends Klein's Erlangen Program for Planar Geometries| N J Wildberger

<div id="text-container" class="style-scope ytd-channel-name"><a class="yt-simple-endpoint style-scope yt-formatted-string" spellcheck="false" href="https://www.youtube.com/channel/UCXl0Zbk8_rvjyLwAR-Xh9pQ">Insights into Mathematics</a></div>

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<div id="description" class="style-scope ytd-video-secondary-info-renderer">We give a pictorial introduction to chromogeometry, a remarkable new three-fold symmetry which brings together Euclidean geometry and two relativistic geometries to transform our understanding of planar geometry. And it also urges us to re-evaluate Felix Klein's Erlangen Program---which viewed geometry as a group acting transitively on a space. There is actually quite a lot more to it than that. We give a quick introduction to Rational Trigonometry, introduce three fundamental planar metrical geometries, and then go on to generalize Euler lines, orthocenters, circumcentres, and put them together as the Omega triangle of a triangle. We also have a novel look at the conic sections, introduce the diagonals of an ellipse, and then illustrate chromogeometric aspects of ellipses and parabolas. There is a lot of new mathematics here. It really shows the power of thinking rationally, and putting aside all those dreamy arithmetical fantasies about "infinite sums" and "real numbers". When we start doing correct mathematics, a lot of doors open for us! Thanks to Joshua Ho for videoing.</div>

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How Chromogeometry transcends Klein's Erlangen Program for Planar Geometries| N J Wildberger

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