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Original scientific paper

Universal Hyperbolic Geometry III: First Steps in Projective Triangle Geometry

Norman John Wildberger orcid id ; School of Mathematics and Statistics UNSW, Sydney, Australia

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page 25-49

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We initiate a triangle geometry in the projective metrical setting, based on the purely algebraic approach of universal geometry, and yielding in particular a new form of hyperbolic triangle geometry. There are three main strands: the Orthocenter, Incenter and Circumcenter hierarchies, with the last two dual. Formulas using ortholinear coordinates are a main objective. Prominent are five particular points, the b, z, x, h and s points, all lying on the Orthoaxis A. A rich kaleidoscopic aspect colours the subject.


universal hyperbolic geometry, triangle geometry, projective geometry, bilinear form, ortholinear coordinates, incenter, circumcenter, orthoaxis

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