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KoG, Vol.15. No.15. Prosinac 2011.

Izvorni znanstveni članak

Universal Hyperbolic Geometry III: First Steps in Projective Triangle Geometry

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

Puni tekst: pdf (896 KB), Engleski, Str. 25 - 49 , preuzimanja: 821 *

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.

Ključne riječi
universal hyperbolic geometry; triangle geometry; projective geometry; bilinear form; ortholinear coordinates; incenter; circumcenter; orthoaxis


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