Acute Triangulation of a Triangle in a General Setting

Abstract We prove that, in ordered plane geometries endowed with a very weak notion of orthogonality, one can always triangulate any triangle into seven acute triangles, and, in case the given triangle is not acute, into no fewer than seven.

[1]  W. Pejas.  Eine algebraische Beschreibung der angeordneten Ebenen mit nichteuklidischer Metrik , 1964 .

[2]  N. Düvelmeyer.  Angle Measures and Bisectors in Minkowski Planes , 2005, Canadian Mathematical Bulletin.

[3]  N. Düvelmeyer.  A new characterization of Radon curves via angular bisectors , 2004 .

[4]  Ileana Streinu,et al.  Acute Triangulations of Polygons , 2005, Discret. Comput. Geom..

[5]  O. Bachmann.  Zur spiegelungsgeometrischen Begründung von Geometrien , 1976 .

[6]  von David Hilbert.  Über den Satz von der Gleichheit der Basiswinkel im gleich-schenkligen Dreieck , 1902 .

[7]  Friedrich Bachmann,et al.  Aufbau der Geometrie aus dem Spiegelungsbegriff , 1959 .

[8]  W. A. Coppel.  Foundations of Convex Geometry , 1998 .

[9]  Jin-ichi Itoh,et al.  Acute Triangulations of the Regular Icosahedral Surface , 2004, Discret. Comput. Geom..

[10]  Jin-ichi Itoh,et al.  Acute triangulations of the regular dodecahedral surface , 2007, Eur. J. Comb..

[11]  Jorge Nuno Silva,et al.  Mathematical Games , 1959, Nature.

[12]  Die Winkelmetrik in der affin-orthogonalen Ebene , 1955 .

[13]  Gruppentheoretisches Axiomensystem einer verallgemeinerten euklidischen Geometrie , 1956 .

[14]  H. Martini,et al.  Antinorms and Radon curves , 2004, math/0409200.

[15]  ARTHUR RICHARD SCHWEITZER.  ON A SYSTEM OF AXIOMS FOR GEOMETRY ' BY , 2010 .

[16]  Hiroshi Maehara.  On Acute Triangulations of Quadrilaterals , 2000, JCDCG.

[17]  Carol T. Zamfirescu.  Acute triangulations of the double triangle , 2004 .

[18]  Tudor Zamfirescu,et al.  Acute Triangulations of Flat Mobius Strips , 2007, Discret. Comput. Geom..