The existence of rainbow triangles in weak geometries

4 October 2018  prof. Victor Pambuccian  from  the Arizona State University gave a talk “The existence of rainbow triangles in weak  geometries” in the Yerevan State University, Faculty of Mathematics and Mechanics.

Abstract. We show that in any ordered plane with a symmetric orthogonality relation
which allows for a meaningful definition of acute and obtuse angles, in which all pointsare colored with three colors, such that each color is used at least once, there must existboth an acute triangle whose vertices have all three colors and an obtuse triangle with thesame property. We also show that, in both a geometry endowed with an orthogonalityrelation, in which there is a reflection in every line, in which all right angles are bisectable,which satisfies Bachmann‚Äôs Lotschnittaxiom (the perpendiculars raised on the sides of aright angle intersect), and in plane absolute geometry, in which all points are colored withthree colors, such that each color is used at least once, there exists a right triangle with allvertices of different colors.

 

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