A theorem on equiareal triangles with a fixed base

  • Victor Pambuccian

    Arizona State University, Phoenix, USA
A theorem on equiareal triangles with a fixed base cover
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Abstract

The statement: "Given two fixed points, and , the locus of the midpoints of and , when varies such that the area of triangle is constant, consists of two lines symmetric with respect to " is shown to be provable in very weak geometries, that is, Bachmann's non-elliptic metric planes in which every pair of points has a midpoint.