BooksirmaCollected Volumepp. 427–437

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, AA and CC, the locus of the midpoints of ABAB and CBCB, when BB varies such that the area of triangle ABCABC is constant, consists of two lines symmetric with respect to ACAC" 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.