A lower bound on the angles of triangles constructed by LE-trisection

Abstract

The longest-edge (LE) trisection of a triangle is obtained by joining the two equally spaced points of its longest-edge with the opposite vertex. Let alfa > 0 be the smallest interior angle of the triangle and alfa' the smallest angle of any triangle obtained after iteration of the LE-trisection. In this paper we prove that alfa' > alfa/c, where c = (pi/3)·(arctan(sqr(3)/11))