Colleen Nielsen and Christa Powers, Intersecting equilateral triangles,
Forum Geometricorum, 13 (2013) 219--225.

Abstract. In 1980, J. Fickett proposed the following problem: Assume two congruent rectangles R_1 and R_2 intersect in at least one point. Let a be the length of the part of the boundary of R_1 that lies inside R_2 and let b be the length of the part of the boundary of R_2 that lies inside R_1. The conjecture was that the ratio a/b is no smaller than 1/3 and no larger than 3. This paper presents the solution to the problem when R_1 and R_2 are replaced by equilateral triangles of the same size. We have proved that the ratio a/b is no smaller than 1/2 and no larger than 2.

[ps file] [pdf]

Join yahoo discussion group Advanced Plane Geometry
to receive FG publication announcements.