Similarity Classes of the Longest-Edge Trisection of Triangles

This paper studies the triangle similarity classes obtained by iterative application of longest-edge trisection triangles. The (3T-LE) a is joining two points which divide longest edge in three equal parts with opposite vertex. partition, as well bisection (2T-LE), does not degenerate, means that there positive lower bound to minimum angle generated. However, unlike what happens 2T-LE, number appearing 3T-LE single initial finite general. There are only exceptions this fact: right its sides ratio 1:2:3 and other triangles orbit. result, although combinatorial nature, proved here machinery discrete dynamics shape space hyperbolic metric. It also shown for point an infinite orbit, orbit circles centers at orbits.