Orbits of triangles obtained by interior division of sides
Sato Hajime · Proceedings of the Japan Academy Series A Mathematical Sciences · 1998
Plane triangles are classified by similarity.Let Q be the set of these equiva- lence classes of triangles, and lAB C] /2 be the class of triangles which are similar to AABC, Putting x ZA, y /B, z-Z C, [ABC] is represented by a point in II-{(x, y, z) Ix q-y q-z 7r, x, y, z > 0}.By making interior division of sides of AABC, we define an orbit in II, starting from [ABC].It is determined by a differentiable dynamical system, and is the intersection of II and the surface cot x q-cot y q-cot z const.Key words" Triangles" interior division" convex closed curve'four-vertex theorem.1. Introduction.We consider here the set