The Number of Congruent Non-Acute Isosceles Triangles Induced by n Points

Changqing Xu and Ren Ding
Department of Applied Mathematics, Hebei University of Technology,
Tianjin 300130,
P.R.China

Abstract    
The present paper proves that any set of n points in strictly convex position in the plane induces at most n congruent copies of a fixed non-acute isosceles triangle, this bound is best possible. At most 2n-2 congruent isosceles triangles can be induced by a set of n points in convex position. Furthermore, it is proved that this bound can be reduced to 2n-4 when the given isosceles triangle is non-acute.