On Some Properties of the First Brocard Triangle in the Isotropic Plane

Abstract

In this paper we introduce the first Brocard triangle of an allowable triangle in the isotropic plane and derive the coordinates of its vertices in the case of a standard triangle. We prove that the first Brocard triangle is homologous to the given triangle and that these two triangles are parallelogic. We consider the relationships between the first Brocard triangle and the Steiner axis, the Steiner point, and the Kiepert parabola of the triangle. We also investigate some other interesting properties of this triangle and consider relationships between the Euclidean and the isotropic case.

Keywords

• isotropic plane
• first Brocard triangle
• Brocard circle
• parallelogy