Hamilton Triangle of a Triangle in the Isotropic Plane

Abstract

In this paper we introduce the concept of the Hamilton triangle of a given triangle in an isotropic plane and investigate a number of important properties of this concept. We prove that the Hamilton triangle is homological with the observed triangle and with its contact and complementary triangles. We also consider some interesting statements about the relationships between the Hamilton triangle and some other significant elements of the triangle, like e.g. the Euler and the Feuerbach line, the Steiner ellipse and the tangential triangle.