View More View Less
  • 1 Chemnitz University of Technology Faculty of Mathematics D-09107 Chemnitz Germany
  • 2 University of Sofia Faculty of Mathematics and Informatics 5 James Bourchier 1164 Sofia Bulgaria
Restricted access

Abstract  

Some theorems from inversive and Euclidean circle geometry are extended to all affine Cayley-Klein planes. In particular, we obtain an analogue to the first step of Clifford’s chain of theorems, a statement related to Napoleon’s theorem, extensions of Wood’s theorem on similar-perspective triangles and of the known fact that the three radical axes of three given circles are parallel or have a point in common. For proving these statements, we use generalized complex numbers.