Search Results

You are looking at 1 - 2 of 2 items for

  • Author or Editor: Margarita Spirova x
Clear All Modify Search

Summary  

Napoleon's original theorem refers to arbitrary triangles in the Euclidean plane. If equilateral triangles are externally erected on the sides of a given triangle, then their three corresponding circumcenters form an equilateral triangle. We present some analogous theorems and related statements for the isotropic (Galilean) plane.

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.

Restricted access