Stammler\u27s circles, Stammler\u27s triangle and Morley\u27s triangle of a given triangle

By means of complex coordinates shorter proofs of the results of L. Stammler [1], [2] will be given, plus several statements connected with them

Metrical relationships in a standard triangle in an isotropic plane

Each allowable triangle of an isotropic plane can be set in a standard position, in which it is possible to prove geometric properties analytically in a simplified and easier way by means of the algebraic theory developed in this paper

Six concyclic points

The theorem about six concyclic points, some of them obtained by means of the symmedians and a median of a triangle, is proved in [1] applying two auxiliary theorems and some complex studies. In this paper the statement of that theorem is a result of some simple considerations

Affine regular icosahedron circumscribed around the affine regular octahedron in GS--quasigroup

summary:The concept of the affine regular icosahedron and affine regular octahedron in a general GS-quasigroup will be introduced in this paper. The theorem of the unique determination of the affine regular icosahedron by means of its four vertices which satisfy certain conditions will be proved. The connection between affine regular icosahedron and affine regular octahedron in a general GS-quasigroup will be researched. The geometrical representation of the introduced concepts and relations between them will be given in the GS-quasigroup $\mathbb{C}(\frac{1}{2}(1+\sqrt 5))$