The degrees of certain strata of the dual variety
The Desargues configuration and inversive geometry
The development of the oloid.
The Double Tangency Symmetries in Laguerre Plane
The group generated by double tangency symmetries in a Laguerre plane is investigated. The geometric classification of involutions of a symmetric Laguerre plane is given. We introduce the notion of projective automorphisms using the double tangency and parallel perspectivities. We give the description of the groups of projective automorphisms and automorphisms generated by double tangency symmetries as subgroups of the group M(𝔽,ℝ) of automorphisms of a chain geometry Σ(𝔽,ℝ) following Benz.
The dynamics of two-circle and three-circle inversion
We study the dynamics of a map generated via geometric circle inversion. In particular, we define multiple circle inversion and investigate the dynamics of such maps and their corresponding Julia sets.
The edge-minimal polyhedral maps of Euler characteristic .
The Elation Group of a 4-DImensional Laguerre Plane.
The elementary geometry of a triangular world with hexagonal circles.
The Elements of Geometry [Book]
The envelope of the Wallace-Simpson lines of a triangle. A simple proof of the Steiner problem on the deltoid.
A simple proof is presented of a famous, and difficult, theorem by Jakob Steiner. By means of a straightforward transformation of the triangle, the proof of the theorem is reduced to the case of the equilateral triangle. Several relations of the Steiner deltoid with the Feuerbach circle and the Morley triangle appear then as obvious.
The Euclidean inscribed polygon.
The Euclidean plane kinematics
Restricting his considerations to the Euclidean plane, the author shows a method leading to the solution of the equivalence problem for all Lie groups of motions. Further, he presents all transitive one-parametric system of motions in the Euclidean plane.
The Euler Line Revisited.
The finite Moufang hexagons coordinatized.
The four known biplanes with k=11.
The functional equation of distance preservance in spaces over rings.
The functional equation of distance preservance in spaces over rings. (Short Communication).
The fundamental theorem for the projective line over commutative rings. (Short Communication).
The fundamental theorem for the projective line over commutative rings.
The future or graphical communication education in the new South Africa.