Ternärringe ohne Planaritätsbedingung
Ternary rings with a left quasi-zero belonging to translation planes
The Betten-Walker spread and Cayley's ruled cubic surface.
The classification of SPG-systems of index 2.
The classification of spreads in admitting linear groups of order . II: Even order.
The classification of subplane covered nets.
The Conic y = x2 in Moufang Planes
The contributions of Hilbert and Dehn to non-archimedean geometries and their impact on the italian school
In this paper we investigate the contribution of Dehn to the development of non-Archimedean geometries. We will see that it is possible to construct some models of non-Archimedean geometries in order to prove the independence of the continuity axiom and we will study the interrelations between Archimedes’ axiom and Legendre’s theorems. Some of these interrelations were also studied by Bonola, who was one of the very few Italian scholars to appreciate Dehn’s work. We will see that, if Archimedes’...
The degrees of certain strata of the dual variety
The Desargues configuration and inversive geometry
The elementary geometry of a triangular world with hexagonal circles.
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 generating rank of the symplectic line-Grassmannian.
The geometry of in translation planes of even order .
The geometry of GL(2,q) in translation planes of even order (Corrigendum).
The geometry of null systems, Jordan algebras and von Staudt's theorem
We characterize an important class of generalized projective geometries by the following essentially equivalent properties: (1) admits a central null-system; (2) admits inner polarities: (3) is associated to a unital Jordan algebra. These geometries, called of the first kind, play in the category of generalized projective geometries a rôle comparable to the one of the projective line in the category of ordinary projective geometries. In this general set-up, we prove an analogue of von Staudt’s...
The group of projectivities in free-like geometries
The hyperplanes of .
The n-point-invariants of the projective line and cross-ratios of n-tuples
The number of triangles in a tringulation of a set of points in the plane.