The orthogonality in affine parallel structure
The partition problem for equifacetal simplices.
The pedal point generation of circular curves of order three in the isotropic plane. (Die Fußpunkterzeugung der zirkulären Kurven 3. Ordnung in der isotropen Ebene.)
The pedal surfaces of -congruences with a one-parameter set of ellipses.
The Planarity of the Equilateral, Isogonal Pentagon.
The Polytope of m-Subspaces of a Finite Affine Space
The m-subspace polytope is defined as the convex hull of the characteristic vectors of all m-dimensional subspaces of a finite affine space. The particular case of the hyperplane polytope has been investigated by Maurras (1993) and Anglada and Maurras (2003), who gave a complete characterization of the facets. The general m-subspace polytope that we consider shows a much more involved structure, notably as regards facets. Nevertheless, several families of facets are established here. Then the...
The Problem of the Circular Billiard.
The projective interpretation of the eight 3-dimensional homogeneous geometries.
The proof of the isomorphism of the -dimensional projective spaces defined axiomatically
The paper gives a proof (without of using of “great” Desargues’ axiom) that any two axiomatically defined n - dimensional projective spaces are isomorphic.
The rank 2 geometries of the simple Suzuki groups .
The Recent Generalizations of Colored Symmetry
The refinement and reverse of a geometric inequality.
The Regge symmetry is a scissors congruence in hyperbolic space.
The residually weakly primitive geometries of .
The return sequence of the Bowen-Series map for punctured surfaces
For a non-compact hyperbolic surface M of finite area, we study a certain Poincaré section for the geodesic flow. The canonical, non-invertible factor of the first return map to this section is shown to be pointwise dual ergodic with return sequence (aₙ) given by aₙ = π/(4(Area(M) + 2π)) · n/(log n). We use this result to deduce that the section map itself is rationally ergodic, and that the geodesic flow associated to M is ergodic with respect to the Liouville measure. ...
The role of Sommerville tetrahedra in numerical mathematics
In this paper we summarize three recent results in computational geometry, that were motivated by applications in mathematical modelling of fluids. The cornerstone of all three results is the genuine construction developed by D. Sommerville already in 1923. We show Sommerville tetrahedra can be effectively used as an underlying mesh with additional properties and also can help us prove a result on boundary-fitted meshes. Finally we demonstrate the universality of the Sommerville's construction by...
The Rotation Group
We introduce length-preserving linear transformations of Euclidean topological spaces. We also introduce rotation which preserves orientation (proper rotation) and reverses orientation (improper rotation). We show that every rotation that preserves orientation can be represented as a composition of base proper rotations. And finally, we show that every rotation that reverses orientation can be represented as a composition of proper rotations and one improper rotation.
The second extension of the Thas-Walker construction.
The Skew-Hyperbolic Motion Group of the Quaternion Plane.
The smallest arithmetic hyperbolic three-orbi-fold.