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 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 smallest arithmetic hyperbolic three-orbi-fold.
The Steiner Ratio Conjecture for Cocircular Points.
The theorems of Stewart and Steiner in the Poincaré disc model of hyperbolic geometry
In [Comput. Math. Appl. 41 (2001), 135--147], A. A. Ungar employs the Möbius gyrovector spaces for the introduction of the hyperbolic trigonometry. This Ungar's work plays a major role in translating some theorems from Euclidean geometry to corresponding theorems in hyperbolic geometry. In this paper we explore the theorems of Stewart and Steiner in the Poincaré disc model of hyperbolic geometry.
The theorems of Urquhart and Steiner-Lehmus in the Poincaré ball model of hyperbolic geometry
The use of visual schema to find properties of a hexagon
The weighted Fermat triangle problem.
Théorème relatif à la courbe de Watt
Théorème sur les surfaces
Theorie der goniometrischen und der longimetrischen Quaternionen [Book]
Theory of equidistance and betweenness relations in regular metric spaces
There are no new homometric Golomb ruler pairs with 12 marks or less.
To construct a regular polygon of 17 sides. (Mit 1 Figur im Text)
Traces, lengths, axes and commensurability
The focus of this paper are questions related to how various geometric and analytical properties of hyperbolic 3-manifolds determine the commensurability class of such manifolds. The paper is for the large part a survey of recent work.
Transformaciones que conservan el área.
Transformation of Hyperbolic Escher Patterns