The Hilbert metric between two points 𝑥, 𝑦 in a bounded convex domain 𝐺 is defined as the
logarithm of the cross-ratio 𝑥, 𝑦 and the intersection points of the Euclidean line passing …

In hyperbolic geometry there are several concepts to measure the breadth or width of a
convex set. In the first part of the paper we collect them and compare their properties. Than …

We relate small 1-form Laplacian eigenvalues to relative cycle complexity on closed
hyperbolic manifolds: small eigenvalues correspond to closed geodesics no multiple of …

We study certain points significant for the hyperbolic geometry of the unit disk. We give
explicit formulas for the intersection points of the Euclidean lines and the stereographic …

We describe a system for automated ruler and compass triangle constructions in hyperbolic
geometry. We discuss key differences between constructions in Euclidean and hyperbolic …

We recall the notion of generalized hyperbolic angle between proper and improper straight
lines, which is only available in Hungarian and Esperanto. Then we summarize the …

We consider a hyperbolic space CH3 of positive curvature in the projective Cayley–Klein
model. In this model the space CH3 is realized on the ideal domain of a Lobachevskii space …

It is surprising, but an established fact that the field of elementary geometry referring to
normed spaces (= Minkowski spaces) is not a systematically developed discipline. There are …

We investigate several topics of triangle geometry in the elliptic and in the extended
hyperbolic plane, such as: centers based on orthogonality, centers related to circumcircles …

In this paper we overview the theory of conics and roulettes in four non-Euclidean planes.
We collect the literature about these classical concepts, from the eighteenth century to the …