8 citations · 10 across the 15 of their papers we have counts for
18 papers
Strongly self-dual polytopes
Ákos G. Horváth, István Prok
This article aims to study the class of strongly self-dual polytopes (ssd-polytopes for short), defined in a paper by Lovász \cite{lovasz}. He described a series of such polytopes…
Elementary Constructions of conic sections
Ákos G. Horváth
In classical geometry, there is no such well-known and much-studied topic as the construction of conic sections (or briefly conics) from its five points. Its importance in many app…
The bridge between Desargues' and Pappus' theorems
Ákos G. Horváth
In this paper, we investigate the configuration theorems of Desargues and Pappus in a synthetic geometric way. We provide a bridge between the two configurations with a third one t…
An extremal problem of regular simplices-The higher dimensional case
Ákos G. Horváth
The new result of this paper connected with the following problem: Consider a supporting hyperplane of a regular simplex and its re ected image at this hyperplane. When will be the…
A note on the centers of a closed chain of circles
Ákos G. Horváth
In this note we prove that the centers of a closed chain of circles for which every two consecutive members meet in the points of two given circles form a tangent polygon of a coni…
Proper quadrics in the Euclidean -space
Ákos G. Horváth
In this paper we investigate the metric properties of quadrics and cones of the -dimensional Euclidean space. As applications of our formulas we give a more detailed description…
Constructive curves in non-Euclidean planes
Ákos G. Horváth
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…
On the non-Paschian ordered planes
Ákos G. Horváth
We give a non-Paschian plane based on the property of betweenness which cannot be derived from an ordering of the points of a line. In this model there is no possibility to define…
On the volume growth of the hyperbolic regular -simplex
Ákos G. Horváth
In this paper we give lower and upper bounds for the volume growth of a regular hyperbolic simplex, namely for the ratio of the -dimensional volume of a regular simplex and the…
Volume of convex hull of two bodies and related problems
Ákos G. Horváth
In this paper we deal with problems concerning the volume of the convex hull of two "connecting" bodies. After a historical background we collect some results, methods and open pro…
On the icosahedron inequality of László Fejes-Tóth
Ákos G. Horváth
In this paper we deal with the problem to find the maximal volume polyhedra with a prescribed property and inscribed in the unit sphere. We generalize those inequality (called by \…
On the hyperbolic triangle centers
Ákos G. Horváth
Using the method of C. Vörös, we establish results on hyperbolic plane geometry, related to triangles. In this note we investigate the orthocenter, the concept of isogonal conjugat…
Hyperbolic plane geometry revisited
Ákos G. Horváth
Using the method of C. Vörös, we establish results in hyperbolic plane geometry, related to triangles and circles. We present a model independent construction for Malfatti's proble…
Isometries of Minkowski geometries
Ákos G. Horváth
In this paper we review the known facts on isometries of Minkowski geometries and prove some new results on them. We give the normal forms of two special classes of operators and a…
Relativity theory in time-space
Ákos G. Horváth
The concept of time-space defined in an earlier paper of the author is a certain generalization of the so-called space-time. In this paper we introduce the concept of time-space ma…
Generalized Minkowski space with changing shape
Ákos G. Horváth
In earlier papers we changed the concept of the inner product to a more general one, to the so-called Minkowski product. This product changes on the tangent space hence we could in…
Premanifolds
Ákos G. Horváth
The tangent hyperplanes of the "manifolds" of this paper equipped a so-called Minkowski product. It is neither symmetric nor bilinear. We give a method to handing such an object as…
Projection pencil of quadrics and Ivory theorem
Ákos G. Horváth
We rewrite the property of confocality with respect to a pseudo-Euclidean space. Our observation is that the generalized definition of confocality in $\cite{stachel}$ does not give…