Zobrazeno 1 - 10
of 80
pro vyhledávání: '"Horváth, Ákos G."'
A central problem of geometry is the tiling of space with simple structures. The classical solutions, such as triangles, squares, and hexagons in the plane and cubes and other polyhedra in three-dimensional space are built with sharp corners and flat
Externí odkaz:
http://arxiv.org/abs/2402.04190
Autor:
Horváth, Ákos G.
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 applications of mechanical engineering, civil engineering and architectur
Externí odkaz:
http://arxiv.org/abs/2310.08919
Autor:
Horváth, Ákos G.
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 that can be considered a specification for both. We do not use the theo
Externí odkaz:
http://arxiv.org/abs/2305.08859
We regard a smooth, $d=2$-dimensional manifold $\mathcal{M}$ and its normal tiling $M$, the cells of which may have non-smooth or smooth vertices (at the latter, two edges meet at 180 degrees.) We denote the average number (per cell) of non-smooth ve
Externí odkaz:
http://arxiv.org/abs/2110.02323
Autor:
Horváth, Ákos G.
Finding the shortest vectors in a lattice is an NP-hard problem, so low-dimensional results also play an essential role in lattice reduction theory. Using Ryskov's result for the admissible centerings and Tammela's result for determining the Minkowsk
Externí odkaz:
http://arxiv.org/abs/2102.05154
Autor:
Horváth, Ákos G., Lángi, Zsolt
The aim of this note is to investigate the properties of the convex hull and the homothetic convex hull functions of a convex body $K$ in Euclidean $n$-space, defined as the volume of the union of $K$ and one of its translates, and the volume of $K$
Externí odkaz:
http://arxiv.org/abs/2012.08955
Autor:
Horváth, Ákos G.
This paper contains a new concept to measure the width and thickness of a convex body in the hyperbolic plane. We compare the known concepts with the new one and prove some results on bodies of constant width, constant diameter and given thickness.
Externí odkaz:
http://arxiv.org/abs/2011.14739
Autor:
Horváth, Ákos G.
The "old-new" concept of convex-hull function was investigated by several authors in the last seventy years. A recent research on it led to some other volume functions as the covariogram function, the widthness function or the so-called brightness fu
Externí odkaz:
http://arxiv.org/abs/1908.03196
Autor:
Horváth, Ákos G.
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 volume of the convex hull of these two simplices maximal? We prove th
Externí odkaz:
http://arxiv.org/abs/1811.12399
Autor:
Horváth, Ákos G.
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 conic.
Comment: 3 pages,3 figures
Comment: 3 pages,3 figures
Externí odkaz:
http://arxiv.org/abs/1804.10345