Related papers: Optimal constants in normed planes
Extracting planes from a 3D scene is useful for downstream tasks in robotics and augmented reality. In this paper we tackle the problem of estimating the planar surfaces in a scene from posed images. Our first finding is that a surprisingly…
Gradients of the perimeter and area of a polygon have straightforward geometric interpretations. The use of optimality conditions for constrained problems and basic ideas in triangle geometry show that polygons with prescribed area…
We study homogeneity aspects of metric spaces in which all triples of distinct points admit pairwise different distances; such spaces are called isosceles-free. In particular, we characterize all homogeneous isosceles-free spaces up to…
We introduce an algorithm which can be directly used to feasible and optimum search in linear programming. Starting from an initial point the algorithm iteratively moves a point in a direction to resolve the violated constraints. At the…
Some methods for the determination and the most precise values of constants of an extended Standard Model, which include the gravitation interaction and massive neutrinos, are presented. Accuracies of constants at different energy scales…
We discuss solutions of several questions concerning the geometry of conformal planes.
We discuss and compare several geometric structures which imply an upper bound to the acceleration of a particle measured in its rest system. While all of them have the same implications on the motion of a point particle, they differ in…
The objects of study are triangulations of the dilated standard triangle in the plane. Motivated by work on T-curves (Geiselmann et al., 2026), the focus lies on unimodular triangulations with a fixed symmetry axis. Lower and upper bounds…
The first main results of this note establish forms of the hyperbolic laws of cosines and sines for certain classes of quadrilaterals and pentagons in the hyperbolic plane, having at least one ideal vertex and right angles at non-ideal…
The optimal one-sided parametric polynomial approximants of a circular arc are considered. More precisely, the approximant must be entirely in or out of the underlying circle of an arc. The natural restriction to an arc's approximants…
The optimal constants are found for Lebesgue norm multilinear inequalities of Holder-Brascamp-Lieb type for arbitrary discrete Abelian groups. Previously a criterion for finiteness of the constants had been established for finitely…
We consider the distances between a line and a set of points in the plane defined by the L^p-norms of the vector consisting of the euclidian distance between the single points and the line. We determine lines with minimal geometric…
The traditional study of plane and space algebraic curves by looking at their tangent vectors, curvatures and torsions provides geometric, but unfortunately not sufficient information about individual curves in order to be able to…
The purpose of this paper is to present the critical cases of the trace theorems for the restriction of functions to closed surfaces, and to give the asymptotics for the norms of the traces under dilations of the surface. We also discuss…
The algorithm for finding the optimal consistent approximation of an inconsistent pairwise comparisons matrix is based on a logarithmic transformation of a pairwise comparisons matrix into a vector space with the Euclidean metric.…
A new class of random spatial tessellations is introduced -- the so-called column tessellations of three-dimensional space. The construction is based on a stationary planar tessellation. Each cell of the spatial tessellation is a prism…
In this article we will represent some ideas and a lot of new theorems in Euclidean plane geometry.
We study some properties convex functions fulfill. Among the conclusions we obtain from such result, we are able to prove some nontrivial inequalities among real numbers, and we give an improvement of the reverse triangle inequality in the…
Optimal search strategies where targets are observed at several different angles are found. Targets are assumed to exhibit rectangular symmetry and have a uniformly-distributed orientation. By rectangular symmetry, it is meant that one side…
A new way to define the notion of $\C$-orthocenter will be displayed by studying some propierties of four points in the plane which allows to extend the notion of Euler's line, the Six Point Circles and the three-circles theorem, for normed…