Related papers: In Limbo: Three Triangle Centers

We obtain new upper and lower bounds on the number of unit perimeter triangles spanned by points in the plane. We also establish improved bounds in the special case where the point set is a section of the integer grid.

A completely well-centered tetrahedral mesh is a triangulation of a three dimensional domain in which every tetrahedron and every triangle contains its circumcenter in its interior. Such meshes have applications in scientific computing and…

Difference triangle sets are useful in many practical problems of information transmission. This correspondence studies combinatorial and computational constructions for difference triangle sets having small scopes. Our algorithms have been…

We present a theory which predicts if the locus of a triangle center over certain Poncelet triangle families is a conic or not. We consider families interscribed in (i) the confocal pair and (ii) an outer ellipse and an inner concentric…

The purpose of this article is threefold. First, it provides the reader with a few useful and efficient tools which should enable her/him to evaluate nontrivial determinants for the case such a determinant should appear in her/his research.…

In this work, we review the concept of center of a geometric object as an equivariant map, unifying and generalizing different approaches followed by authors such as C. Kimberling or A. Edmonds. We provide examples to illustrate that this…

We use the idea of the broken stick problem (which goes back to Poincare) and calculate the corresponding probabilities for the cases in which the three broken part are: the medians in a triangle, the altitudes, radii of excircles, angle…

A triangulation of a polygon has an associated Stanley-Reisner ideal. We obtain a full algebraic and combinatorial understanding of these ideals, and describe their separated models. More generally we do this for stacked simplicial…

A mostly expository account of old questions about the relationship between polyhedra and topological manifolds. Topics are old topological results, new gauge theory results (with speculations about next directions), and history of the…

We discuss different approaches for the enumeration of triangulated surfaces. In particular, we enumerate all triangulated surfaces with 9 and 10 vertices. We also show how geometric realizations of orientable surfaces with few vertices can…

Tight triangulated manifolds are generalisations of neighborly triangulations of closed surfaces and are interesting objects in Combinatorial Topology. Tight triangulated manifolds are conjectured to be minimal. Except few, all the known…

One of the possible variants of the classification of trigonometric interpolation splines is considered, depending on the chosen convergence factors, the distribution of signs of the basis functions and the interpolation factors. The…

In this paper we provide a review of the concept of center of a $n$-gon, generalizing the original idea given by C. Kimberling for triangles. We also generalize the concept of central line for $n$-gons for $n\geq 3$ and establish its basic…

Delaunay triangulations of a point set in the Euclidean plane are ubiquitous in a number of computational sciences, including computational geometry. Delaunay triangulations are not well defined as soon as 4 or more points are concyclic but…

We introduce explicit families of good interpolation points for interpolation on a triangle in $\mathbb{R}^2$ that may be used for either polynomial interpolation or a certain rational interpolation for which we give explicit formulas.

We introduce the triangulant of two matrices, and relate it to the existence of orthogonal eigenvectors. We also use it for a new characterization of mutually unbiased bases. Generalizing the notion, we introduce higher order triangulants…

We give a brief introduction to some of the recent works on finding geometric structures on triangulated surfaces using variational principles.

We study some properties of a triad of circles associated with a triangle. Each circle is inside the triangle, tangent to two sides of the triangle, and externally tangent to the circle on the third side as diameter. In particular, we find…

Historic steps in the emergence, the derivation and the use of three-nucleon forces, genuine and effective, for calculations of few-nucleon systems and of the structure of heavier nuclei are recalled. The research focus is on few-nucleon…

We show that for an integer $\ell$, there exists an acute integer lattice triangle of lattice perimeter $\ell$ such that its orthocenter is an integer lattice point, if and only if $\ell=6 $ or $\ell\ge 8$. Analogous results are obtained…