Related papers: Outer median triangles
We found a class of triangulated surfaces in Euclidean space which have similar properties as isothermic surfaces in Differential Geometry. We call a surface isothermic if it admits an infinitesimal isometric deformation preserving the mean…
We study parallel surfaces and dual surfaces of cuspidal edges. We give concrete forms of principal curvature and principal direction for cuspidal edges. Moreover, we define ridge points for cuspidal edges by using those. We clarify…
We study tetrahedra and the space of tetrahedra from the viewpoint of local and global maxima for intrinsic distance functions.
We study the generalized analogues of conics for normed planes by using the following natural approach: It is well known that there are different metrical definitions of conics in the Euclidean plane. We investigate how these definitions…
The main focus of the present paper is the following inequality $\left( \sqrt{bc}-a\right) m_a+ \left(\sqrt{ac}-b\right)m_b+\left(\sqrt{ab}-c\right)m_c \geq 0,$ where $a,b,c$ are the sides of a non-degenerate triangle and $m_a,m_b,m_c,$ the…
We construct solitons in affine orbifold nets associated with outer automorphisms, and we show that our construction gives all the twisted representations of the fixed point subnet. This allows us to settle a number of questions concerning…
In this paper we have discussed different possible orthogonalities in matrices, namely orthogonal, quasi-orthogonal, semi-orthogonal and non-orthogonal matrices including completely positive matrices, while giving some of their…
Differential properties for orthogonal polynomials in several variables are studied. We consider multivariate orthogonal polynomials whose gradients satisfy some quasi--orthogonality conditions. We obtain several characterizations for these…
We continue the work begun in OEIS sequence A332636 which presents recursive sequences that have triangles that appear embedded in them. This paper i) generalizes the main result presented in A332636, ii) provides a complete set of…
Some geometric structures with associated Riemannian metrics have been considered in the book.
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
We study the order of tangency between two manifolds of same dimension and give that notion three quite different geometric interpretations. Related aspects of the order of tangency, e.g., regular separation exponents, are also discussed.
We establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below, in the spirit of the classical bound on the distances between conjugates points in surfaces…
A rational triangle is a triangle with sides of rational lengths. In this short note, we prove that there exists a unique pair of a rational right triangle and a rational isosceles triangle which have the same perimeter and the same area.…
Using the method of C. V\"or\"os, we establish results on hyperbolic plane geometry, related to triangles. In this note we investigate the orthocenter, the concept of isogonal conjugate and some further center as of the symmedian of a…
We consider outer billiard outside regular convex polygons. We deal with the case of regular polygons with $\{3,4,5,6,10\}$ sides, and we describe the symbolic dynamics of the map and compute the complexity of the language.
We introduce the concept of protometric and present some properties of protometrics.
We introduce and study the concept which we call the splitting of a graph and compare algebraic properties of the edge ideals of graphs and those of their splitting graphs.
We construct isoperimetric regions from separating hypersurfaces in closed manifolds. This yields isoperimetric boundaries exhibiting a wide variety of topological types and singular sets.
We give a necessary and sufficient condition for two circles, each with finitely many points added inside, to be betweenness isomorphic. We fully characterize the betweenness isomorphism classes in the family consisting of all circles with…