Related papers: Random triangle problem: geometrical approach
One of the best things about geometry is that it's cool! Geometry enables us to create incredible designs and astounding patterns. This article shows how to use a simple technique (iteration) to create designs that are both cool and…
It is shown that there exists a dihedral acute triangulation of the three-dimensional cube. The method of constructing the acute triangulation is described, and symmetries of the triangulation are discussed.
This paper presents the classification of a general quadric into an axisymmetric quadric (AQ) and the solution to the problem of the proximity of a given point to an AQ. The problem of proximity in $R^3$ is reduced to the same in $R^2$,…
The random greedy algorithm for constructing a large partial Steiner-Triple-System is defined as follows. Begin with a complete graph on $n$ vertices and proceed to remove the edges of triangles one at a time, where each triangle removed is…
A random matrix model of black holes is given based on analysis of Gaussian complex ensembles, based on the generalization of chRMT of QCD. Spacetime freedoms are incorporated in terms of eigenvalues of the ensemble. Classical observables…
We define transversal tropical triangles (affine and projective) and characterize them via six inequalities to be satisfied by the coordinates of the vertices. We prove that the vertices of a transversal tropical triangle are tropically…
A problem that is simple to state in the context of spherical geometry, and that seems rather interesting, appears to have been unexamined to date in the mathematical literature. The problem can also be recast as a problem in the real…
The classical quadratic formula and some of its lesser known variants for solving the quadratic equation are reviewed. Then, a new formula for the roots of a quadratic polynomial is presented.
In this article, we introduce an algorithm for automatic generation and categorization of triangle geometry theorems.
We introduce and study a new kind of congruent number problem on the right trapezoid.
The Rascal Triangle was introduced by three middle school students in 2010, and in this paper we describe number triangles that are generalizations of the Rascal Triangle and show that these Generalized Rascal Triangles are characterized by…
Straightedge and compass construction problems are one of the oldest and most challenging problems in elementary mathematics. The central challenge, for a human or for a computer program, in solving construction problems is a huge search…
From among $ {n \choose 3}$ triangles with vertices chosen from $n$ points in the unit square, let $T$ be the one with the smallest area, and let $A$ be the area of $T$. Heilbronn's triangle problem asks for the maximum value assumed by $A$…
We show that for certain triangulations of surfaces, circle packings realising the triangulation can be found by solving a system of polynomial equations. We also present a similar system of equations for unbranched circle packings. The…
Random key graphs are random graphs induced by the random key predistribution scheme of Eschenauer and Gligor under the assumption of full visibility. For this class of random graphs we show the existence of a zero-one law for the…
The paper concerns lattice triangulations, that is, triangulations of the integer points in a polygon in $\mathbb{R}^2$ whose vertices are also integer points. Lattice triangulations have been studied extensively both as geometric objects…
We provide a solution to the problem of simultaneous $diagonalization$ $via$ $congruence$ of a given set of $m$ complex symmetric $n\times n$ matrices $\{A_{1},\ldots,A_{m}\}$, by showing that it can be reduced to a possibly…
Random recursive hypergraphs grow by adding, at each step, a vertex and an edge formed by joining the new vertex to a randomly chosen existing edge. The model is parameter-free, and several characteristics of emerging hypergraphs admit neat…
The randomized row method is a popular representative of the iterative algorithm because of its efficiency in solving the overdetermined and consistent systems of linear equations. In this paper, we present an extended randomized multiple…
A method for solving cyclic block three-diagonal systems of equations is generalized for solving a block cyclic penta-diagonal system of equations. Introducing a special form of two new variables the original system is split into three…