Related papers: Ram's theorem for Trisection

We study the Erdos distance problem over finite Euclidean and non-Euclidean spaces. Our main tools are graphs associated to finite Euclidean and non-Euclidean spaces that are considered in Bannai-Shimabukuro-Tanaka (2004, 2007). These…

The goal of Point Distance Solving Problems is to find 2D or 3D placements of points knowing distances between some pairs of points. The common guideline is to solve them by a numerical iterative method (\emph{e.g.} Newton-Raphson method).…

Using continuation methods, we study the global solution structure of periodic solutions for a class of periodically forced equations, generalizing the case of relativistic pendulum. We obtain results on the existence and multiplicity of…

A direct proof of the Steiner-Lehmus theorem has eluded geometers for over 170 years. The challenge has been that a proof is only considered direct if it does not rely on reductio ad absurdum. Thus, any proof that claims to be direct must…

Circumcentered techniques have been shown to significantly accelerate projection-based methods for convex feasibility problems. Motivated by this success, we propose two direct methods with circumcenter acceleration for solving variational…

The odds theorem and the corresponding solution algorithm (odds algorithm) are tools to solve a wide range of optimal stopping problems. Its generality and tractability have caught much attention. (Google for instance "Bruss odds" to obtain…

A long-standing, unanswered question regarding Euclid's Elements concerns the absence of a theorem for the concurrence of the altitudes of a triangle, and the possible reasons for this omission. In the centuries following Euclid, a…

The paper describes different approaches to generalize the trapezoidal method to fractional differential equations. We analyze the main theoretical properties and we discuss computational aspects to implement efficient algorithms. Numerical…

One of the main problems in the study of system of equations of the gravitational lens, is the computation of coordinates from the known position of the source. In the process of computing finds the solution of equations with two unknowns.…

As one type of incidence theory, the geometry of pentagram map seems quite classical at first. However, this is an excellent example of such a classical idea developed into a marvellous insight by some modern approach. We introduce an…

In this paper, we develop new techniques for understanding surfaces in $\mathbb{CP}^2$ via bridge trisections. Trisections are a novel approach to smooth 4-manifold topology, introduced by Gay and Kirby, that provide an avenue to apply…

Classical problem of random triangle in square is solved by simple and transparent geometrical method.

Geometric predicates are a basic ingredient to implement a vast range of algorithms in computational geometry. Modern implementations employ floating point filtering techniques to combine efficiency and robustness, and state-of-the-art…

The goal of this paper is to provide computational tools able to find a solution of a system of polynomial inequalities. The set of inequalities is reformulated as a system of polynomial equations. Three different methods, two of which…

A natural analogue to angles and trigonometry is developed in taxicab geometry. This structure is then analyzed to see which, if any, congruent triangle relations hold. A nice application involving the use of parallax to determine the exact…

We evaluate in closed form several classes of finite trigonometric sums. Two general methods are used. The first is new and involves sums of roots of unity. The second uses contour integration and extends a previous method used by two of…

This work wishes to support various mathematical issues concerning the iterative methods with the help of new programming languages. We consider a way to show how problems in math have an answer by using different academic resources and…

We survey some results that provide different versions of classical results through different summability methods. Specifically, in order to adapt such classical results, we analyze which properties should satisfy the summability methods.…

This work investigates the theoretical performance of the alternating-direction method of multipliers (ADMM) as it applies to nonconvex optimization problems, and in particular, problems with nonconvex constraint sets. The alternating…

A non-traditional approach to the discretization of differential-geometrical connections was suggested by the authors in 1997. At the same time we started studying first order difference ``black and white triangle operators (equations)'' on…