Related papers: On the Construction of Even Order Magic Squares
We study the problem of perfect tiling in the plane and exploring the possibility of tiling a rectangle using integral distinct squares. Assume a set of distinguishable squares (or equivalently a set of distinct natural numbers) is given,…
In this article we consider square permutations, a natural subclass of permutations defined in terms of geometric conditions, that can also be described in terms of pattern avoiding permutations, and convex permutoninoes, a related subclass…
The purpose of this note is to present a formulation of a given nonlinear ordinary differential equation into an equivalent system of linear ordinary differential equations. It is evident that the easiness of a such procedure would be able…
We give some concrete constructions of real equiangular line sets. The emphasis here is on {\em building blocks} for certain angles which are then used to build up larger equiangular line sets. We concentrate on angles greater than or equal…
Our goal is to present, in what we believe is the most efficient way possible, a construction of four mutually tangent circles.
Based on the rules of magic cubes, a game of two-dimensional magic cube was deliberately designed. This essay will explore its properties with the assistance of group theory and computer programming. It will first elaborate the rules of…
The purpose of this short manuscript is to show that all point constructions that can be done via ruler and compass, can also be done with compass exclusively. If we are using compass and ruler the way we construct new points is by first…
We give a simple direct proof of Fermat's two squares theorem. Our argument uses no intricate notions or ideas; one might say that it is a proof by careful bookkeeping. As such, the proof may be particularly easy to comprehend by students…
We review a general parameterization of an order-3 magic square derived by Lucas and we compound it to produce a parameterized order-9 magic square. Sequential compounding to higher order also is treated. Expressions are found for the…
In this note we study how to share a good between n players in a simple and equitable way. We give a short proof for the existence of such fair divisions.
A general method for constructing essential uniform algebras with prescribed properties is presented. Using the method, the following examples are constructed: an essential, natural, regular uniform algebra on the closed unit disc; an…
In this paper, we give a direct construction for a set of dice realizing any given tournament $T$. The construction for a tournament with $n$ vertices requires a number of sides on the order of $n$, which appears to be the best general…
This article contains the last part of the mini-course `Spaces: a perspective view' delivered at the IFWGP2012. Here I deal with the part of the mini-course which centers on the classification questions associated to the simple real Lie…
P. J. Federico used the term low-order for perfect squared squares with at most 28 squares in their dissection. In 2010 low-order compound perfect squared squares (CPSSs) were completely enumerated. Up to symmetries of the square and its…
In this work we present a new simple but efficient scheme - Subsquares approach - for development of algorithms for enclosing the solution set of overdetermined interval linear systems. We are going to show two algorithms based on this…
A cyclically ordered quiver is a quiver endowed with an additional structure of a cyclic ordering of its vertices. This structure, which naturally arises in many important applications, gives rise to new powerful mutation invariants.
Schemes for exact multiplication of small matrices have a large symmetry group. This group defines an equivalence relation on the set of multiplication schemes. There are algorithms to decide whether two schemes are equivalent. However, for…
This paper is an investigation of a procedure for constructing lattices by means of taking the sum of a pair of isometric lattices. We present various general results pertaining to this construction and discuss several examples of it…
We propose a notion of a generalized order, which can be used for the notion of a strict partial order. We introduce a weak order to replace the usual weak order defined from a strict partial order. In a constructive setting, that usual…
The purpose of this article is to give a complete and general answer to the recurrent problem in continuum mechanics of the determination of the number and the type of symmetry classes of an even-order tensor space. This kind of…