Linear programming constitutes university students’ first approach to numerical optimization. The involved concepts require a high level of abstraction. It is thus important to understand how they are constructed. This study presents the results obtained from the use of an APOS Theory based didactical model together with a simple modeling problem t...

In this article, we discuss at length a combinatorial problem which has been of historic interest. It has appeared as a puzzle in several different versions with varying degrees of difficulty. It can be simply stated as follows: We are given a number of coins which are otherwise identical except that there may be at most one fake coin among them wh...

Tolerance graphs model interval relations in such a way that intervals can tolerate a certain amount of overlap without being in conflict. In one of the most natural generalizations of tolerance graphs with direct applications in the comparison of DNA sequences from different organisms, namely multitolerance graphs, two tolerances are allowed for e...

Agner Bitencourt, LopesVargas, Paulo RobertoFelicetti, Vera Lucia

This article presents an educational proposal accomplished in a higher education class in the Undergraduate Mathematics, in the discipline Complex Variables, about the content of complex numbers and their geometric representation on the Argand-Gauss plane, more specifically, about the rotation of vectors on the complex plane. The proposal is based ...

A Free Triangle order is a partially ordered set in which every element can be represented by a triangle. All triangles lie between two parallel baselines, with each triangle intersecting each baseline in exactly one point. Two elements in the partially ordered set are incomparable if and only if their corresponding triangles intersect. A unit free...

The notion of a free triangle representation of a partially ordered set was first introduced by Josh Laison [4] as a generalization of the ideas of interval and trapezoid representations. A free triangle representation assigns a triangle to each element of a partially ordered set, with all triangles having one vertex on each of two parallel baselin...

A graph G is a queens graph if the vertices of G can be mapped to queens on the chessboard such that two vertices are adjacent if and only if the corresponding queens attack each other, i.e. they are in horizontal, vertical or diagonal position. We prove a conjecture of Beineke, Broere and Henning that the Cartesian product of an odd cycle and a pa...