Helena Campos

Interactive Expansion of Achiral Polyhedra

The representation of geometric concepts of three-dimensional space is a well-identified predicament that can undermine the understanding of geometry in particular, and mathematics, in general. Branco Grunbaum mentioned that no method of presentation is satisfactory for much more than the simplest situations and expressed the hope “that computer-based modes of presentation will alleviate this difficulty in the near future” [1]. Aiming to address specific concepts of polyhedral geometry, we’ve been exploring a 3D modelling software and its graphical algorithm editor as digital tools to illustrate certain concepts through accurate graphical descriptions that are dynamic and interactive and imply the knowledge of several geometric operations. Among the several possibilities that could illustrate the software potential, we have chosen the concepts of expansion and contraction of polytopes conceived by the Irish mathematician Alicia Boole Stott in 1910 [2], in our opinion, one of the most visually interesting for a dynamic description. For the sake of concision, we will restrict our presentation to two- and three-dimensional polytopes and illustrate the possibilities of dynamically interact with virtual models to visualize, in real-time, the expansion and contraction of regular polygons and uniform convex polyhedra. The purpose of this research is thus to graphically clarify Stott’s methods through a dynamic approach made possible with contemporary digital tools and demonstrate how this kind of analysis may simplify further researches on the subject and enhance the didactics of these concepts in particular and, more generally, of polyhedral geometry.

The Views of Engineering Students on Creativity

Creativity plays a growing role in education, from elementary school to higher education. Nowadays, both employers and universities develop research and are committed to the development of the twenty-first-century interpersonal, applied skills—creativity included—foreseen as fundamental to all professionals, engineers added. Generally, engineering degrees focus on the content of their scientific areas. In some higher education degrees, creativity still plays a small role. In order to reinforce the importance of creativity in the engineering degrees in a Portuguese northeastern university, it was pertinent to study the conceptions of engineering students about creativity. This study presents the conceptions of creativity of the first-year students of higher education, in the engineering area in two school years. The answers of 128 first-year students from two academic years (61 from 2014/15 and 67 from 2016/17) and four different degrees to the open question—“What is creativity?” were analyzed. It was a mixed study, qualitative to deepen students’ conceptions and quantitative to study some proportions differences and variables crossing. The results show low personal involvement even in the use of the first person plural in either school year, although the students’ most used sentence was “for me.” In both academic years, students’ definitions mentioned more the creation of the implicit category in the content analysis. The words “new” and “way” were common to all the word clouds produced, and creativity and innovation appear somehow connected. In general, proportion differences were not statistically significant and degree crossed with categories showed no dependency.

A note on Gaussian Modified Pell numbers

Abstract Gaussian Modified Pell sequence is defined in this study. Some properties involving this sequence, including the Binet-style formula and the generating function are also presented.

Breaking the habit: engineering students’ understanding of mathematical creativity

ABSTRACT In higher education, engineering students have to be prepared for their future jobs, with knowledge but also with several soft skills, among them creativity. In this paper, we present a study carried on with 128 engineering undergraduate students on their understanding of mathematical creativity. The students were in the first year of different engineering first degrees in a north-eastern Portuguese university and we analysed the content of their texts for the question ‘What do you understand by mathematical creativity?’. Data collection was done in the first semester of the academic years 2014/2015 and 2016/2017 in a Linear Algebra course. The results showed that ‘problem solving’ category had the majority of the references in 2014/2015, but not in the academic year 2016/2017 were ‘involving mathematics’ category had the majority. This exploratory study pointed out for ‘problem solving’ and ‘involving mathematics’ categories and gave us hints for teaching mathematics courses in engineering degrees.

k-Pell, k-Pell-Lucas and modified k-Pell numbers: some identities and norms of Hankel matrices

In this paper we present some identities involving terms of k-Pell, k-Pell-Lucas and Modified k-Pell sequences. We also give some results on the column and row norms of Hankel matrices which entries are numbers of these sequences. Mathematics Subject Classification: 11B37, 11B83, 15A60