Ana Breda | University of Aveiro (original) (raw)

Papers by Ana Breda

The existence of tilings of by crosses, a cluster of unit cubes comprising a central one and arms... more The existence of tilings of by crosses, a cluster of unit cubes comprising a central one and arms, has been studied by several authors. We have completely solved the problem for characterizing the crosses which lattice tile as well as determining the maximum packing density for the crosses which do not lattice tile the plane. In this paper we motivate a similar approach to study lattice packings of by crosses.

Delmastro, Marco (ttaly): "The ATLAS liquid Argon electromagnetic calorimeter: main features, req... more Delmastro, Marco (ttaly): "The ATLAS liquid Argon electromagnetic calorimeter: main features, requested physics performances and test-beam results" Doke, Tadayodhi (Japan): "Fundamental properties of liquid Ar, Kr, and Xe and their new application to calorimeters"

Lecture Notes in Computer Science, 2002

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2011

The main idea behind this work is the study of the potential of resorting to other models of Plan... more The main idea behind this work is the study of the potential of resorting to other models of Plane Geometry (e.g. Hyperbolic Geometry, Taxicab Geometry) to help students to progress towards a proper/better understanding of what a mathematical proof is about. A teaching experiment carried out with students of 15 to 17 years-old attending the 10th and11thgrade (the two first years of secondary school) of a Portuguese school. The experience started in the10th grade and lasted in the 11thgrade. Our main focus is the analysis of primary and secondary relationships of geometric objects involved in argumentation and proof (in the sense of Godino et al. and Gutiérrez et al.) activated by the students during production of arguments.

Beiträge zur Algebra und Geometrie, 2003

The World Wide Web has increased extraordinarily the level of communications and collaborations a... more The World Wide Web has increased extraordinarily the level of communications and collaborations among people via technology. As a consequence the use of computer systems in the teaching and learning processes has in the last few years moved to a new form of technology-supported instruction: web-based instruction. Web-based instruction is rapidly becoming one of the major sources to deliver courses to students ([2], [15], [16]). Besides the facility to communicate and collaborate with other students [11], one of the reasons for this fast increasing system of instruction delivery is its cost-effective. Mathematics is a privileged subject to take advantage of the internet potential. It is a subject area with a recognized hierarchy of topics, which can be introduced with varying degrees of depth to a wide range of users. TextMat is an interdisciplinary academic project whose objective is the development (conception and implementation) of a maths web-based electronic textbook, i.e. an ap...

The classification of spherical tilings is a problem far from being solved. Here we show how to g... more The classification of spherical tilings is a problem far from being solved. Here we show how to generate new families of antiprismatic spherical tilings using GeoGebra, a well known free software commonly used as a tool to teach and learn mathematics. Within the described propose some spherical geometry capabilities of GeoGebra had to be extended. The outline of the algorithms behind some of the newly designed and implemented GeoGebra tools and appli- cations will be given.publishe

EDULEARN21 Proceedings, 2021

In this work, we show the first results of a project where a combinatorial mobile application is ... more In this work, we show the first results of a project where a combinatorial mobile application is used as a tool to gather users’ data, allowing some understanding about the learning behaviour of users solving combinatorial tasks, in particular, related with the NIM game. To obtain the results, 6.514 games and 29.667 moves where analysed and players where considered as production units, that transform input resources, i.e. attempts, moves of game pieces, number of games played; into output results, e.g. number of victories. This approach may give some insights to the use of digital games as research tools in Education.

Portugaliae Mathematica, 2018

AIP Conference Proceedings, 2007

Here we give the complete description of the symmetry group and transitive properties of the set ... more Here we give the complete description of the symmetry group and transitive properties of the set of all of monohedral triangulations of the Riemannian sphere by f-tilings. We shall also show that each monohedral f-tiling of the Riemannian sphere can be seen, up to a spherical isometry, as the singular set of a spherical isometric folding.

Journal of Geometry, 1994

We take up the study of transnormal graphs a9ain. We recall that some results on this topic appea... more We take up the study of transnormal graphs a9ain. We recall that some results on this topic appeared in [2], [3], [4] and [8]. The purpose of this paper is twofold. We start by considering curves in Euclidean n-space and extend the results in [3]. The main result shows that no polynomial curve of positive even de9ree (see below for the definitions) has transnormal 9raph. In section 3 we deal with polynomial functions f:IR-~IR of odd de9ree. Some conditions are proved to be necessary and sufficient for the transnormality of the graph. The results obtained enable us to characterize the polynomial functions of de9ree less than or equal to 5 which have transnormat 9raph. 1. Let f:~R ~ ~ n be a C 1 curve. We consider the curve F:IR ~iR n+l given by' F(t)=(t,f(t)). Obviously F(LR) is the graph of f which from now on we shali denote by G. The normal n-plane to F at t will be denoted by N t and we shah say that G is transnormal if whenever (s,f(s))r t we have Ns=N t, For a survey on transnormality see [6]. The curve f:lR ~ iR n is regular if it has non-vanishin 9 derivative and is polynomial if its components are polynomial functions. If f is polynomial we define its degree as bein 9 the maximum of the degrees of its components. The symbols (I) and ii II will stand for the standard inner product and norm in ~n. 2. It follows from a result of B. Wegner [7] that the graph G is transnormaf if and only if every normal hyperplane to F meets G in just a point. However in [3] an elementary proof, which also works in the present context with the obvious modifications, of this fact is given.

Geometriae Dedicata, 1992

Acta Mathematica Sinica, English Series, 2009

In this paper we present the first research steps regarding the development of BioMat, an enterta... more In this paper we present the first research steps regarding the development of BioMat, an entertainment collaborative/competitive/guided computer educational game in mathematics with incursions in other social and scientific areas and where intelligent agents play a crucial role, monitoring the user's interactions with the game. The main propose of the multi-mode educational game BioMat is the upgrading of social and cognitive skills for teenagers age ten to fourteen, maintaining a continuous challenge to the players.