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Formal methods for verification of programs are extended to testing of programs. Their combination is intended to lead to benefits in reliable program development, testing, and evolution. Our geometric theory of testing is intended to serve…
Many entities managed by HEP Software Frameworks represent spatial (3-dimensional) real objects. Effective definition, manipulation and visualization of such objects is an indispensable functionality. GraXML is a modular Geometric Modeling…
In this paper we make some considerations about using a dynamic geometry software for teaching history of mathematica at university level. After a short introduction to the software GeoGebra, we discuss four activities. The first is an…
We describe our ongoing project of formalization of algebraic methods for geometry theorem proving (Wu's method and the Groebner bases method), their implementation and integration in educational tools. The project includes formal…
In order to implement a STEAM approach including the use of technology, namely the use of interactive mathematics software GeoGebra, in mathematics classes, in the lusophone space, the materials presented here were conceived, to be…
A Java software framework allows modules written in different languages to be used in a high level Object-Oriented (OO) environment. Java Native Interfaces (JNI) for Linear Collider (LC) physics event generators are used in defining a…
The idea of assisting teachers with technological tools is not new. Mathematics in general, and geometry in particular, provide interesting challenges when developing educative softwares, both in the education and computer science aspects.…
Geometry problem solving, a crucial aspect of mathematical reasoning, is vital across various domains, including education, the assessment of AI's mathematical abilities, and multimodal capability evaluation. The recent surge in deep…
This article is intended as a kind of precursor to the document Geometry for Post-primary School Mathematics, part of the Mathematics Syllabus for Junior Certicate issued by the Irish National Council for Curriculum and Assessment in the…
The effects of computer-assisted and distance learning of geometric modeling and computer aided geometric design are studied. It was shown that computer algebra systems and dynamic geometric environments can be considered as excellent tools…
The use of World Web Wide for distance education has received increasing attention over the past decades. The real challenge of adapting this technology for engineering education and training is to facilitate the laboratory experiments via…
We develop an Easy Java Simulation (EJS) model for students to visualize geostationary orbits near Earth, modeled using Java 3D implementation of the EJS 3D library. The simplified physics model is described and simulated using simple…
For a novice programmer, coding is equivalent to a nightmare. A novice programmer tries to replicate steps provided by the faculty and on compilation gets a number of errors which the novice programmer is not able to resolve. This system…
Geometry theorem proving forms a major and challenging component in the K-12 mathematics curriculum. A particular difficult task is to add auxiliary constructions (i.e, additional lines or points) to aid proof discovery. Although there…
Automated assessment has been shown to greatly simplify the process of assessing students' programs. However, manual assessment still offers benefits to both students and tutors. We introduce Gradeer, a hybrid assessment tool, which allows…
A tutorial of the Mathematica package CGAlgebra, for conformal geometric algebra calculations is presented. Using rule-based programming, the 5-dimensional conformal geometric algebra is implemented and defined functions simplify the…
We survey some recent applications of machine learning to problems in geometry and theoretical physics. Pure mathematical data has been compiled over the last few decades by the community and experiments in supervised, semi-supervised and…
In this work, we present a program in the computational environment, GeoGebra, that enables a graphical study of Newton's Method. Using this computational device, we will analyze Newton's Method convergence applied to various examples of…
This note summarizes the talk by the author at the workshop "Geometry and Computer Science" held in Pescara in February 2017. We present how SageMath can help in research in Complex and Differential Geometry, with two simple applications,…
Designing software systems for Geometric Computing applications can be a challenging task. Software engineers typically use software abstractions to hide and manage the high complexity of such systems. Without the presence of a unifying…