Related papers: Illustrating Mathematics using 3D Printers
High-aspect-ratio polymer materials are widely utilized in applications ranging from everyday materials such as clothing to specialized equipment in industrial and medical fields. Traditional fabrication methods, such as extrusion and…
We illustrate the concept of mathematical proof.
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
Quantum physics modeling is technically complex and often non-descriptive. This article presents some approaches how quantum physical ideas can be represented by haptic models. For this purpose, models made from 3D printers, models made…
During the last decades, anatomy has become an interesting topic in education---even for laymen or schoolchildren. As medical imaging techniques become increasingly sophisticated, virtual anatomical education applications have emerged.…
Increasingly there is a need to develop astronomical visualisation and manipulations tools which allow viewers to interact with displayed data directly, in real time and across a range of platforms. In addition, increases in dynamic range…
Visualization plays a relevant role for discovering patterns in big sets of data. In fact, the most common way to help a human with a pattern interpretation is through a graphic. In 2D/3D virtual environments for procedural training the…
3-dimensional (3D) reconstruction is an emerging field in image processing and computer vision that aims to create 3D visualizations/ models of objects/ scenes from image sets. However, its commercial applications and benefits are yet to be…
The aim of this research is to get a better understanding of the future of large-scale 3D printing. By developing the market analysis, it will be clear whether large-scale 3D printing is becoming more of a preferred way of printing…
In this short essay, we show how computer experiments, and especially visualization, allowed for the investigation and discovery of phenomena which would have passed unnoticed. We shall also highlight the importance of interactivity between…
Over the past thirty years or so the authors have been teaching various programming for mathematics courses at our respective Universities, as well as incorporating computer algebra and numerical computation into traditional mathematics…
3D scene modeling techniques serve as the bedrocks in the geospatial engineering and computer science, which drives many applications ranging from automated driving, terrain mapping, navigation, virtual, augmented, mixed, and extended…
Computer graphics, often associated with films, games, and visual effects, has long been a powerful tool for addressing scientific challenges--from its origins in 3D visualization for medical imaging to its role in modern computational…
Interactive proof assistants make it possible for ordinary mathematicians to write definitions and theorems in a formal proof language, like a programming language, so that a computer can parse them and check them against the rules of a…
Three-dimensional (3D) printed preoperative planning models serve a critical role in the success of many medical procedures. However, many of these models do not portray the patient's complete anatomy due to their monolithic and static…
Astronomy has been an inherently visual area of science for millenia, yet a majority of its significant discoveries take place in wavelengths beyond human vision. There are many people, including those with low or no vision, who cannot…
This paper focuses on digitally-supported research methods for an important group of cultural heritage objects, the Greek pottery, especially with figured decoration. The design, development and application of new digital methods for…
Most if not all of today's revolutionary technologies have a common foundation, namely the intelligent use of information. It is clear that computers play a central role: but the contribution of mathematics, though less visible, is no less…
Symbolic equations are one of the many representations used in physics. Understanding these representations is important for students because they are how students access knowledge in physics. In this paper I build off of the work by Redish…
This panel draws on research of the teaching of mathematical proof, conducted in five countries at different levels of schooling. With a shared view of proof as essential to the teaching and learning of mathematics, the authors present…