Related papers: Illustrating Mathematics using 3D Printers
We present a simple but efficient concept for the realization of blended teaching of mathematics and its applications in theoretical mechanics that was conceived, tested and implemented at the University of Trento, Italy, during the…
We present simple models of trajectories in space, both in 2D and in 3D. The first examples, which model bicircular moves in the same direction, are classical curves (epicycloids, etc.). Then, we explore bicircular moves in reverse…
In Geographical Information search, map visualization can challenge the user because results can consist of a large set of heterogeneous items, increasing visual complexity. We propose a novel visualization model to address this issue. Our…
Teaching proofs is a crucial component of any undergraduate-level program that covers formal reasoning. We have developed a calculational reasoning format and refined it over several years of teaching a freshman-level course, "Logic and…
In order to describe natural phenomena, science develops sophisticated models that use mathematical and formal languages which seem, and often are, very far from common experience. When a phenomenon is not accessible to our senses, its…
Computer-supported learning is an increasingly important form of study since it allows for independent learning and individualized instruction. In this paper, we discuss a novel approach to developing an intelligent tutoring system for…
We present an educational tool, a microscope with a video camera, that can be fabricated either from a standard microscope or assembled from inexpensive, commercially available components (objectives, beam splitters, LEDs, linear stages)…
Borrowing methods and formulas from Prof. Goodman's classic Introduction to Fourier Optics textbook [1], I have developed a software package [2] that has been used in both industrial research and classroom teaching [3]. This paper briefly…
Recent advancements in 3D reconstruction, especially through neural rendering approaches like Neural Radiance Fields (NeRF) and Plenoxel, have led to high-quality 3D visualizations. However, these methods are optimized for digital…
Volume approximation is an important problem found in many applications of computer graphics, vision, and image processing. The problem is about computing an accurate and compact approximate representation of 3D volumes using some simple…
Portable quantum technologies require robust, lightweight apparatus with superior performance. For techniques dependent upon high-vacuum environments, such as atom interferometers and atomic clocks, 3D-printing enables new avenues to tailor…
The formalization of existing mathematical proofs is a notoriously difficult process. Despite decades of research on automation and proof assistants, writing formal proofs remains arduous and only accessible to a few experts. While previous…
Elements of experimental equipment for the production of biofuel components must meet high reliability and safety requirements. At the same time, in the course of research on the subject of creating equipment for the production of biofuels,…
We introduce Patchwork, a new general-purpose shape representation capable of modeling 2D and 3D geometry with a small number of parameters. Patchwork is grounded in a rigorous mathematical framework, providing provable complexity bounds…
Three-dimensional (3D) printing has emerged as a powerful tool for material, food, and life science research and development, where the technology democratization necessitates the advancement of open-source platforms. Herein, we developed a…
Usually the first course in mathematics is calculus. Its a core course in the curriculum of the Business, Engineering and the Sciences. However many students face difficulties to learn calculus. These difficulties are often caused by the…
This essay considers ways that recent uses of computers in mathematics challenge contemporary views on the nature of mathematical understanding. It also puts these challenges in a historical perspective and offers speculation as to a…
We report on an exploratory project aimed at performing immersive 3D visualization of astronomical data, starting with spectral-line radio data cubes from galaxies. This work is done as a collaboration between the Department of Physics and…
We give an overview of combinatorial methods to represent 3D data, such as graphs and meshes, from the viewpoint of their amenability to analysis using machine learning algorithms. We highlight pros and cons of various representations and…
3D Gaussian Splatting (3DGS) has emerged as a prominent technique with the potential to become a mainstream method for 3D representations. It can effectively transform multi-view images into explicit 3D Gaussian through efficient training,…