Design and computer graphics curricula for tertiary education include 3-D modeling skills. Students must learn to represent (complex) 3-D objects by means of parametric surfaces or polygonal meshes. Three-dimensional modeling may be a complex task, and students must be able to accrue a certain deal of experience in the field before passing the…

This paper describes outcomes from a project conducted at a small US university where 23 secondary school mathematics teachers participated in the study. Based on sketches created in a dynamic geometry software (DGS) and written responses to an assignment related to developing the trapezoid area formula, we explored how teachers used DGS when…

Digital model platforms and applications are common in anatomy education and continue to grow in number, which suggests that educators and students find use for these tools despite the lack of widely accepted best practices. Consequently, it is a challenge for educators to mindfully integrate digital models into curriculum. This short-term,…

This study developed four AR games and investigated their influence on learning in a Grade 5 English course by integrating theories of digital game-based learning, the attention relevance confidence-satisfaction (ARCS) model, and different types of digital games. Moreover, the elements between AR game design and the ARCS model were examined. 147…

The representation of figures in mongean projection (double system planned orthographic projection used in the studies of Descriptive Geometry), specially when placed in a particular situation in relation to the projection plans, possesses the quality that, through them, the actual dimensions of represented spatial objects can be found directly…

The refraction problem, well-known in calculus and physics, continues to reveal new insights. This paper presents a geometric solution in which the trammel of Archimedes plays the prominent role. When properly configured, the trammel generates an ellipse and its family of normal lines. One normal line in particular intersects the boundary…

This study hypothesized that increased intensity of graphic information, presented in computer-generated instruction, could be differentially beneficial for students with hyperactivity and inattention by improving their ability to sustain attention and hold information in-mind. To this purpose, 18 2nd-4th grade students, recruited from general…

This paper describes the genesis and purpose of our geometry methods course, focusing on a geometry-teaching technology we created using NVIDIA[R] Chameleon demonstration. This article presents examples from a sequence of lessons centered about a 3D computer graphics demonstration of the chameleon and its geometry. In addition, we present data…

This paper deals with a brief historical introduction to fractals, fractal dimension and fractal geometry. Many fractals including the Cantor fractal, the Koch fractal, the Minkowski fractal, the Mandelbrot and Given fractal are described to illustrate self-similar geometrical figures. This is followed by the discovery of dynamical systems and…

Developing a software environment to enhance 3D geometric proficiency demands the consideration of theoretical views of the learning process. Simultaneously, this effort requires taking into account the range of tools that technology offers, as well as their limitations. In this paper, we report on the design of Virtual Spaces 1.0 software, a…

This paper describes how parametric cubic splines and cubic Bezier curves may be used in designing a two dimensional shape. A simple aerofoil shape is designed using both methods. The mathematics is described and the shape drawn using Excel. The effect of varying parameters is shown in both methods.

Cubic symmetry is used to build the other four Platonic solids and some formalism from classical geometry is introduced. Initially, the approach is via geometric construction, e.g., the "golden ratio" is necessary to construct an icosahedron with pentagonal faces. Then conventional elementary vector algebra is used to extract quantitative…

WebTOP is a three-dimensional, Web-based, interactive computer graphics system that helps instructors teach and students learn about waves and optics. Current subject areas include waves, geometrical optics, reflection and refraction, polarization, interference, diffraction, lasers, and scattering. Some of the topics covered are suited for…

Through the use of graphic computer simulation, this paper analyzes the combinatorial and geometric mathematics underlying a four-dimensional variation of the Rubik's Cube. This variation is called the Rubik's Tesseract and has dimensions, 3 x 3 x 3 x 3. (JJK)

Five guidelines for enhancing the value of a computer graphics program are described and illustrated. Using a well-structured program, correct scaling, normalized device coordinates, word coordinates, and illusions are discussed. (MNS)