This site provides a rich environment to visualize and explore a variety of mathematical objects and includes Java applets, Quicktime movies and pdf descriptive documents of the mathematics involved in the objects displayed. It will reward considerable exploration but is not for the mathematically faint of heart.
Type of Material:
Interactive applets, movie demonstrations and related mathematical explanations. The material is created by an international volunteer group called the 3DXM Consortium and is supported by a National Science Foundation award. The website is hosted by the University of California at Irvine.
Hands-on interactive exploration of the mathematics, plus background explanations - or simple visual enrichment.
Web browser with Java 5.0
Adobe pdf reader
Identify Major Learning Goals:
To explore and visualize mathematical objects in an interactive environment.
Target Student Population:
College math students; math majors in particular
Prerequisite Knowledge or Skills:
Calculus and Analytic Geometry / Some differential equations.
Evaluation and Observation
This site contains a large collection of geometric visual objects to explore. It starts with an artistic front page leading to 9 galleries which each have a range of subtopics (# in parentheses): plane curves (5), space curves (4), conformal maps (4), fractals/chaos (4), surfaces (7), mathematical art (9 artists), sounds, polyhedra (2) and ordinary differential equations (many). Each of these is broken down into many layers. For example, within plane curves, the category of ancient curves includes ten specific curves. The ordinary differential equation gallery is particularly comprehensive with over thirty varieties, including first- and second- order in one, two and three dimensions. In several places, it allows for exploration of user-defined equations. For most objects there is a linked pdf document that explains the related mathematics. The site also contains occasional outside references and a link to the homepage for the 3D-XplorMath software involved in creating the material. Software and documentation can be downloaded without charge.
Potential Effectiveness as a Teaching Tool
The site could be used at two entirely different levels. The first would be a visual tour without understanding. Many of the artistic renderings are visually striking and the Quicktime movies are rewarding. The second level would be to use the interactive applets to explore the mathematics in detail and from a variety of viewpoints. For example you can examine tangents, normals and osculating circles for the curves featured in the plane curves gallery.
The second level of use would not be easy nor lead to much understanding without prior knowledge of the background mathematical material.
Ease of Use for Both Students and Faculty
Each gallery has a document that explains the overall mathematics of the exhibits. Most objects have three items a Quicktime movie with no explanation, a pdf document that explains the mathematics and a Java applet that allows exploration of the specific object in a variety of ways. Many of the mathematical explanations include background history.
Many of the explanations are not designed for the beginning user and the applets dont have much in the way of reassuring instructions.