This article discusses parameterized knots (polynomial and trigonometric) and includes an interactive gallery of selected knots and their equations.
This article explores analogues of the Pythagorean Theorem in non-Euclidean geometries.
Modeling the Mirascope Using Dynamic Technology
This article analyzes the physical and mathematical properties of the mirascope and models the mirascope using dynamic learning technology.
Life After Wolfram|Alpha: What You (and Your Students) Need to Know
This article introduces several basic features of Wolfram|Alpha, provides examples, and discusses along the way how this new technology can influence what we do in our classrooms.
This article uses a game, called Google-opoly, played on a small directed graph to describe and model the Google PageRank algorithm.
A Gallery of Ray Tracing for Geometers
This gallery of images and animations shows many examples of how the POVray ray-tracing software can be used to display examples in three-dimensional geometry.
Trisecting a Line Segment (With World Record Efficiency!)
This article looks at several geometric, straightedge-and-compass constructions for trisecting a line segment, comparing them based on the numbers of lines or circles required for the construction.
Thinking Outside the Box -- or Maybe Just About the Box
This article presents a fresh look at an age-old calculus optimization problem, the "box problem." (Also includes a Student Module condensed from the article.)
Seashells: the Plainness and Beauty of Their Mathematical Description
In this article, a very simple model is used to describe and generate many types of seashell shapes.
Visualizing Lie Subalgebras using Root and Weight Diagrams
This paper uses graphics and animations to illustrate how to construct root and weight diagrams for Lie algebras, and how the root and weight diagrams can be used to identify subalgebras.
Math on the Web Made Easier
This article describes a document style for authors which combines HTML and LaTeX structures as a bridge to advanced Web technologies.