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This article explores the symmetry method in elementary differential equations, which uses the invariance of the equation under certain transformations to create a coordinate system in which the equation greatly simplifies.

This article discusses parameterized knots (polynomial and trigonometric) and includes an interactive gallery of selected knots and their equations.

This article analyzes the physical and mathematical properties of the mirascope and models the mirascope using dynamic learning technology

This article explores analogues of the Pythagorean Theorem in non-Euclidean geometries.

Geometry Playground (v1.3) is a free Java application for doing "ruler and compass" constructions in both Euclidean, Spherical, Projective, Hyperbolic, Toroidal, Manhattan and Conical geometries. Its purpose is to help users develop a familiarity with various conceptualizations of these geometries.

The purpose of this collection of applets and activities is to make students familiar with the basic principles of complex numbers. Combining explanatory text, exercises and interactive GeoGebra applets, this resource is suitable for both classroom lectures and distance learning.
A collection of GeoGebra applets and activities for exploring the properties of reflections, rotations, translations and glide reflections in the plane.

Users toss a virtual coin or die to investigate the law of averages. The outcomes of multiple experiments (consisting of 10000 tosses each) can be graphed on the same plot to facilitate visualization of trends. An activity is provided to facilitate thinking about the law of averages with the applet.

This Supplement provides an applet which allows readers to explore symmetries of "Yin-Yang" shapes generated by polar graphs of Fermat spirals.

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.

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