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This dynamic Java applet developed with support from the NSF (Dynamic Visualization Tools for Multivariable Calculus, DUE-CCLI Grant #0736968)) allows the user to simultaneously graph multiple 3D surfaces, space curves, parametric surfaces, vector fields, contour plots, and more in a freely rotatable 3D plot. This tool is intended as a dynamic visualization and exploration environment for multivariable calculus. Use it to illustrate the geometric relationships of many of the concepts of multivariable calculus, including dot and cross products, velocity and acceleration vectors for motion in the plane and in space, the TNB-frame, the osculating circle and curvature, surfaces, contour plots and level surfaces, partial derivatives, gradient vectors and gradient fields, Lagrange multiplier optimization, double integrals as volume, defining the limits of integration for double and triple integrals, parametric surfaces, vector fields, line integrals, and more. See the corresponding web page for documentation and a list of guided explorations developed for students to use with this exploration applet.

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.