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In this article we use Java applets to interactively explore some of the classical results on approximation using Chebyshev polynomials. We also discuss an active research area that uses the Chebyshev polynomials.

In this article, we use on-line resources and computational tools to approximate the volume of the space occupied by each planet as it orbits the Sun.

 

Poems sometimes have interesting connections to mathematics, either because of mathematical imagery in the poem or because of mathematics in the structure of the poem (word or syllable counts or shape). This article explores some of these connections
This article uses interactive mathlets to explore various methods of determining the winner of a three party election. Methods of constructing paradoxical examples are also given.
This article argues for pedagogical reasons that the dot and cross products should be defined by their geometric properties, from which algebraic representations can be derived, rather than the other way around.
This article unifies four numerical procedures for solving nonlinear equations: the regula falsi, Newton--Raphson, secant, and Steffensen methods.

This Editor's Note discusses best practices for writing web-based expository mathematics.

This is a Developer's Area article that describes how to use a Java applet called LiveGraphics3D to speed up the process of creating interactive graphics by removing the need to create a graphics engine in Java, Flash, or other programming languages.
An article describing the author's first experience with teaching an online course, with suggestions for those who find themselves in similar circumstances
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.

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