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# Loci: Resources

The Resources section of Loci provides a select collection of free online learning materials which are available through the site. These materials have been classroom tested and peer reviewed. Many items are posted with editorial reviews and a link to a moderated discussion group focused on the materials.

Looking for archived Digital Classroom Resources? All DCR material posted before July 2008 can be accessed by "Search" or "Browse" through the Loci Archives.

Featured Items:

## CalcPlot3D, an Exploration Environment for Multivariable Calculus

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.

## Geometry Playground

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.

## An Interactive Introduction to Complex Numbers

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.

## Exploring Geometric Transformations in a Dynamic Environment

A collection of GeoGebra applets and activities for exploring the properties of reflections, rotations, translations and glide reflections in the plane.

## Law of Averages Applet

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.

## Mathematics Animations with SVG

We highlight five pages written in XHTML with links to SVG files that produce animations illustrating calculus concepts such as the sign of the derivative, inflection points, conic sections, area between two curves, and multivariable functions.

## Applets and Activities for Real Analysis

This suite of five interactive applets (written with GeoGebra) allows exploration of definitions and theorems commonly presented in first-year analysis courses. Topics include sequence convergence, continuity at a point, the Mean Value theorem, Taylor series, and Riemann sums. Included with each applet is a pair of activities: one for becoming comfortable using the applet, and one for using the applet to explore the associated topic in depth.

## Probability Aquarium

Simple probability concepts such as sampling with or without replacement are illustrated in this engaging tiered activity for beginning students and future teachers of probability.