Geometry and its Applications (GeoMAP) is an exciting National Science Foundation project to introduce new discoveries and real-world applications of geometry to high school students. The materials are flexible enough to be used in almost any class from algebra and geometry through precalculus, and are ideal for discrete mathematics or college preservice classes.

Each of these modules is available, free of charge, to COMAP members for use in the classroom. Photocopying is permitted for use only within a single class of students or teachers. The material may not be sold or modified in any way without written permission from COMAP.

COMAP members can download and use any of these units:

Graph Models, by Joseph Malkevitch
Looking at the problems faced by delivery people, storeowners, coaches, airline operations managers, and more, your students learn how to analyze real situations using mathematical models.

Shortest Paths, by Nancy Crisler & Walter Meyer
Robots like SARAH, a robot that performs neurosurgical procedures, often use graph theory to make "decisions" about where to go. Students explore a variety of algorithms designed to calculate efficient routes and try to find their own optimal solutions.

Rigidity & Braced Grids, by Brigitte Servatius
Whether it's the Cathedral of Notre Dame or the Statue of Liberty, an architect needs to create structures that won't collapse. Your students will learn how to determine whether a grid (of steel or wood, for example) is braced, or unstable and dangerous.

Knottedness, by Bridget Arvold & Peter Cromwell
From magic tricks to sailing, to Egyptian hieroglyphics, knots have appeared throughout history and in virtually all cultures. Using topology, students explore the nature of knots, a new and exciting area of mathematical research.

Symmetry & Patterns, by Nancy Crisler
Through the eyes of an archaeologist, students learn about mathematical patterns and how they can be used to help us understand ancient civilizations.

Tessellations, by Philip Mallinson
Tessellations are found in art, architecture, and the natural world. Students work with increasingly difficult polygons (from triangles and squares to pentagons, hexagons, decagons, and beyond) as they explore the mathematics of tessellations.

Geometric Probability, by Art Johnson
Through the visual world of geometry, students experience probability as a tangible issue, allowing them to more easily grasp this important but challenging concept.

Voronoi Diagrams & Proximity Problems, by Matthew Dickerson & Scott Drysdale
Students use the properties of Voronoi diagrams to explore issues such as choosing a location for a restaurant and deciding which emergency unit should respond to a crisis.