# Geometry Playground

## Description

Geometry Playground (v1.3) is a free Java application for doing "ruler and compass" constructions in  Euclidean, Spherical, Projective, Hyperbolic, Manhattan and Conical geometries.  Each geometry can be displayed using one or more models; for example, Spherical Geometry can be shown using Sphere, Plane or Mercator models.  The purpose of the program is to help users develop a familiarity with various conceptualizations of these geometries.

The command menu and program messages can be displayed not only in English, but in twelve other languages: Japanese, Spanish, Marathi, French, Arabic, Korean, Russian, Hungarian, Chinese, Italian, Portuguese and Turkish.

Click here to open the Geometry Playground applet in a new window.

Click here to open a pdf help file which offers a brief explanation for each of the commands in the applet.

For further information, updates, and access to the source code, you can visit the Geometry Playground website.

The following pages contain some examples of potential classroom activities involving the Geometry Playground application.

## Activity: Families of Lines

This activity explores the idea of trying to create coordinate systems similar to Cartesian coordinates in Spherical and Hyperbolic geometries.  The authors would like to thank Elly Claus-McGahan, who contributed this activity.

Click here to open the Geometry Playground applet in a new window.

Click here to open a pdf file which contains the instructions for the activity.

## Activity: Fitting Circles

This activity explores the idea of area in the Inverted model of the Euclidean plane, as well as in Spherical and Hyperbolic geometry.  The authors would like to thank Ksenija Simic-Muller, who contributed this activity.

Click here to open the Geometry Playground applet in a new window.

Click here to open a pdf file which contains the instructions for the activity.

## Activity: The Perfect Triangle

This activity explores the construction and properties of an equilateral triangle in Euclidean, Spherical and Hyperbolic geometries. The authors would like to thank Elly Claus-McGahan, who contributed this activity.

Click here to open the Geometry Playground applet in a new window.

Click here to open a pdf file which contains the instructions for the activity.

## Activity: Projective Geometry

This activity explores projective geometry, comparing it to Euclidean and Spherical geometries.

Click here to open the Geometry Playground applet in a new window.

Click here to open a pdf file which contains the instructions for the activity.

## Activity: Comparing Spherical and Hyperbolic Geometries

This activity compares and contrasts Spherical and Hyperbolic geometries by performing similar constructions (triangles, perpendicular and parallel lines, circles) in both and examining the results.

Click here to open the Geometry Playground applet in a new window.

Click here to open a pdf file which contains the instructions for the activity.

## Credits: Translators

The authors would like to thank the following translators for their work:

Feryal Alayont
Rachid Benkhalti
Erlinda Cano
Ajit Datar
Yumiko Heath
Matthew Kim
Guillaume Lajoie
Laszlo Miklos Lovasz
Natalya Manko
Laura Matrajt
Daniil Perebeynos
Hyun-Jong Song
Hideto Tsutsui
Jeffrey Weeks
Yachuan Yu
Xioquian Zhang
Qiang Zheng