# Geometry Explorer

### Description of the Program:

• What is the Program Designed to do ?

• Geometry Explorer is designed as a geometry laboratory where one can create geometric objects (like points, circles, polygons, areas, etc), carry out transformations on these objects (dilations, reflections, rotations, and translations), and measure aspects of these objects (like length, area, radius, etc).  As such, it is much like doing geometry on paper (or sand) with a ruler and compass. However, on paper such constructions are static -- points placed on the paper can never be moved again.  In Geometry Explorer, all constructions are dynamic. One can draw a segment and then grab one of the endpoints and move it around the canvas, with the segment moving accordingly.  Thus, one can create a construction and test out hypotheses about the construction with an infinite number of possible variations of the original construction. Geometry Explorer is just what the name implies -- an environment to explore geometry.

Geometry Explorer can easily be used to access Web-based information. There is an Internet browser built in to the program that allows hyperlinks to Web pages to be inserted directly into a geometry construction. The Help system consists of a series of inter-linked Web pages that are accessed via the built-in browser.  (You do not need to be connected to the Internet to use the Help system.)

Non-Euclidean geometry can easily be explored using Geometry Explorer. Constructions can be carried out in a Euclidean or non-Euclidean (Hyperbolic, Elliptic, or Spherical Geometry) environment using the same user interface. Almost all actions that apply in the Euclidean environment can be carried out in the non-Euclidean environment (with a few important exceptions that depend on the parallel postulate).

Fractal geometry can be explored using turtle graphics and grammatical descriptions of fractals. In turtle graphics, one controls a "turtle" on the screen by telling it to move, draw, rotate, change color, etc. Grammar-based descriptions of fractals encapsulate a fractal's structure by sentences of symbols. These sentences can then be interpreted as a series of turtle actions.

Analytic Geometry can be explored in a dynamic fashion.  Graphs of functions can be constructed and then changed dynamically based on parameters. Points can be attached to graphs allowing for the study of tangents and reflection properties. "Cobweb" diagrams for iterated functions can be easily created and updated dynamically.

Geometry Explorer is designed to assist the classroom teacher. Text areas can be created on the screen so that additional information can be included with a construction.  If a large amount of textual information must accompany a construction, this can be included in a separate Notebook with the construction.  Web pages can be referenced directly from the Geometry Explorer window. A fully functional calculator is included for carrying out detailed calculations with measurements and other numerical values. Images in a wide variety of formats can be imported and exported from the program.  Finally, there is the ability to make ``recordings'' of sequences of steps (macros) that can then be used in other constructions.