### Geometric Constructions

A **geometric construction** is a step-by-step process to
__determine__ and __build__ a geometric figure or configuration.
A *configuration* is a set of interrelated geometric shapes.
A geometric construction is called
a *construction* for short. Traditionally, constructions
were done on paper or on a chalkboard using a writing tool,
straightedge, and compass.

Nowadays, constructions can be simulated using
**interactive, dynamic** geometry software on
computers and handheld devices. Not just the software but
the constructions themselves are interactive and
dynamic. They are interactive because they are readily modified.
They are dynamic because the user can move and
manipulate the constructed geometric configuration
without changing its dependency relationships.

The **dependency relationships** of a configuration are
determined by the nature and order of the steps in the
construction process. As the figure is built step by step,
relationships are established by how and where the parts
of the figure are attached.
The configuration becomes somewhat like the skeletal system of the
human body or a mechanical device with interconnected parts, levers, and
linkages.

The dynamic aspect of a construction helps to reveal what changes
and what stays the same when the figure is manipulated.
This reveals **invariants** - properties of the figure
determined by the inherent dependency
relationships in the construction process.

### Sketchpad

Sketchpad is a dynamic visualization software
package that encourages mathematical discovery. Students manipulate geometric sketches that they have
constructed themselves by movements that do not change the dependency relationships. This enables them to discover invariants and make conjectures of
theorems. In this way they develop an ownership of the material and
experience the excitement of discovering mathematics. The latest
version of Sketchpad features enhancements such as built-in web integration,
improved sample explorations, and manipulation of
functions that make it an effective learning environment in
a greater variety of classes.