*Sketchpad 3* is the largest single upgrade to The Geometer's Sketchpad
program yet. It
reflects both our findings in four years of (NSF-sponsored) research
into how the original *Sketchpad* was being used in classes across the
country (and more recently: the world), as well as the shifting nature
of geometry in today's math classroom. As the role of the new *Standards*
has begun to shift from that of elegant rhetoric to an actual
foundation for classroom action, so too has the purpose and nature of
geometry and geometry education. In addition to being one of the
traditional math disciplines most readily adapted to some form of
"laboratory" practice, geometry is one of the most versatile in its
connections to other mathematical subjects, to the sciences, and to
general logic, analysis, and reasoning. *Sketchpad 3*
delivers on all of these fronts.

Here's a preview of what you can expect:

- Improvements in the program's ease of use. This encompasses a variety of enhancements, from simplified commands to continuous visual, textual, and tactile interface feedback (no more questions: "how close is 'close enough?"), to the ability to configure the program's geometry menus to a level appropriate to your students, to specific functionality aimed at special populations (a keyboard interface for people who aren't agile with the mouse; "large text" option for the vision-impaired and for presenters using inadequately-lit projection devices), and so on.

- Script Tools. These allow you to turn *Sketchpad* scripts -- geometric
constructions which you've recorded -- into full-blown
interactive drawing tools. Are your students interested in the
applications of geometry to architecture? If so, they can augment
the standard Compass and Straightedge tools with tools to draw
Ogee arches, to calculate building-facades in the Golden Ratio,
to add fleur-de-lys and quatre-foil ornamentation...tools which
they've authored themselves, using Euclid's tools to define
Le Corbusier's, and then Le Corbusier's to define their own. Are
you instead interested in introducing them to the Poincare disk?
Then turn off the Construct, Transform, and Measure menu, and
give them a custom-built microworld based on script tools which
draw hyperbolic lines, segments, bisectors, etc.

Script tools extend the geometric vocabulary of the program
indefinitely, by allowing you, your students, or other *Sketchpad*
curricula developers to define new easy-to-use primitives and add
them to the program transparently.

- Analytic geometry. In addition to being able to create coordinate
systems, grids, and axes, and measure coordinates and equations of
objects with the coordinate system, *Sketchpad 3* lets you plot
measurements and calculations--from whatever source--directly
onto your coordinate system. Because *Sketchpad's* dynamic, every
calculation is an equation, which you means you can not only
move from geometry to algebra, but from algebra -- or trig, calculus,
physics, personal finance, what have you -- back to geometry.

The program inherently supports both rectangular and polar
coordinate systems. But by allowing you to plot -- and dynamically
vary -- any calculation or measurement, you can readily model other
coordinate systems: complex, conjugate, etc. In addition, coupled
with the program's ability to construct loci, the ability to
plot calculations allows you to define new objects analytically:
conics, quartics, Bezier and B-splines...if you can come up with
an analytic definition, *Sketchpad* can create it. (You can use
regular geometric measurements, coordinate values, and the coefficients and
parameters of measured equations as terms in
your calculations.)

- Mathematical notation. In the days when computer displays were
limited to text characters, and when processors ran as quickly
as the last drops of ketchup from its bottle, symbolic notation
like "sqrt((dx^2)+((dy^2))" was, if not acceptable, a necessary
inconvenience. Since that time, such notation has been foisted
on the math classroom by the calculator industry largely without
good reason. *Sketchpad 3's* notation -- for measurements,
calculations, geometry and algebra -- is the same you'll find in
your textbooks.

- And other stuff. Arcs, arc segments, sectors, and loci round out the program's built-in constructions; greater control over labeling lets you easily recreate existing diagrams or develop your own notation; animation is more powerful, transformations and fractals can be computed by any calculation, the calculator has received a face-lift, etc.

We've also significantly improved the dynamic geometry engine (short version: drag anything, anytime), extended the on-line help, and greatly increased the program's ability to serve both as an exploration environment, for students and researchers, and as an authoring environment, for teachers and curriculum developers.

Return to the Foyer.

*Sketches, scripts, and web pages by Bill Finzer
and Nick Jackiw.*