MathsNet: Review of Geometer's Sketchpad 4

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Geometer's Sketchpad 4
dynamic geometry software for exploring mathematics

Published by: Key Curriculum Press.
System requirements: Windows/Macintosh

Visit the MathsNet Discussion forum on Geometer's Sketchpad

According to its publishers in USA, Geometer's Sketchpad 4 is " a software system for creating, exploring and analyzing a wide range of mathematics. You can construct interactive mathematical models ranging from basic investigations about shape and number to advanced, animated illustrations of complex systems."

Version 3 has been around since 1995 and has established itself internationally as a top quality piece of software. Its creator, Nicholas Jackiw has been instrumental in its further development and the creation of versions of it for Windows, Mac and even the Casiopiea calculator. Its publishers even own the copyright on the phrase "Dynamic Geometry".

This review will assume that the basic dynamic geometry options will be familiar already (if you want to know more about this visit the interactive geometry page or the Geometry page on MathsNet) and so it will concentrate on two aspects of Version 4: how it differs from Version 3 and how its Web version JavaSketchpad is developing.

Differences from Version 3
When loaded up, its initial appearance is almost identical to Version 3: same menu options along the top; same buttons down the left hand side - though in plain grey now and with the "Help" button replaced with a "Custom tools" button. This similarity is a good sign, since it enables previous users to quickly adapt to the new version. The buttons work in the same way as before. The new "Custom tools" opens up new ways of customising the display and in effect allows easy creation of macros.

To find out more about the changes in Version 4 we need to look closely at the way it works. Changes have been made to how you select and animate objects which make the processes involved more intuitive, more powerful and avoid the need to find out about scripts (which have been replaced by Custom tools). The coordinate geometry options have been greatly enhanced to allow plotting of all manner of cartesian, parametric and polar graphs. Equations themselves can include arbitary constants. .

Figure 1 shows the graph of the quadratic curve y = (x-a)(x-b). The motion controller allows the constants a and b to be changed dynamically with the effect of this shown by the graph

Figure 1

Equations can be entered using correct mathematical notation and then differentiated and the graph of the derivative displayed, as shown in Figure 2. If the equation f(x) is edited then the function f'(x) and its graph change automatically.

All the trig functions including inverses, log and modulus functions are available. With the introduction in Version 4 of advanced graphing, it becomes apparent that Geometer's Sketchpad is not just for dynamic geometry but dynamic graphing too, and as such it offers similar facilitiies to the likes of Omnigraph and Autograph. (Incidentally Autograph also includes some interactive geometry elements too.)

Figure 2

The custom tool can be used to allow easy access to previously prepared constructions (called scripts previously, or macros in other similar programs like Cabri).

This example shows two sets of tools, Conics and Polygons and the drawings produced. Once again, the way Skwethpad facilitates these drawing tools is simple and straightforward.

Figure 3

You can now split points away from their construction, or, conversally, merge them. You can have multiple pages within one file. You can add tables that collect data from a graph or an interaticve process. The use of colour and formatting and linking has been enhanced too. There is no doubt that, whilst Sketchpad has been kept the same at an initial superficial level, the more you explore the more you discover enhanced features. It is a very clever program - in the best sense of the phrase.

Integration with the web - JavaSketchpad
MathsNet has long had an area dedicated to JavaSketchpad. Web pages can be created which contain an interactive Java applet which allows some of the functionality of the full Geometer's Sketchpad program to be realised. What new things does Version 4 bring to this area? At first glance it is hard to tell. The Help files and printed documentation make explicit how you can create an interactive web page from within Sketchpad, using the new Save As...HTML/JavaSketchpad Document (*.htm) option, and you are warned that some aspects of your Sketchpad file cannot be translated to web format. But which aspects? Pages on the KeyPress website tell you which objects are supported by JavaSketchpad.

The significant changes between versions 3 and 4 (illustrated here) are listed below:

Layers: you can now control which object lies "on top" of other objects.
Buttons: an action button can now use an image (.gif or .jpg) instead of the standard text-based style.
Text style: various style formats can be applied to text, including bold, italic, justification, font and size.
Rotation: a construction that defines a rotation round a given point by a measured direction
Image on point: you can now attach an image to an object.
Image between points: you can control the size of an image by fixing it between two points.
Simultaneous button: a button that causes the actions defined by several other buttons to start
Captions: constructions to create fixed captions or titles.

The graphing options do not translate, which is disappointing. Every one of the files that come in the samples folder would not save as an HTML page without losing key aspects of the interactivity. The documentation also points out that, though points and lines can be dragged in the web page, there are no facilties for construction new points or lines. In this respect the interactive geometry program Cinderella remains a clear market leader.

Conclusion
There is no doubt that Sketchpad, previous a great program, has marched on much further and now offers teachers a wealth of useful tools and options for investigating not just plane geometry but coordinate geometry too. The books that accompany the software, particularly "101 Project Ideas", make its usefulness clear. There are other interactive geometry programs around - Cinderella, Cabri Geometre, Dr Geo and other free software on the web - but as a software tool for investigating visual maths it probably stands alone in the lead. The one disappointment at present is JavaSketchpad, which is my own main interest. For producing online interactive geometry I will stick with Cinderella.

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