Mathwright Visualization Studio free demonstration Interactive Web Book:

Cardano: An Adventure in Algebra for all ages

This Interactive Web Book is a demonstration of a possible shape for mathematics books of the future. It presents its story in the familiar way that a static text might present it, but with the exception that the pages of the story "come to life" and offer the reader the opportunity to make and test hypotheses, to experiment and explore in a visual and interactive way many of its main constructions and concepts. For many readers, this active participation in the story can add a dynamic dimension that will help them visualize certain of its ideas for the first time. Of course, the reader may print any web page in order to read it in the traditional way as static text offline between experiments, but these interactions are not ancillary; they are from the beginning an essential part of the narrative.

All of the documentation is available in the book itself as page-by-page HTML Help. Most pages are dynamic interaction pages, where you experiment with the ideas of the story as it unfolds. They offer simulations and command lines that range through topics like graphing and factoring polynomials to solving cubic equations to making constructions in abstract algebra. As you come to each page, open the Help, Help for This Page menu to read (or print) the story, then roll up your sleeves and ... play!

The mathematical documentation for this story was created fairly easily using Design Science MathPage™ technology with Microsoft Word 2000™ and Microsoft Help Compiler. And the mathematical interactions were created with Mathwright32 Author™. The Cardano Book may be read in Microsoft Windows™ (95, 98, Me, 2000, or XP) using Internet Explorer Browser 5.0 or later. In order to read it, you should sure you have MathwrightWeb Version 2.10 (after May 12, 2003, or later).

Cardano is not actually intended to teach the mathematical topics it develops to any particular student target audience. It covers a range of topics from high school to graduate-level mathematics. It moves at warp speed across several centuries of mathematics, beginning perhaps in the 16th Century, and ending with some results obtained by the authors, and published in the November 2001 issue of The American Mathematical Monthly. But it was written so that almost anyone who has studied a little algebra can "jump in" and play with it. Some topics that it covers are accessible to high school students, others to university students of Modern Algebra and Theory of Equations, and others may be of interest to graduate students, teachers, and professional mathematicians. So the aim is not to teach the mathematics but to demonstrate the range and the efficacy of a new style of web pedagogy and of authorship.

Requires the free Java MathwrightWeb ActiveX Control to read in your Browser.

For proper viewing, be sure to use Version 2.10 or later, dated May 12, 2003
Download free MathwrightWeb to view Microworlds in your browser, then press


or

Download and extract the Word 2000 version if you wish to print it (55 pages)

Library members, download the free Mathwright32 Reader, then press

For proper viewing, be sure to use Version 2.10 or later, dated May 12, 2003


Microworld: Cardano: An Adventure in Algebra for all ages

or Everything you always wanted to know about Cubic Equations
...but were afraid to ask

Click the Hyperlink above to visit the Microworld.
Author: James White

It may appear that the interactions that one finds on the eight exploration pages are simply Java applets. While they behave like applets, they are different from them for several reasons. Perhaps the most important from the viewpoint of authorship and web design is that they were not written in Java, but were created in a high level object-oriented mathematics scripting language called MathScript. Further the visual design was graphical "point-and-click" or "What you see is what you get." This combination, using our new Mathwright32 Author™ program, produces efficient Java code, but does not require any knowledge of Java itself. It is much simpler to write books with than Java.

One might also point to the range of resources available to this book, and to every interactive web book that uses the MathwrightWeb Control. It uses a symbolic Expert System, computer algebra, sprite animation and graphics, command-line tools, and a special-purpose command language to represent and manipulate ring-theoretic objects. All of this is immediately available to the book. An applet would, in principle, have to download these resources each time this book (or a similar book) was read.

Another difference is this. The "microworld" is a multi-page mathematically savvy interactive story that invites you to ask questions, and (usually) gives you answers. You read it with page-by-page HTML Help that provides sophisticated navigation, attractive and colorful mathematical formulas, charts, illustrations and text. It is a new medium. Welcome to the future!

Once you download our free Mathwright32 Reader above, then simply click Get This Microworld, and it will be downloaded to your machine and installed in a directory there. You may find it whenever you want to view it, by going to the Start, Programs, Mathwright32 Reader menu.

To visit our Microworlds in your browser, it must be able to read ActiveX controls. Microsoft Internet Explorer 4.0 Browser (or later) is so equipped. You should check that the Security Settings under Tools, Internet Options, Security for the Internet, Custom Level has:

  • "Run ActiveX Controls and Plugins" set either to enable or prompt.
  • "Initialize and Script ActiveX Controls not marked as safe" set either to enable or prompt.


Return to the listing of MathwrightWeb Microworlds


    - James E. White, Ph.D. , Library Director,
    author of this website, Mathwright 2000, MindScapes,
    MathwrightWeb, and Mathwright32