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
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:
![]()
Return to the listing of MathwrightWeb Microworlds
| - James E. White, Ph.D. , Library Director, | ||
| author of this website, Mathwright 2000, MindScapes, | ||
| MathwrightWeb, and Mathwright32 |