This
Interactive Web Book explores the geometry behind Heron's formula for the
area of a triangle in terms of its sides. The formula may be understood by
asking which quadrilateral with assigned side lengths has the largest area.
This book has several experiments embedded in its pages, one of which allows
the reader to vary the shape of the quadrilaterals to discover the surprising
answer, and thereby, to discover Heron's formula.
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 in geometry, algebra, and single-variable calculus.
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 Heron 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).
Nearly
all of the topics discussed will be accessible to a student who is comfortable
with Algebra and Geometry. The crucial step of the argument, however, uses
elementary Calculus and may, as a surprising application of the ideas of Limit
and Derivative, be taken as a motivation for studying those concepts.
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 (18 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
Interactive Web Book: Heron's Formula
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
geometric 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!
To
visit our Interactive Web Books 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 |
