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Introducing Mathwright Microworlds - Web Book: Heron's Formula

James E. White
The Interactive Web Book Heron's Formula explores the geometry behind Heron's famous equation 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.

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.

To visit Heron's Formula, click the hyperlink or the image above.

Perhaps the most important difference between the interactions that appear on the pages of the Heron book, from the viewpoint of authorship and web design, is that they were not written directly 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 the Mathwright32 Author™ program, produces efficient Java code but does not require any knowledge of Java itself. It is much simpler to write books with this system than with Java.

Another difference is this: The "microworld rooms" that appear on each interaction page are actually multi-page stories themselves. When they have a "Continue Arrow" at the top, you will be told to click the arrow to continue the experiment before leaving the web page. That will take you to a different room that "remembers" what you did. The web page itself does not change, and the various objects you create (functions, graphs, algebraic constructions, and so on) persist; they will be there waiting for you if you decide to return to the room by clicking the "Return Arrow" at the top of the page. If you leave the web page (say, by clicking the Back Button) the microworlds are then closed, and you would have to start the experiment over afresh if you return to it again.

James E. White, "Introducing Mathwright Microworlds - Web Book: [i]Heron's Formula[/i]," Convergence (December 2004)