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THE MATHWRIGHT LIBRARY NEWSLETTER, June 2002, VOL
4, #4
A publication of Bluejay Lispware
James E. White, Editor
The official publication of the New Mathwright Library and Café:
In this issue:
The MAA Journal of Online Mathematics and its Applications introduces Mathwright Microworlds!
New Free Interactive Web Books at the Café
Online Help for Authors, a Card Catalog for Readers, and 3D Graphics for Everybody
1) The MAA Journal of Online Mathematics and its Applications introduces Mathwright Microworlds!
The
Mathematical Association of America's new Journal
of Online Mathematics and its Applications (JOMA) represents the frontier
of the emerging collaboration between technology and mathematics education.
Please go there and read about the new role for Java that we are developing
here at the Café.
Our article in the June issue of JOMA entitled "Introducing Mathwright
Microworlds" discusses Mathwright Microworlds both from the viewpoints
of their readers (students) and their authors (teachers). If you read the
JOMA article, please follow the instructions there to download the Personal
MathwrightWeb ActiveX control, because that is different from the Library
MathwrightWeb Control that we use here at the Library. As of June, 2002, we
have 44 Interactive Web Books and Microworlds in place at the
Library.
If
you are among those visitors to the Café
who have not yet sampled the fruit of this new approach to teaching and learning
mathematics online (or offline) then you may easily fix that. Just visit our
Free Stuff page and download the Library
MathwrightWeb ActiveX Control. Then cruise to the bottom of the Free
Stuff page to the Free
Demo Microworlds
for MathwrightWeb and Mathwright32,
and select something to read in your browser. These do not even count as your
"first 3 free" so you get them without any fuss at all. If you decide
that you would like to read some of these offline, then download the Mathwright32
Reader from the Free Stuff Page and add what you like to your home collection.
2) Free Interactive Web Books at the Café
Speaking
of Free Stuff, we now have three Interactive Web Books at the Library,
and they are completely free to view in your browser. These Interactive Web
Books represent the cutting edge of our research in educational technology,
and if you are interested in such things, please visit them whenever you like
in your browser. You will not have to sign in to view them online, as we mentioned.
Interactive
Web Books go beyond Microworlds in that they attempt to tell self-contained
mathematical stories that allow the readers to participate in simulations,
to view demonstrations, and to ask their own "what if" questions.
At the same time, they try to make fuller use of the browser environment to
tell those stories. So the mathematical notation is realistic and readable,
and the screens are designed to be compelling and attractive. Put this all
together, and you have something completely fresh and different.
In coming
months, we will have a wide variety of Interactive Web Books here at the Library,
written at all levels, as our authors begin contributing their own efforts
to the Café.
Currently,
we offer three
examples of things to come, all somewhat esoteric (being developed, as they
were, by yours truly, in the spirit of testing the limits of range, flexibility
and expressiveness of the Mathscript language).
If you are not daunted by the pioneer spirit, and if you would like a glimpse
of a possible future for mathematics education on the web, please check these
out:
Our
newest Interactive Web Book: Odds and Integrals
states and solves an interesting problem in Probability, while it introduces
and illustrates concepts in 3 Dimensional Geometry, Integration of functions
of several variables, Simplicial Topology, and Linear Algebra. The printable
text version is downloadable as a 33-page Word 2000 document..
The
Cardano Interactive Web Book teaches
a new way to learn and remember Cardano's famous method for
solving cubic equations. Along the way, it introduces the "cubic formula"
that you will not have to (or want to) remember, and uses an expert system
to solve cubic equations step by step.
The
solutions of 
are
given by the cubic formula:
If
we let
then
the expression
|
|
|
yields the 3 roots.
Finally,
the Interactive Web Book: Heron's Formula
translates the question of how to determine the area of a triangle from the
lengths of its sides into a problem in optimization, and then solves that
problem. 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 are 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.
3) Online Help for Authors, a new Card Catalog for Readers, and 3D Graphics for Everybody
Our
Mathscript Language is what makes Microworlds and Interactive Web Books work.
While it is much too large a topic to discuss in this Newsletter, we have
fully documented the language online at the Café
with a complete discussion of its 275 built-in commands and functions and
all of its Display Objects and Gadgets (including the new 3D Graphics objects,
and the inclusion of a large part of OpenGL in Mathscript). To see what OpenGL
can do, visit our new 3D Graphics Microworld!
Mathwright
authors and prospective authors may now visit our Online
Help Center and read this documentation, together with a complete Tutorial
that takes you step-by-step through seven authoring projects, showing all
the details involved in building and deploying Microworlds at your own website.
If
you prefer to read the Help offline, then simply download it to your machine,
and read at your leisure.
Finally,
in our ongoing effort to keep abreast of our growing collection, and to make
it easy for readers to find what they are looking for quickly, we have built
an Online Card Catalog at the Café.
Using the new Mathematics Digital Library Classification, you may search the
tree for 1817 separate topics. Plenty of room to find whatever you want, quickly
and efficiently. You will find the Card Catalog at the home page of the Library.
James E. White, Ph.D.
Library Director