This
9-page Interactive Web Book is
a symphony of good mathematical pedagogy, artificial intelligence, and graphic
art. It is an introduction to quadratic functions and quadratic growth. And
it is full of experiments that will help you understand the ideas, beginning
with Galileo's law of freely falling bodies. You control the simulations,
so that you may step into Galileo's shoes and discover for yourself the mystery
of "Natural Motion" - of uniform acceleration.
This
Interactive Web Book
tells its story on each page in a new way. Right-click where indicated on
each screen to pop-up a menu, and choose Help, Help for this Page to
view the Windows HTML Help for that page. These Help pages guide the
reader through each topic with lively illustrations and with a discussion
that presents the mathematics in textbook quality displayed formulas and charts.
Other
experiments include tossing a ball up with various velocities, and applying
the brakes to stop a car moving at various speeds. Different representations
for quadratic functions are explored, and the relations of those representations
to their graphs is developed through interaction.
Solving
quadratic equations, both by graphing, and algebraically, is the central theme
of this unique work. For this, the Book generates quadratic equations randomly,
or allows you to make them up. In either case, it draws the graph and so displays
the solution graphically, then explains, step-by-step, how to solve the quadratic
equation algebraically. It does this for your problems also!
This
is followed by a masterful treatment of quadratic inequalities. Whether you
use an inequality it generates, or you make one up, it graphs the inequality,
and shows which interval(s) in the line provide(s) the solution, by drawing
those interval(s). Next, it gives a step-by-step explanation (using its built-in
Expert System) of how the inequality can be solved algebraically.
All
in all, it is a self-contained, animated exploration of the basic facts about
quadratic functions. You may read it on the web in your browser, or off-line.
Read at your own pace and enjoy this thoughtful discussion as a supplement
to your studies. The book is full of questions (literally an unlimited number
of them!) but the most important questions will be your own. And the book
invites you to ask them. It will supply detailed answers for many questions
that you may have about solving quadratic equations or solving quadratic inequalities.
The
Windows HTML Help files can easily be printed, and they offer the familiar
amenities. In particular, Help, Help for this Microworld provides a
Table of Contents, so that readers can navigate smoothly from one topic to
the next. It also explains how to prepare your machine to use Access Databases
in case it is not ready to do so.
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
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:
Exploring
Quadratic Functions
Click the Hyperlink above
to visit the Microworld.
Author:
Samad
Mortabit
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.
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 |
