THE MATHWRIGHT LIBRARY NEWSLETTER, Jan 2002, VOL 4, #1
A publication of Bluejay Lispware
James E. White, Editor

The official publication of the New Mathwright Library and Café:

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In this issue:

Back to Basics: 6 Easy Pieces

We are very pleased to present three new authors and 6 new Microworlds in the Library this month. The theme of this issue is "Back to Basics," and these new Microworlds each contribute to the theme, as you will see. Before we describe the new books to you, we will say a little about how to read these Microworlds. The simplest way to read a Microworld is off-line in the Mathwright32 Reader. Just download and install the Reader and then get these Microworlds to read whenever you like, on-line or not. If you enjoy reading in your browser, then you will need the MathwrightWeb Control. Download and install the Control, and you may read these books on-line in your Microsoft Internet Explorer browser. You may have to "tune" your browser settings for this, so see the instructions on the Title Page of any Microworld.

Our 6 Easy Pieces are ordered below from the easiest to the most challenging. They are all designed to take you step-by-step through their topics, giving you plenty of opportunity to stop and view the scenery, and to ask your own questions.

1) Playing with Points by new author Kanchan Manaktala (Alcorn State University), is a 6-page Microworld that shows how to plot points on graph paper, how to measure the distance between pairs of points, and how to determine whether three points lie on a line. What is novel about this Story is that it presents two games that you may play either against the computer or with a partner to develop your skills in plotting points and determining distances. This is an excellent book for beginners.

2) Graphs of Functions and Symmetry is another book by Kanchan Manaktala. This delightful 6-page Microworld is a gentle introduction to the symmetries of a graph. It approaches this idea through the metaphor of reflection, as in reflection through a mirror. The basic reflections that it considers are: reflections through the x-axis and y-axis, and through the line y=x. Beginning with reflections of points through these lines, it moves on to let the reader experiment with the reflections of graphs and curves through these lines, and gives a visual tour of the various notions of symmetry associated with these geometric operations.

3) Transformations of a Function by veteran WorkBook author Mike Pepe (Seattle Central Community College) marks his debut as a Microworld author, and is his translation to a Microworld of the Library WorkBook by the same name. This book examines various standard transformations of functions and their associated graphs. In each case, it is a matter of showing how an algebraic transformation leads to the corresponding geometric transformation of the graph of f. For example if we start with the function f(x) = x^2 we can create a new function F by defining F(x) = f(x)+3, so F(x) = x^2 +3. In words, F is the function that adds three to the output of the function f. We refer to this new function F as a "transformation" of the function f. On the other hand, we could construct a function G(x) = f(x+3). This has a different graph: the graph of (x+3)^2. The Microworld shows you what to expect in this, and several other cases. With MathwrightWeb downloaded after 1/13/02, this Microworld will blend seamlessly into the web page.

4) Graphs of Quadratic Functions is the first Library Microworld by new Mathwright author Kwok-Wai Mok of Munsang College, Hong Kong. This 6-page Microworld explores with lively animation and interactive algebra, the properties of the graphs of quadratic functions, and symbolic and graphical ways of understanding the solutions of quadratic equations. While it provides plenty of examples and step-by-step instructions for its many exercises, its real strength is that it offers you challenging and interesting exercises that will really invite you to think about what it all means, and to ask your own questions. It begins by discussing the general qualitative features of the parabolic graph y = a*x^2+b*x+c (creating examples and testing your understanding of the meaning of parameters a, b, and c as they relate to properties of the graph). Next, it shows you how to find the vertex of the parabola by rewriting the function in the standard form: y = a*(x-h)^2 + k.

5) Shortest Paths is a joint project by Mathwright Authors Ravinder Kumar and Kanchan Manaktala. In this 7-page Microworld, the authors explore the concept of shortest distance from a point to a line, and from a point to a general curve. The user is given an opportunity to explore consequences/characteristics of the shortest distance. Shortest distance from a point to a curve is obtained using an optimization technique in single variable calculus. Shortest distance from a point to a line is studied using both a formula from Cartesian geometry as well as optimization techniques. At the end of each section the reader can practice finding shortest distance using well-explained commands with randomly generated problems.

6) Finally, Triangle Optimization by Mathwright Author Ravinder Kumar may be used for PreCalculus and Calculus I courses. It breathes new life into the art of optimization (and that's a trick in itself) by giving a compelling visual demonstration, as well as a formal proof, of the fact that a triangle with maximum area of a fixed perimeter is equilateral. In his proofs, the first argument depends upon multivariable calculus. The second proof depends essentially on single variable calculus. What is unique and powerful about this mode of presentation is the way the author intercalates formal argument with illustration and experimentation. This is the most advanced of our "basic" pieces, but is also one of the most memorable and compelling.

Enjoy!

James E. White, Ph.D.

Library Director