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Mathographics
Dixon R., Dover Publications, Inc., New York, NY, 1991. Type: Book (9780486266398)
Date Reviewed: Apr 1 1992

Mathematics consists of more than numbers and symbols; it also encompasses a variety of drawings. These drawings include geometric figures, compass drawings, and various forms of computer graphics. Dixon tries to share the fun and esthetic appeal of mathematical drawings with students and hobbyists. The book starts with a section on compass drawings, which shows how to draw continuous curves made up of arcs that differ in radius, Euclidean constructions, and the centers of a triangle, among other things. The next two sections briefly cover string and perspective drawings. Section 4 focuses on trigonometry, including Pythagoras’s theorem, pi, square roots, and trigonometric functions. The final section covers computer graphics, such as drawing flower petals, perspective drawings, transformations, and a few fractal images. The book includes a bibliography of moderate length, an accurate index, and answers for some of the problems posed in the text.

This book has a few shortcomings. For example, Dixon uses the word “tangent” on page 13 but does not define it until page 28. Similarly, he recommends the use of a look-up array (p. 203) but does not define it. A book that is intended for people who are unfamiliar with an area should define terms the first time that they appear. Another source of confusion is the numbering system used to label the illustrations. The book includes large illustrations intended to demonstrate the various techniques discussed in the text, which are numbered in sequential order. This sometimes makes it hard to find where these large illustrations are discussed in the text. It also contains small illustrations numbered by the section and subsection in which they are discussed. If more than one illustration appears in a subsection, the number is followed by a letter. Unfortunately, the same number, such as 3.1B, can refer to several drawings. The illustrations themselves are done in black and white, which makes it difficult to see how some of the compass drawings were constructed. A system of color coding lines that go together or the use of dashed, solid, and dotted lines would make it much easier to understand and reproduce the drawings.

The book contains only a few typographical errors. Several of the examples are bad or questionable, however. “Maria Imbrium” is used as an example of a large lunar crater. First, the correct spelling of this term is “Mare Imbrium.” Second, although the Mare Imbrium may be a lava-filled crater, it is not a good example of a typical lunar crater. Tycho or Copernicus would be much better choices. Further bad examples may be found in the pseudo-BASIC program fragments in the final section of the book. In the very first program (p. 122), the first iteration produces a Y coordinate of 10,000, which exceeds the limits of the displays on most PCs. The second program (p. 122) adds a scaling factor to correct this problem, but it contains further flaws. In this program the variable X is used as the counter in a FOR…NEXT loop, but the code within that loop modifies the value of X. It is necessary to change the name of the variable used as the counter to something like XCOUNT. In general, the programs are not examples of good programming style. They use one-letter variable names that are not mnemonic. They do not use indentation or spacing to show the programs’ structure, and they sometimes make use of magic numbers. A magic number is one that appears in the program (for instance, X = 10 * X) but is picked on an arbitrary basis and not explained. It is much better to assign numbers to meaningful variable names at the start of the programs (for example, XSCALE = 10…X = X * XSCALE) and explain why those numbers were used. That way, if the readers want to alter a value they simply need to make one change at the start of the program, rather than having to change all occurrences of the number in the program. The programs are fairly easy to convert into BASIC, although users of other languages may have to make some modifications. TurboPascal, for example, does not allow the use of fractional values as counters in a FOR loop.

The book, according to the author, “is aimed at a wide range of ages and abilities” (p. vi). Dixon deliberately leaves out details so that readers may puzzle them out for themselves. This approach is unlikely to work for those readers who are young or not very proficient at math or programming; they may find this lack of guidance to be frustrating rather than challenging. Novice computer programmers will find some of the programs confusing and may learn bad programming habits. It is not clear who the book is aimed at. Teachers of primary or secondary school mathematics or computer studies may find a few interesting demonstrations here, but the book is definitely not suitable for use as a textbook. Many good textbooks on computer graphics do a better job of presenting this material; better books are also available for those who want to produce interesting and educational graphics on their computers.

All things considered, I cannot recommend this book. The author seems to find the material in the first sections on compass and string drawings and Euclidean geometry exciting, but his enthusiasm is not contagious. The final section on computer graphics may lead to frustration, especially for novices.

Reviewer:  Kent A. Campbell Review #: CR115291
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Mathematics And Statistics (J.2 ... )
 
 
General (K.3.0 )
 
 
General (K.8.0 )
 
 
Graphics Utilities (I.3.4 )
 
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