Synopses & Reviews
Stimulating, unique book explores the possibilities of mathematical drawing through compass constructions and computer graphics. Over 100 full-page drawings demonstrate possibilities: five-point egg, golden ratio, 17-gon, plughole vortex, blancmange curve, Durer’s pentagons, pentasnow, turtle geometry, many more. Exercises (with answers). "...wealth of intriguing and lovely ideas."—Information Technology & Learning.
Synopsis
-A wealth of intriguing and lovely ideas.- -- Information Technology & Learning.
While the beauty of mathematics is often discussed, the aesthetic appeal of the discipline is seldom demonstrated as clearly as in this intriguing journey into the realms where art and mathematics merge. Aimed at a wide range of ages and abilities, this engrossing book explores the possibilities of mathematical drawing through compass constructions and computer graphics.
Compass construction is an extremely ancient art, requiring no special skills other than the care it takes to place a compass point accurately. For the computer graphics part of the present work, however, readers will need some familiarity with basic high school mathematics-mainly algebra and trigonometry. Still, much of the book can be enjoyed even by -mathophobes, - for it is about lines and circles and how to put them together to make various patterns, both abstract and natural.
One hundred and six full-page drawings, ranging from totally abstract to somewhat pictorial, demonstrate the possibilities of mathematical drawing and serve as inspiration to readers to carry out their own creative investigations. Among the illustrations are such intriguing configurationsas a five-point egg, golden ratio, 17-gon, plughole vortex, blancmange curve, Durer's pentagons, pentasnow, turtle geometry, and many more. In guiding students toward the comprehension and creation of such figures, the author explains helpful basic principles (of number, length and angle) as well as reviewing relevant fundamentals of trigonometry. In addition, he has provided numerous useful exercises (with answers} at the ends of the chapters, together with recommended further reading, detailed in the bibliography. 211 black-and-white illustrations. Bibliography. Index.
Synopsis
Stimulating, unique book explores the possibilities of mathematical drawing through compass constructions and computer graphics. Over 100 full-page drawings demonstrate possibilities: five-point egg, golden ratio, 17-gon, plughole vortex, blancmange curve, pentasnow, turtle geometry, many more. Exercises (with answers). "A wealth of intriguing and lovely ideas."
Information Technology & Learning.Synopsis
Stimulating, unique book explores mathematical drawing through compass constructions and computer graphics. Over 100 full-page drawings: five-point egg, golden ratio, plughole vortex, blancmange curve, more. Exercises. 1987 edition.
Description
Includes bibliographical references (p. 207) and index.
Table of Contents
List of drawings
Preface
How to Use this Book
1 Compass Drawings
1.1 Eggs for beginners
1.2 Euclidean constructions
1.3 Euclidean approximations
1.4 Gauss extends Euclid
1.5 The eight centres of a triangle
1.6 Inverse points and mid-circles
2 String Drawings
3 Perspective Drawings
4 The Story of Trigonometry
4.1 The theorem of Pythagoras
4.2 Square roots
4.3 The story of pi (p)
4.4 The story of sine and cosine
5 Computer Drawings
5.1 On drawing a daisy
5.2 Drawing in perspective
5.3 Ten elementary transformations
5.4 The fractal universe
Bibliography
Answers
Index