Book of Curves
Cambridge University Press, 8/21/2008
EAN 9780521044448, ISBN10: 0521044448
Paperback, 212 pages, 24.6 x 18.9 x 1.2 cm
Language: English
This book opens up an important field of mathematics at an elementary level, one in which the element of aesthetic pleasure, both in the shapes of the curves and in their mathematical relationships, is dominant. This book describes methods of drawing plane curves, beginning with conic sections (parabola, ellipse and hyperbola), and going on to cycloidal curves, spirals, glissettes, pedal curves, strophoids and so on. In general, 'envelope methods' are used. There are twenty-five full-page plates and over ninety smaller diagrams in the text. The book can be used in schools, but will also be a reference for draughtsmen and mechanical engineers. As a text on advanced plane geometry it should appeal to pure mathematicians with an interest in geometry, and to students for whom Euclidean geometry is not a principal study.
Frontispiece
section of the shell of a Pearly Nautilus fossil
Preface
Historical Introduction
Notation
Part I. Special Curves
1. The parabola
2. The ellipse
3. The hyperbola
4. The cardioid
5. The limaçon
6. The astroid
7. The nephroid
8. The deltoid
9. The cycloid
10. The right strophoid
11. The equiangular spiral
12. The lemniscate of bernoulli
13. The tractrix and catenary
Part II. Ways of Finding New Curves
14. Conchoids
15. Cissoids
16. Strophoids
17. Roulettes
18. Pedal curves
19. Negative pedals
20. Glissettes
21. Evolutes and involutes
22. Spirals
23. Inversion
24. Caustic curves
25. Bipolar coordinates
Further reading
Glossary
Index of names
Index of subjects.