Description
Book SynopsisThis 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.
Table of ContentsFrontispiece: 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.
