The Handbook and Atlas of Curves describes available analytic and visual properties of plane and spatial curves. Information is presented in a unique format, with one half of the book detailing investigation tools and the other devoted to the Atlas of Plane Curves. Main definitions, formulas, and facts from curve theory (plane and spatial) are discussed in depth. They comprise the necessary apparatus for examining curves.
An important and original part of the book is the Atlas, consisting of nearly 200 plane curve classes, more than 700 figures, and nearly 2,000 drawings of specific curves. The classes have been scrupulously chosen for their interesting and useful properties. The dynamics of each class is visually represented by a series of specially arranged precise drawings showing the qualitative change of a curve's behavior as the parameters defining the class vary.
The book provides numerous application examples, descriptions of mechanisms for drawing various curves, and discussions of geometric spline possibilities. It includes more than 20 various geometric and linguistic indices and an update on world literature on curve theory. The Handbook and Atlas of Curves will be an invaluable reference for researchers, practitioners, students, and amatuers of mathematics.
Table of Contents
Main Definitions and Facts
Some General Classes of Plane Curves
Atlas of Plane Curves
Structure of the Atlas
Atlas of Curves
Geometric Indices for Atlas of Curves
Main Defintions and Facts
Some Classes of Space Curves
Applications of Curves
Dynamic Properties of Plane Curves
Plane Curves and Mechanisms
Smooth Functions of One and Two Variables
Vector Functions of Scalar Argument
Coordinate Systems. Coordinate Transformations
Search of Some Geometric Characteristics
Greek Roots of Names for Some Curves
Index of Terms