1st Edition

Handbook and Atlas of Curves

By Eugene V. Shikin Copyright 1995

    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.

    Plane Curves
    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
    Space Curves
    Main Defintions and Facts
    Some Classes of Space Curves
    Applications of Curves
    Dynamic Properties of Plane Curves
    Plane Curves and Mechanisms
    Geometric Splines
    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
    English-German-French Indices
    Index of Terms


    Eugene V. Shikin