## Handbook and Atlas of CurvesThe 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. |

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### Contents

Introduction | 1 |

Plane Curves | 7 |

Atlas of Plane Curves | 71 |

Space Curves | 407 |

Some Applications of Curves | 463 |

Appendix A Smooth Functions of One and Two Variables | 511 |

Coordinate Systems Coordinate | 517 |

Appendix E Greek Roots of Names for Some Curves | 523 |

535 | |

### Common terms and phrases

Additional equation Area-hyperbolic axes Axial symmetry axis of symmetry Basic geometric properties bounded connected closed Boundedness center of symmetry Central symmetry central-symmetric curve free Characterized points circle K cissoid connected closed curve Connectedness cos2 cosinusoid courbe curvature curve of Lamet curves 7i cusp cuspidal point cycloid defined end-points Epitrochoid Figure free of singular Geometric petal hypocycloid hypotrochoid inclined asymptotes infinitely large number intersection point isolated point kampyle Kurve lemniscate lemniscate of Bernoulli lemniscate of Booth logarithmic multiple point natural parametrization oval pancappa parameter values parametric equations Pericycloid perpendicular plane curve point MO polar axis polyod of straight present quadratrix radius regular curve sectrix of Okinghaus Self-intersection points single axis single singular point single vertical asymptote singular point node sinusoidal spiral slider space curve strophoid tangent tangentoid tractrix trifolium trisectrix Trochoidal rose unbounded branches unbounded connected curve unbounded unconnected consisting Unboundedness values of parameters variable beam vector function virtual parabola

### References to this book

Differential Geometry of Curves and Surfaces: A Concise Guide Victor Andreevich Toponogov Limited preview - 2005 |

Differential Geometry of Curves and Surfaces: A Concise Guide Victor Andreevich Toponogov Limited preview - 2005 |