Geometry of Curves

Meer over het boek

Integrating the three main areas of curve geometry-parametric, algebraic, and projective curves-Geometry of Curves offers a unique approach that provides a mathematical structure for solving problems, not just a catalog of theorems. Almost entirely self-contained, this book begins with the basics then takes readers on a fascinating journey from conics through the properties of parametric curves and the classification of limacons to the application of projective curves to asymptotes and boundedness. The uniqueness of this work lies in its integration of the different types of curves, its use of analytic methods, and its plentiful examples, exercises, and illustrations. Inhaltsverzeichnis PreliminariesLines, Circles and ConicsConics: General PositionSome Higher Algebraic and Transcendental CurvesParameters, Tangents, Normals. Contact, InflexionsUndulationsCusps, Non-Regular PointsCurvatureCurvature ApplicationsCircle of CurvatureLimaconsEvolutesParallels, InvolutesRoulettesEnvelopesSingular Points of Algebraic CurvesProjective Curves