Geometry of Curves - Rutter, J. W.

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Résumé :
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. The author begins with the basics, then takes readers on a fascinating journey from conics, higher algebraic curves, and transcendental curves, through the properties of parametric curves, the classification of limaçons, and envelopes of curve families, to projective curves, their relationship to algebraic curves, and their application to asymptotes and boundedness. The uniqueness of this volume lies in its integration of the different types of curves, its use of analytic methods, and its generous number of examples, exercises, and illustrations. The result is a practical work - almost entirely self-contained - that not only imparts a deeper understanding of the theory, but a heightened appreciation of geometry and interest in more advanced studies.

Biographie:
J.W. Rutter is an honorary fellow at the University of Liverpool. He received his Ph.D. from Oxford University and has taught at Oxford, Stanford, and California universities, and has held visiting positions at Cambridge University. Institut Hautes Etudes Scientifiques, Paris. and Centre de Recerca Matemàtica, Barcelona. He is the author of more than 30 research papers and monographs.

Sommaire:
["Lines, circles, and conics","Conics: general position","Some higher curves","Parameters, tangents, normal","Contact, inflexions, undulations","Cusps, non-regular points","Curvature","Curvature: applications","Circle of curvature","Limaçons","Evolutes","Parallels, involutes","Roulettes","Envelopes","Singular points of algebraic curves","Projective curves","Practical work","Drawn curves","Further reading."]