The Theory of Plane Curves

The Theory of Plane Curves
Author: Surendramohan Ganguli
Publisher:
Total Pages: 422
Release: 1925
Genre: Curves, Algebraic
ISBN:

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Introduction to Plane Algebraic Curves

Introduction to Plane Algebraic Curves
Author: Ernst Kunz
Publisher: Springer Science & Business Media
Total Pages: 286
Release: 2007-06-10
Genre: Mathematics
ISBN: 0817644431

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* Employs proven conception of teaching topics in commutative algebra through a focus on their applications to algebraic geometry, a significant departure from other works on plane algebraic curves in which the topological-analytic aspects are stressed *Requires only a basic knowledge of algebra, with all necessary algebraic facts collected into several appendices * Studies algebraic curves over an algebraically closed field K and those of prime characteristic, which can be applied to coding theory and cryptography * Covers filtered algebras, the associated graded rings and Rees rings to deduce basic facts about intersection theory of plane curves, applications of which are standard tools of computer algebra * Examples, exercises, figures and suggestions for further study round out this fairly self-contained textbook

Three-Dimensional Link Theory and Invariants of Plane Curve Singularities. (AM-110), Volume 110

Three-Dimensional Link Theory and Invariants of Plane Curve Singularities. (AM-110), Volume 110
Author: David Eisenbud
Publisher: Princeton University Press
Total Pages: 180
Release: 2016-03-02
Genre: Mathematics
ISBN: 1400881927

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This book gives a new foundation for the theory of links in 3-space modeled on the modern developmentby Jaco, Shalen, Johannson, Thurston et al. of the theory of 3-manifolds. The basic construction is a method of obtaining any link by "splicing" links of the simplest kinds, namely those whose exteriors are Seifert fibered or hyperbolic. This approach to link theory is particularly attractive since most invariants of links are additive under splicing. Specially distinguished from this viewpoint is the class of links, none of whose splice components is hyperbolic. It includes all links constructed by cabling and connected sums, in particular all links of singularities of complex plane curves. One of the main contributions of this monograph is the calculation of invariants of these classes of links, such as the Alexander polynomials, monodromy, and Seifert forms.

Topological Invariants of Plane Curves and Caustics

Topological Invariants of Plane Curves and Caustics
Author: Vladimir Igorevich Arnolʹd
Publisher: American Mathematical Soc.
Total Pages: 70
Release: 1994
Genre: Mathematics
ISBN: 0821803085

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This book describes recent progress in the topological study of plane curves. The theory of plane curves is much richer than knot theory, which may be considered the commutative version of the theory of plane curves. This study is based on singularity theory: the infinite-dimensional space of curves is subdivided by the discriminant hypersurfaces into parts consisting of generic curves of the same type. The invariants distinguishing the types are defined by their jumps at the crossings of these hypersurfaces. Arnold describes applications to the geometry of caustics and of wavefronts in symplectic and contact geometry. These applications extend the classical four-vertex theorem of elementary plane geometry to estimates on the minimal number of cusps necessary for the reversion of a wavefront and to generalizations of the last geometrical theorem of Jacobi on conjugated points on convex surfaces. These estimates open a new chapter in symplectic and contact topology: the theory of Lagrangian and Legendrian collapses, providing an unusual and far-reaching higher-dimensional extension of Sturm theory of the oscillations of linear combinations of eigenfunctions.

Mechanisms for the Generation of Plane Curves

Mechanisms for the Generation of Plane Curves
Author: I. I. Artobolevskii
Publisher: Elsevier
Total Pages: 295
Release: 2013-09-03
Genre: Technology & Engineering
ISBN: 1483152421

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Mechanisms for the Generation of Plane Curves focuses on the possibility of generating plane curves through kinematic linkages. The book first offers information on the basic theory of the generation of curves by mechanisms with higher pairs of the fourth class and fundamentals of the theory of the generation of curves using mechanisms with lower pairs of class V. Discussions focus on generation of curves by centrode and trajectory pairs; generation of curves with five-link and six-link kinematic chains; basic theorem for the mechanical generation of algebraic curves; and use of the properties of individual forms of transformation mechanisms. The text then examines mechanical generation of straight lines and circles and mechanical generation of ellipses, hyperbolas, and parabolas. The publication ponders on the mechanical generation of third degree curves and mechanical generation of curves of the fourth degree. Topics include mechanisms for generating curves of the focal type; mechanisms for generating special forms of curves; and mechanisms for the generation of the conchoids of the straight line and the circle. The text is a dependable reference for readers interested in the mechanisms involved in plane curves.

The Theory of Plane Curves

The Theory of Plane Curves
Author: Surendramohan Ganguli
Publisher:
Total Pages:
Release: 1925
Genre:
ISBN:

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Plane Algebraic Curves

Plane Algebraic Curves
Author: Harold Hilton
Publisher:
Total Pages: 416
Release: 1920
Genre: Curves, Algebraic
ISBN:

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Introduction to Plane Algebraic Curves

Introduction to Plane Algebraic Curves
Author: Ernst Kunz
Publisher: Springer Science & Business Media
Total Pages: 285
Release: 2007-06-10
Genre: Mathematics
ISBN: 0817644431

Download Introduction to Plane Algebraic Curves Book in PDF, Epub and Kindle

* Employs proven conception of teaching topics in commutative algebra through a focus on their applications to algebraic geometry, a significant departure from other works on plane algebraic curves in which the topological-analytic aspects are stressed *Requires only a basic knowledge of algebra, with all necessary algebraic facts collected into several appendices * Studies algebraic curves over an algebraically closed field K and those of prime characteristic, which can be applied to coding theory and cryptography * Covers filtered algebras, the associated graded rings and Rees rings to deduce basic facts about intersection theory of plane curves, applications of which are standard tools of computer algebra * Examples, exercises, figures and suggestions for further study round out this fairly self-contained textbook

A Catalog of Special Plane Curves

A Catalog of Special Plane Curves
Author: J. Dennis Lawrence
Publisher: Courier Corporation
Total Pages: 244
Release: 2013-12-31
Genre: Mathematics
ISBN: 0486167666

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DIVOne of the most beautiful aspects of geometry. Information on general properties, derived curves, geometric and analytic properties of each curve. 89 illus. /div