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Author : J. Dennis Lawrence
Publisher : Courier Corporation
Page : 218 pages
File Size : 55,9 Mb
Release : 2013-12-31
Category : Mathematics
ISBN : 9780486167664
DIVOne of the most beautiful aspects of geometry. Information on general properties, derived curves, geometric and analytic properties of each curve. 89 illus. /div
Author : Eduardo Casas-Alvero
Publisher : Cambridge University Press
Page : 363 pages
File Size : 50,5 Mb
Release : 2000-08-31
Category : Mathematics
ISBN : 9780521789592
Comprehensive and self-contained exposition of singularities of plane curves, including new, previously unpublished results.
Author : Hilário Alencar,Walcy Santos,Gregório Silva Neto
Publisher : American Mathematical Society
Page : 416 pages
File Size : 50,5 Mb
Release : 2022-04-27
Category : Mathematics
ISBN : 9781470469597
This book features plane curves—the simplest objects in differential geometry—to illustrate many deep and inspiring results in the field in an elementary and accessible way. After an introduction to the basic properties of plane curves, the authors introduce a number of complex and beautiful topics, including the rotation number (with a proof of the fundamental theorem of algebra), rotation index, Jordan curve theorem, isoperimetric inequality, convex curves, curves of constant width, and the four-vertex theorem. The last chapter connects the classical with the modern by giving an introduction to the curve-shortening flow that is based on original articles but requires a minimum of previous knowledge. Over 200 figures and more than 100 exercises illustrate the beauty of plane curves and test the reader's skills. Prerequisites are courses in standard one variable calculus and analytic geometry on the plane.
Author : Edward Harrington Lockwood
Publisher : Cambridge University Press
Page : 290 pages
File Size : 46,5 Mb
Release : 1967
Category : Curves
ISBN : 1001224116
Describes the drawing of plane curves, cycloidal curves, spirals, glissettes and others.
Author : C. Zwikker
Publisher : Courier Corporation
Page : 316 pages
File Size : 51,6 Mb
Release : 2011-11-30
Category : Mathematics
ISBN : 9780486153438
"Of chief interest to mathematicians, but physicists and others will be fascinated ... and intrigued by the fruitful use of non-Cartesian methods. Students ... should find the book stimulating." — British Journal of Applied Physics This study of many important curves, their geometrical properties, and their applications features material not customarily treated in texts on synthetic or analytic Euclidean geometry. Its wide coverage, which includes both algebraic and transcendental curves, extends to unusual properties of familiar curves along with the nature of lesser known curves. Informative discussions of the line, circle, parabola, ellipse, and hyperbola presuppose only the most elementary facts. The less common curves — cissoid, strophoid, spirals, the leminscate, cycloid, epicycloid, cardioid, and many others — receive introductions that explain both their basic and advanced properties. Derived curves-the involute, evolute, pedal curve, envelope, and orthogonal trajectories-are also examined, with definitions of their important applications. These range through the fields of optics, electric circuit design, hydraulics, hydrodynamics, classical mechanics, electromagnetism, crystallography, gear design, road engineering, orbits of subatomic particles, and similar areas in physics and engineering. The author represents the points of the curves by complex numbers, rather than the real Cartesian coordinates, an approach that permits simple, direct, and elegant proofs.
Author : I. I. Artobolevskii
Publisher : Elsevier
Page : 294 pages
File Size : 55,6 Mb
Release : 2013-09-03
Category : Technology & Engineering
ISBN : 9781483152424
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.
Author : C. T. C. Wall
Publisher : Cambridge University Press
Page : 386 pages
File Size : 53,8 Mb
Release : 2004-11-15
Category : Mathematics
ISBN : 0521547741
Publisher Description
Author : Thomas Henry Eagles
Publisher : Unknown
Page : 404 pages
File Size : 50,5 Mb
Release : 1885
Category : Conic sections
ISBN : HARVARD:HN1KRF
Author : Julian Lowell Coolidge
Publisher : Courier Corporation
Page : 554 pages
File Size : 52,5 Mb
Release : 2004-01-01
Category : Mathematics
ISBN : 0486495760
A thorough introduction to the theory of algebraic plane curves and their relations to various fields of geometry and analysis. Almost entirely confined to the properties of the general curve, and chiefly employs algebraic procedure. Geometric methods are much employed, however, especially those involving the projective geometry of hyperspace. 1931 edition. 17 illustrations.
Author : R. H. Fowler
Publisher : Forgotten Books
Page : 128 pages
File Size : 46,9 Mb
Release : 2015-06-12
Category : Mathematics
ISBN : 1330044401
Excerpt from The Elementary Differential Geometry of Plane Curves This tract is intended to present a precise account of the elementary differential properties of plane curves. The matter contained is in no sense new, but a suitable connected treatment in the English language has not been available. As a result, a number of interesting misconceptions are current in English text books. It is sufficient to mention two somewhat striking examples, (a) According to the ordinary definition of an envelope, as the locus of the limits of points of intersection of neighbouring curves, a curve is not the envelope of its circles of curvature, for neighbouring circles of curvature do not intersect. (b) The definitions of an asymptote - (1) a straight line, the distance from which of a point on the curve tends to zero as the point tends to infinity; (2) the limit of a tangent to the curve, whose point of contact tends to infinity - are not equivalent. The curve may have an asymptote according to the former definition, and the tangent may exist at every point, but have no limit as its point of contact tends to infinity. The subjects dealt with, and the general method of treatment, are similar to those of the usual chapters on geometry in any Cours d' Analyse, except that in general plane curves alone are considered. At the same time extensions to three dimensions are made in a somewhat arbitrary selection of places, where the extension is immediate, and forms a natural commentary on the two dimensional work, or presents special points of interest (Frenet's formulae). To make such extensions systematically would make the tract too long. The subject matter being wholly classical, no attempt has been made to give full references to sources of information; the reader however is referred at most stages to the analogous treatment of the subject in the Cours or Traite d' Analyse of de la Vallée Poussin, Goursat, Jordan or Picard, works to which the author is much indebted. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Author : Gerd Fischer
Publisher : American Mathematical Soc.
Page : 249 pages
File Size : 45,7 Mb
Release : 2001
Category : Curves, Algebraic
ISBN : 9780821821220
This is an excellent introduction to algebraic geometry, which assumes only standard undergraduate mathematical topics: complex analysis, rings and fields, and topology. Reading this book will help establish the geometric intuition that lies behind the more advanced ideas and techniques used in the study of higher-dimensional varieties.
Author : R. H. Fowler
Publisher : Unknown
Page : 120 pages
File Size : 54,8 Mb
Release : 2005
Category : Curves, Plane
ISBN : CORNELL:31924102063157
This precise account of elementary differential properties of plane curves provides a link between analysis and more complicated geometrical theorems, offering background and practice to geometry and analysis students. 1920 edition.
Author : C. Orzech
Publisher : CRC Press
Page : 244 pages
File Size : 52,7 Mb
Release : 1981-01-01
Category : Mathematics
ISBN : 0824711599
Plane Algebraic Curves is a classroom-tested textbook for advanced undergraduate and beginning graduate students in mathematics. The book introduces the contemporary notions of algebraic varieties, morphisms of varieties, and adeles to the classical subject of plane curves over algebraically closed fields. By restricting the rigorous development of these notions to a traditional context the book makes its subject accessible without extensive algebraic prerequisites. Once the reader's intuition for plane curves has evolved, there is a discussion of how these objects can be generalized to higher dimensional settings. These features, as well as a proof of the Riemann-Roch Theorem based on a combination of geometric and algebraic considerations, make the book a good foundation for more specialized study in algebraic geometry, commutative algebra, and algebraic function fields. Plane Algebraic Curves is suitable for readers with a variety of backgrounds and interests. The book begins with a chapter outlining prerequisites, and contains informal discussions giving an overview of its material and relating it to non-algebraic topics which would be familiar to the general reader. There is an explanation of why the algebraic genus of a hyperelliptic curve agrees with its geometric genus as a compact Riemann surface, as well as a thorough description of how the classically important elliptic curves can be described in various normal forms. The book concludes with a bibliography which students can incorporate into their further studies. Book jacket.
Author : Egbert Brieskorn,Horst Knörrer
Publisher : Springer Science & Business Media
Page : 721 pages
File Size : 54,7 Mb
Release : 2012-08-27
Category : Mathematics
ISBN : 9783034804936
In a detailed and comprehensive introduction to the theory of plane algebraic curves, the authors examine this classical area of mathematics that both figured prominently in ancient Greek studies and remains a source of inspiration and a topic of research to this day. Arising from notes for a course given at the University of Bonn in Germany, “Plane Algebraic Curves” reflects the authorsʼ concern for the student audience through its emphasis on motivation, development of imagination, and understanding of basic ideas. As classical objects, curves may be viewed from many angles. This text also provides a foundation for the comprehension and exploration of modern work on singularities. --- In the first chapter one finds many special curves with very attractive geometric presentations ‒ the wealth of illustrations is a distinctive characteristic of this book ‒ and an introduction to projective geometry (over the complex numbers). In the second chapter one finds a very simple proof of Bezout’s theorem and a detailed discussion of cubics. The heart of this book ‒ and how else could it be with the first author ‒ is the chapter on the resolution of singularities (always over the complex numbers). (...) Especially remarkable is the outlook to further work on the topics discussed, with numerous references to the literature. Many examples round off this successful representation of a classical and yet still very much alive subject. (Mathematical Reviews)
Author : George Salmon
Publisher : Unknown
Page : 340 pages
File Size : 42,8 Mb
Release : 1852
Category : Curves, Plane
ISBN : BL:A0018199729