The Advanced Geometry Of Plane Curves And Their Applications

Author : C. Zwikker
Publisher : Courier Corporation
ISBN 13 : 0486153436
Total Pages : 316 pages
Book Rating : 4.38/5 ( download)

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Download or read book The Advanced Geometry of Plane Curves and Their Applications written by C. Zwikker and published by Courier Corporation. This book was released on 2011-11-30 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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 : Cornelis Zwikker
Publisher :
ISBN 13 :
Total Pages : 299 pages
Book Rating : 4.12/5 ( download)

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Download or read book The Advanced Geometry of Plane Curves and Their Applications written by Cornelis Zwikker and published by . This book was released on 1977 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : J.W. Rutter
Publisher : CRC Press
ISBN 13 : 1482285673
Total Pages : 381 pages
Book Rating : 4.73/5 ( download)

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Download or read book Geometry of Curves written by J.W. Rutter and published by CRC Press. This book was released on 2018-10-03 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interest in the study of geometry is currently enjoying a resurgence-understandably so, as the study of curves was once the playground of some very great mathematicians. However, many of the subject's more exciting aspects require a somewhat advanced mathematics background. For the "fun stuff" to be accessible, we need to offer students an introduction with modest prerequisites, one that stimulates their interest and focuses on problem solving. Integrating parametric, algebraic, and projective curves into a single text, Geometry of Curves offers students 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 students on a fascinating journey from conics, higher algebraic and transcendental curves, through the properties of parametric curves, the classification of limaçons, envelopes, and finally to projective curves, their relationship to algebraic curves, and their application to asymptotes and boundedness. The uniqueness of this treatment 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 text, almost entirely self-contained, that not only imparts a deeper understanding of the theory, but inspires a heightened appreciation of geometry and interest in more advanced studies.

Author : Ralph Howard Fowler
Publisher :
ISBN 13 :
Total Pages : 124 pages
Book Rating : 4.88/5 ( download)

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Download or read book The Elementary Differential Geometry of Plane Curves written by Ralph Howard Fowler and published by . This book was released on 1920 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Thomas Henry Eagles
Publisher :
ISBN 13 :
Total Pages : 401 pages
Book Rating : 4.01/5 ( download)

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Download or read book Constructive Geometry of Plane Curves written by Thomas Henry Eagles and published by . This book was released on 1885 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : J. Dennis Lawrence
Publisher : Courier Corporation
ISBN 13 : 0486167666
Total Pages : 218 pages
Book Rating : 4.64/5 ( download)

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Download or read book A Catalog of Special Plane Curves written by J. Dennis Lawrence and published by Courier Corporation. This book was released on 2013-12-31 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Gerd Fischer
Publisher : American Mathematical Soc.
ISBN 13 : 0821821229
Total Pages : 249 pages
Book Rating : 4.20/5 ( download)

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Download or read book Plane Algebraic Curves written by Gerd Fischer and published by American Mathematical Soc.. This book was released on 2001 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Ernst Kunz
Publisher : Springer Science & Business Media
ISBN 13 : 0817644431
Total Pages : 286 pages
Book Rating : 4.37/5 ( download)

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Download or read book Introduction to Plane Algebraic Curves written by Ernst Kunz and published by Springer Science & Business Media. This book was released on 2007-06-10 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: * 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

Author : John Oprea
Publisher : American Mathematical Soc.
ISBN 13 : 147045050X
Total Pages : 469 pages
Book Rating : 4.02/5 ( download)

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Download or read book Differential Geometry and Its Applications written by John Oprea and published by American Mathematical Soc.. This book was released on 2019-02-06 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Geometry and Its Applications studies the differential geometry of surfaces with the goal of helping students make the transition from the compartmentalized courses in a standard university curriculum to a type of mathematics that is a unified whole. It mixes geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and notions from the sciences. That mix of ideas offers students the opportunity to visualize concepts through the use of computer algebra systems such as Maple. Differential Geometry and Its Applications emphasizes that this visualization goes hand in hand with understanding the mathematics behind the computer construction. The book is rich in results and exercises that form a continuous spectrum, from those that depend on calculation to proofs that are quite abstract.

Author : Ivaïlo M. Mladenov
Publisher : Springer
ISBN 13 : 3319612441
Total Pages : 212 pages
Book Rating : 4.47/5 ( download)

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Download or read book The Many Faces of Elastica written by Ivaïlo M. Mladenov and published by Springer. This book was released on 2017-08-18 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the mathematical aspects of Euler's elastic theory and its application. The approach is rigorous, as well as visually depicted, and can be easily digested. The first few chapters introduce the needed mathematical concepts from geometry and variational calculus. The formal definitions and proofs are always illustrated through complete derivations and concrete examples. In this way, the reader becomes acquainted with Cassinian ovals, Sturmian spirals, co-Lemniscates, the nodary and the undulary, Delaunay surfaces, and their generalizations. The remaining chapters discuss the modeling of membranes, mylar balloons, rotating liquid drops, Hele-Shaw cells, nerve fibers, Cole's experiments, and membrane fusion. The book is geared towards applied mathematicians, physicists and engineers interested in Elastica Theory and its applications.