The Advanced Geometry Of Plane Curves And Their Applications

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The Advanced Geometry of Plane Curves and Their Applications

Author : C. Zwikker
Publisher : Courier Corporation
ISBN 13 : 0486153436
Total Pages : 316 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis The Advanced Geometry of Plane Curves and Their Applications by : C. Zwikker

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.

The Advanced Geometry of Plane Curves and Their Applications

Author : Cornelis Zwikker
Publisher :
ISBN 13 :
Total Pages : 299 pages
Book Rating : 4.:/5 (113 download)

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Book Synopsis The Advanced Geometry of Plane Curves and Their Applications by : Cornelis Zwikker

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:

Geometry of Curves

Author : J.W. Rutter
Publisher : CRC Press
ISBN 13 : 1482285673
Total Pages : 381 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Geometry of Curves by : J.W. Rutter

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.

The Elementary Differential Geometry of Plane Curves

Author : Ralph Howard Fowler
Publisher :
ISBN 13 :
Total Pages : 124 pages
Book Rating : 4.:/5 (5 download)

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Book Synopsis The Elementary Differential Geometry of Plane Curves by : Ralph Howard Fowler

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:

Constructive Geometry of Plane Curves

Author : Thomas Henry Eagles
Publisher :
ISBN 13 :
Total Pages : 401 pages
Book Rating : 4.L/5 ( download)

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Book Synopsis Constructive Geometry of Plane Curves by : Thomas Henry Eagles

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:

A Catalog of Special Plane Curves

Author : J. Dennis Lawrence
Publisher : Courier Corporation
ISBN 13 : 0486167666
Total Pages : 218 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis A Catalog of Special Plane Curves by : J. Dennis Lawrence

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

Differential Geometry and Its Applications

Author : John Oprea
Publisher : American Mathematical Soc.
ISBN 13 : 147045050X
Total Pages : 469 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Differential Geometry and Its Applications by : John Oprea

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.

Plane Algebraic Curves

Author : Gerd Fischer
Publisher : American Mathematical Soc.
ISBN 13 : 0821821229
Total Pages : 249 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Plane Algebraic Curves by : Gerd Fischer

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.

The Many Faces of Elastica

Author : Ivaïlo M. Mladenov
Publisher : Springer
ISBN 13 : 3319612441
Total Pages : 212 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis The Many Faces of Elastica by : Ivaïlo M. Mladenov

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.

Geometric Methods in Physics XXXIX

Author : Piotr Kielanowski
Publisher : Springer Nature
ISBN 13 : 3031302842
Total Pages : 345 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Geometric Methods in Physics XXXIX by : Piotr Kielanowski

Download or read book Geometric Methods in Physics XXXIX written by Piotr Kielanowski and published by Springer Nature. This book was released on 2023-07-21 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects papers based on lectures given at the XXXIX Workshop on Geometric Methods in Physics, held in Białystok, Poland in June 2022. These chapters provide readers an overview of cutting-edge research in geometry, analysis, and a wide variety of other areas. Specific topics include: Classical and quantum field theories Infinite-dimensional groups Integrable systems Lie groupoids and Lie algebroids Representation theory Geometric Methods in Physics XXXIX will be a valuable resource for mathematicians and physicists interested in recent developments at the intersection of these areas.

On the Conformal Representation of Plane Curves Particularly for the Cases P

Author : Charlotte Elvira Pengra
Publisher : Legare Street Press
ISBN 13 : 9781019979853
Total Pages : 0 pages
Book Rating : 4.9/5 (798 download)

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Book Synopsis On the Conformal Representation of Plane Curves Particularly for the Cases P by : Charlotte Elvira Pengra

Download or read book On the Conformal Representation of Plane Curves Particularly for the Cases P written by Charlotte Elvira Pengra and published by Legare Street Press. This book was released on 2023-07-18 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This mathematical treatise explores the properties of conformal representation of plane curves and provides a detailed analysis of various cases. The author discusses the applications of conformal representation in the theory of functions and the geometry of surfaces. The book is aimed at advanced students and researchers in mathematics. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Modern Differential Geometry of Curves and Surfaces with Mathematica

Author : Elsa Abbena
Publisher : CRC Press
ISBN 13 : 1351992201
Total Pages : 872 pages
Book Rating : 4.3/5 (519 download)

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Book Synopsis Modern Differential Geometry of Curves and Surfaces with Mathematica by : Elsa Abbena

Download or read book Modern Differential Geometry of Curves and Surfaces with Mathematica written by Elsa Abbena and published by CRC Press. This book was released on 2017-09-06 with total page 872 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting theory while using Mathematica in a complementary way, Modern Differential Geometry of Curves and Surfaces with Mathematica, the third edition of Alfred Gray’s famous textbook, covers how to define and compute standard geometric functions using Mathematica for constructing new curves and surfaces from existing ones. Since Gray’s death, authors Abbena and Salamon have stepped in to bring the book up to date. While maintaining Gray's intuitive approach, they reorganized the material to provide a clearer division between the text and the Mathematica code and added a Mathematica notebook as an appendix to each chapter. They also address important new topics, such as quaternions. The approach of this book is at times more computational than is usual for a book on the subject. For example, Brioshi’s formula for the Gaussian curvature in terms of the first fundamental form can be too complicated for use in hand calculations, but Mathematica handles it easily, either through computations or through graphing curvature. Another part of Mathematica that can be used effectively in differential geometry is its special function library, where nonstandard spaces of constant curvature can be defined in terms of elliptic functions and then plotted. Using the techniques described in this book, readers will understand concepts geometrically, plotting curves and surfaces on a monitor and then printing them. Containing more than 300 illustrations, the book demonstrates how to use Mathematica to plot many interesting curves and surfaces. Including as many topics of the classical differential geometry and surfaces as possible, it highlights important theorems with many examples. It includes 300 miniprograms for computing and plotting various geometric objects, alleviating the drudgery of computing things such as the curvature and torsion of a curve in space.

Differential Geometry of Curves and Surfaces

Author : Kristopher Tapp
Publisher : Springer
ISBN 13 : 3319397990
Total Pages : 366 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Differential Geometry of Curves and Surfaces by : Kristopher Tapp

Download or read book Differential Geometry of Curves and Surfaces written by Kristopher Tapp and published by Springer. This book was released on 2016-09-30 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook on differential geometry well-suited to a variety of courses on this topic. For readers seeking an elementary text, the prerequisites are minimal and include plenty of examples and intermediate steps within proofs, while providing an invitation to more excursive applications and advanced topics. For readers bound for graduate school in math or physics, this is a clear, concise, rigorous development of the topic including the deep global theorems. For the benefit of all readers, the author employs various techniques to render the difficult abstract ideas herein more understandable and engaging. Over 300 color illustrations bring the mathematics to life, instantly clarifying concepts in ways that grayscale could not. Green-boxed definitions and purple-boxed theorems help to visually organize the mathematical content. Color is even used within the text to highlight logical relationships. Applications abound! The study of conformal and equiareal functions is grounded in its application to cartography. Evolutes, involutes and cycloids are introduced through Christiaan Huygens' fascinating story: in attempting to solve the famous longitude problem with a mathematically-improved pendulum clock, he invented mathematics that would later be applied to optics and gears. Clairaut’s Theorem is presented as a conservation law for angular momentum. Green’s Theorem makes possible a drafting tool called a planimeter. Foucault’s Pendulum helps one visualize a parallel vector field along a latitude of the earth. Even better, a south-pointing chariot helps one visualize a parallel vector field along any curve in any surface. In truth, the most profound application of differential geometry is to modern physics, which is beyond the scope of this book. The GPS in any car wouldn’t work without general relativity, formalized through the language of differential geometry. Throughout this book, applications, metaphors and visualizations are tools that motivate and clarify the rigorous mathematical content, but never replace it.

Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable

Author : Rida T Farouki
Publisher : Springer Science & Business Media
ISBN 13 : 3540733973
Total Pages : 725 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable by : Rida T Farouki

Download or read book Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable written by Rida T Farouki and published by Springer Science & Business Media. This book was released on 2007-10-11 with total page 725 pages. Available in PDF, EPUB and Kindle. Book excerpt: By virtue of their special algebraic structures, Pythagorean-hodograph (PH) curves offer unique advantages for computer-aided design and manufacturing, robotics, motion control, path planning, computer graphics, animation, and related fields. This book offers a comprehensive and self-contained treatment of the mathematical theory of PH curves, including algorithms for their construction and examples of their practical applications. It emphasizes the interplay of ideas from algebra and geometry and their historical origins and includes many figures, worked examples, and detailed algorithm descriptions.

A Catalog of Special Plane Curves

Author : J. Dennis Lawrence
Publisher : Courier Corporation
ISBN 13 : 0486602885
Total Pages : 244 pages
Book Rating : 4.4/5 (866 download)

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Book Synopsis A Catalog of Special Plane Curves by : J. Dennis Lawrence

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 1972-01-01 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the largest and finest available collections, this catalog covers general properties of curves and types of derived curves. Illustrated by nearly 90 images from a CalComp digital incremental plotter. 1972 edition.

Constructive Geometry of Plane Curves. with Numerous Examples, by T. H. Eagles.

Author : Thomas Henry Eagles
Publisher : Scholarly Pub Office Univ of
ISBN 13 : 9781418167813
Total Pages : 400 pages
Book Rating : 4.1/5 (678 download)

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Book Synopsis Constructive Geometry of Plane Curves. with Numerous Examples, by T. H. Eagles. by : Thomas Henry Eagles

Download or read book Constructive Geometry of Plane Curves. with Numerous Examples, by T. H. Eagles. written by Thomas Henry Eagles and published by Scholarly Pub Office Univ of. This book was released on 2004-01 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Geometry I

Author : Marcel Berger
Publisher : Springer Science & Business Media
ISBN 13 : 354093815X
Total Pages : 446 pages
Book Rating : 4.5/5 (49 download)

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Book Synopsis Geometry I by : Marcel Berger

Download or read book Geometry I written by Marcel Berger and published by Springer Science & Business Media. This book was released on 2009-01-17 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume I of this 2-volume textbook provides a lively and readable presentation of large parts of classical geometry. For each topic the author presents an esthetically pleasing and easily stated theorem - although the proof may be difficult and concealed. The mathematical text is illustrated with figures, open problems and references to modern literature, providing a unified reference to geometry in the full breadth of its subfields and ramifications.