The Advanced Geometry Of Plane Curves And Their Applications

Author : C. Zwikker
Publisher : Courier Corporation
Page : 316 pages
File Size : 54,5 Mb
Release : 2011-11-30
Category : Mathematics
ISBN : 9780486153438

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The Advanced Geometry of Plane Curves and Their Applications by C. Zwikker Pdf

"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 : Unknown
Page : 299 pages
File Size : 42,5 Mb
Release : 1977
Category : Curves. [from old catalog]
ISBN : OCLC:1139480912

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The Advanced Geometry of Plane Curves and Their Applications by Cornelis Zwikker Pdf

Author : J.W. Rutter
Publisher : CRC Press
Page : 381 pages
File Size : 45,9 Mb
Release : 2018-10-03
Category : Mathematics
ISBN : 9781482285673

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Geometry of Curves by J.W. Rutter Pdf

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 : J. Dennis Lawrence
Publisher : Courier Corporation
Page : 218 pages
File Size : 51,7 Mb
Release : 2013-12-31
Category : Mathematics
ISBN : 9780486167664

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A Catalog of Special Plane Curves by J. Dennis Lawrence Pdf

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 : John Oprea
Publisher : American Mathematical Soc.
Page : 469 pages
File Size : 46,8 Mb
Release : 2019-02-06
Category : Electronic
ISBN : 9781470450502

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Differential Geometry and Its Applications by John Oprea Pdf

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 : Gerd Fischer
Publisher : American Mathematical Soc.
Page : 249 pages
File Size : 45,9 Mb
Release : 2001
Category : Curves, Algebraic
ISBN : 9780821821220

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Plane Algebraic Curves by Gerd Fischer Pdf

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 : Thomas Henry Eagles
Publisher : Unknown
Page : 401 pages
File Size : 49,5 Mb
Release : 1885
Category : Conic sections
ISBN : UOMDLP:abn2472:0001.001

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Constructive Geometry of Plane Curves by Thomas Henry Eagles Pdf

Author : Piotr Kielanowski,Alina Dobrogowska,Gerald A. Goldin,Tomasz Goliński
Publisher : Springer Nature
Page : 345 pages
File Size : 45,8 Mb
Release : 2023-07-21
Category : Science
ISBN : 9783031302848

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Geometric Methods in Physics XXXIX by Piotr Kielanowski,Alina Dobrogowska,Gerald A. Goldin,Tomasz Goliński Pdf

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.

Author : Elsa Abbena,Simon Salamon,Alfred Gray
Publisher : CRC Press
Page : 872 pages
File Size : 42,9 Mb
Release : 2017-09-06
Category : Mathematics
ISBN : 9781351992206

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Modern Differential Geometry of Curves and Surfaces with Mathematica by Elsa Abbena,Simon Salamon,Alfred Gray Pdf

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.

Author : Ivaïlo M. Mladenov,Mariana Hadzhilazova
Publisher : Springer
Page : 212 pages
File Size : 50,9 Mb
Release : 2017-08-18
Category : Mathematics
ISBN : 9783319612447

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The Many Faces of Elastica by Ivaïlo M. Mladenov,Mariana Hadzhilazova Pdf

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.

Author : Kristopher Tapp
Publisher : Springer
Page : 366 pages
File Size : 52,9 Mb
Release : 2016-09-30
Category : Mathematics
ISBN : 9783319397993

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Differential Geometry of Curves and Surfaces by Kristopher Tapp Pdf

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.

Author : Ralph Howard Fowler
Publisher : Unknown
Page : 128 pages
File Size : 49,5 Mb
Release : 1964
Category : Curves, Plane
ISBN : PSU:000027157701

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The Elementary Differential Geometry of Plane Curves by Ralph Howard Fowler Pdf

Author : Rida T Farouki
Publisher : Springer Science & Business Media
Page : 725 pages
File Size : 54,7 Mb
Release : 2007-10-11
Category : Mathematics
ISBN : 9783540733973

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

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.

Author : Charlotte Elvira Pengra
Publisher : Legare Street Press
Page : 0 pages
File Size : 51,5 Mb
Release : 2023-07-18
Category : Electronic
ISBN : 1019979852

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On the Conformal Representation of Plane Curves Particularly for the Cases P by Charlotte Elvira Pengra Pdf

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.

Author : Marcel Berger
Publisher : Springer Science & Business Media
Page : 446 pages
File Size : 52,9 Mb
Release : 2009-01-17
Category : Mathematics
ISBN : 9783540938156

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Geometry I by Marcel Berger Pdf

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.