The Advanced Geometry of Plane Curves and Their Applications Book

The Advanced Geometry of Plane Curves and Their Applications


  • Author : C. Zwikker
  • Publisher : Courier Corporation
  • Release Date : 2011-11-30
  • Genre: Mathematics
  • Pages : 320
  • ISBN 10 : 9780486153438
  • Total Read : 93
  • File Size : 11,5 Mb

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The Advanced Geometry of Plane Curves and Their Applications Summary:

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. 1950 edition.

A Catalog of Special Plane Curves Book

A Catalog of Special Plane Curves


  • Author : J. Dennis Lawrence
  • Publisher : Courier Corporation
  • Release Date : 2013-12-31
  • Genre: Mathematics
  • Pages : 218
  • ISBN 10 : 9780486167664
  • Total Read : 79
  • File Size : 15,8 Mb

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A Catalog of Special Plane Curves Summary:

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 Book

Differential Geometry and Its Applications


  • Author : John Oprea
  • Publisher : American Mathematical Soc.
  • Release Date : 2019-02-06
  • Genre: Uncategoriezed
  • Pages : 469
  • ISBN 10 : 9781470450502
  • Total Read : 76
  • File Size : 18,8 Mb

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Differential Geometry and Its Applications Summary:

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.

The Mathematics of Surfaces IX Book

The Mathematics of Surfaces IX


  • Author : Roberto Cipolla
  • Publisher : Springer Science & Business Media
  • Release Date : 2012-12-06
  • Genre: Technology & Engineering
  • Pages : 500
  • ISBN 10 : 9781447104957
  • Total Read : 62
  • File Size : 12,9 Mb

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The Mathematics of Surfaces IX Summary:

These proceedings collect the papers accepted for presentation at the bien nial IMA Conference on the Mathematics of Surfaces, held in the University of Cambridge, 4-7 September 2000. While there are many international con ferences in this fruitful borderland of mathematics, computer graphics and engineering, this is the oldest, the most frequent and the only one to concen trate on surfaces. Contributors to this volume come from twelve different countries in Eu rope, North America and Asia. Their contributions reflect the wide diversity of present-day applications which include modelling parts of the human body for medical purposes as well as the production of cars, aircraft and engineer ing components. Some applications involve design or construction of surfaces by interpolating or approximating data given at points or on curves. Others consider the problem of 'reverse engineering'-giving a mathematical descrip tion of an already constructed object. We are particularly grateful to Pamela Bye (at the Institue of Mathemat ics and its Applications) for help in making arrangements; Stephanie Harding and Karen Barker (at Springer Verlag, London) for publishing this volume and to Kwan-Yee Kenneth Wong (Cambridge) for his heroic help with com piling the proceedings and for dealing with numerous technicalities arising from large and numerous computer files. Following this Preface is a listing of the programme committee who with the help of their colleagues did much work in refereeing the papers for these proceedings.

Modern Differential Geometry of Curves and Surfaces with Mathematica Book

Modern Differential Geometry of Curves and Surfaces with Mathematica


  • Author : Elsa Abbena
  • Publisher : CRC Press
  • Release Date : 2017-09-06
  • Genre: Mathematics
  • Pages : 1016
  • ISBN 10 : 9781351992206
  • Total Read : 66
  • File Size : 13,9 Mb

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Modern Differential Geometry of Curves and Surfaces with Mathematica Summary:

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.

The Many Faces of Elastica Book

The Many Faces of Elastica


  • Author : Ivaïlo M. Mladenov
  • Publisher : Springer
  • Release Date : 2017-08-18
  • Genre: Mathematics
  • Pages : 212
  • ISBN 10 : 9783319612447
  • Total Read : 96
  • File Size : 14,7 Mb

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The Many Faces of Elastica Summary:

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.