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Author: Edward Harrington Lockwood
Publisher: Cambridge University Press
ISBN: 9781001224114
Category : Curves
Languages : en
Pages : 290
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Book Description
Describes the drawing of plane curves, cycloidal curves, spirals, glissettes and others.
Author: Edward Harrington Lockwood
Publisher: Cambridge University Press
ISBN: 9781001224114
Category : Curves
Languages : en
Pages : 290
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Book Description
Describes the drawing of plane curves, cycloidal curves, spirals, glissettes and others.
Author: Deane Arganbright
Publisher: CRC Press
ISBN: 9780849389382
Category : Mathematics
Languages : en
Pages : 218
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Book Description
Practical Handbook of Spreadsheet Curves and Geometric Constructions presents a compelling description of how to use commercially available spreadsheets to design and create high-quality graphs of a variety of curves, including classical curves in mathematics. The book contains more than 65 models for the geometric construction of families of curves such as strophoids, pedals, involutes, and others. Models in the book are designed to be interactive so that users can experiment with them to produce eye-catching curves, designs, and patterns. Examples come from calculus, parametric equations, constructions of classical families, and graphs of conformal mappings of a complex variable. The author, a leading authority on spreadsheets, presents innovative techniques for using spreadsheet graphing to generate large families of lines and circles that describe various curves as envelopes of the families. The final chapter of the book discusses the use of commercial spreadsheets to create animation effects. The book is heavily illustrated, with more than 200 graphs and 60 tables. An accompanying 3.5" disk provides 25 selected examples written in Quattro Pro 2.0, Lotus 1-2-3 2.3, and Microsoft Excel 4.0. Designed for both experienced and novice spreadsheet users, Practical Handbook of Spreadsheet Curves and Geometric Constructions will be an invaluable resource for mathematicians, engineers, scientists, and computer scientists. The book will also benefit professional artists and designers interested in learning new techniques for producing mathematical curves using spreadsheet software.
Author: Julian Havil
Publisher: Princeton University Press
ISBN: 0691206139
Category : Art
Languages : en
Pages : 280
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Book Description
Ten amazing curves personally selected by one of today's most important math writers Curves for the Mathematically Curious is a thoughtfully curated collection of ten mathematical curves, selected by Julian Havil for their significance, mathematical interest, and beauty. Each chapter gives an account of the history and definition of one curve, providing a glimpse into the elegant and often surprising mathematics involved in its creation and evolution. In telling the ten stories, Havil introduces many mathematicians and other innovators, some whose fame has withstood the passing of years and others who have slipped into comparative obscurity. You will meet Pierre Bézier, who is known for his ubiquitous and eponymous curves, and Adolphe Quetelet, who trumpeted the ubiquity of the normal curve but whose name now hides behind the modern body mass index. These and other ingenious thinkers engaged with the challenges, incongruities, and insights to be found in these remarkable curves—and now you can share in this adventure. Curves for the Mathematically Curious is a rigorous and enriching mathematical experience for anyone interested in curves, and the book is designed so that readers who choose can follow the details with pencil and paper. Every curve has a story worth telling.
Author: Eugene V. Shikin
Publisher: CRC Press
ISBN: 1498710670
Category : Mathematics
Languages : en
Pages : 560
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Book Description
The Handbook and Atlas of Curves describes available analytic and visual properties of plane and spatial curves. Information is presented in a unique format, with one half of the book detailing investigation tools and the other devoted to the Atlas of Plane Curves. Main definitions, formulas, and facts from curve theory (plane and spatial) are discussed.
Author: Vladimir Rovenski
Publisher: Springer Science & Business Media
ISBN: 1461221285
Category : Mathematics
Languages : en
Pages : 310
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Book Description
This concise text on geometry with computer modeling presents some elementary methods for analytical modeling and visualization of curves and surfaces. The author systematically examines such powerful tools as 2-D and 3-D animation of geometric images, transformations, shadows, and colors, and then further studies more complex problems in differential geometry. Well-illustrated with more than 350 figures---reproducible using Maple programs in the book---the work is devoted to three main areas: curves, surfaces, and polyhedra. Pedagogical benefits can be found in the large number of Maple programs, some of which are analogous to C++ programs, including those for splines and fractals. To avoid tedious typing, readers will be able to download many of the programs from the Birkhauser web site. Aimed at a broad audience of students, instructors of mathematics, computer scientists, and engineers who have knowledge of analytical geometry, i.e., method of coordinates, this text will be an excellent classroom resource or self-study reference. With over 100 stimulating exercises, problems and solutions, {\it Geometry of Curves and Surfaces with Maple} will integrate traditional differential and non- Euclidean geometries with more current computer algebra systems in a practical and user-friendly format.
Author: J. Dennis Lawrence
Publisher: Courier Corporation
ISBN: 0486167666
Category : Mathematics
Languages : en
Pages : 244
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Book Description
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: J.W. Rutter
Publisher: CRC Press
ISBN: 1482285673
Category : Mathematics
Languages : en
Pages : 381
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Book Description
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: Elsa Abbena
Publisher: CRC Press
ISBN: 1351992201
Category : Mathematics
Languages : en
Pages : 1024
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Book Description
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: Steven Tan
Publisher: Steven Tan
ISBN:
Category : Mathematics
Languages : en
Pages : 1471
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Book Description
Inspired by the Famous Curves Index of the award-winning website by MacTutor History of Mathematics archive maintained by John J. O'Connor and Edmund F. Robertson and hosted by the University of St Andrews, the author wrote this handbook of famous plane curves using Mathematica® as a tool to graph, animate, calculate and to construct derived curves from given ones. Some constructions are extremely difficult to draw by hands, especially those involve numerical integration can be performed with ease with Mathematica®. Even for some simple curves before the invention of computer, drawing them by hands might take a long time. To borrow the words of Rudy Rucker (author of The Fourth Dimension): "if the only thing you're going to be remembered for in 300 years is one single curve, then you don't mind spending a year or two in getting it right!" Plane curves had been studied since antiquity. However, the general theory of plane curves began to be developed only after the invention of Cartesian coordinates by Descartes in the early 1600s. The discovery of calculus in the 17th century led to the study of more complicated plane curves. The methods of calculus, in particular integration, provides solution of finding the arc length and area of a plane curve. Plane curves are of historical interest. It could be said that significant part of classical mathematics deal with them. Most books on history of mathematics include information on various plane curves. Plane curves remain a source of inspiration and a topic of research to this day. Whenever it is applicable the author mentions some research papers in which the curves are used for applications in modern science and technology.
Author: S.S. Abhyankar
Publisher: Springer
ISBN: 3540372806
Category : Mathematics
Languages : en
Pages : 317
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Book Description
