# Modern Differential Geometry of Curves and Surfaces with Mathematica, Third Edition

CRC Press, 21/06/2006 - 1016 páginas
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.

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### Conteúdo

 Curves in the Plane 1 Notebook 1 29 Famous Plane Curves 39 Alternative Ways of Plotting Curves 73 New Curves from Old 99 Determining a Plane Curve from Its Curvature 127 Global Properties of Plane Curves 153 Curves in Space 191
 Intrinsic Surface Geometry 531 Notebook 17 548 Asymptotic Curves and Geodesies on Surfaces 557 Notebook 18 582 Principal Curves and Umbilic Points 593 Canal Surfaces and Cyclides of Dupin 639 The Theory of Surfaces of Constant Negative Curvature 683 Minimal Surfaces via Complex Variables 719

 Construction of Space Curves 229 Calculus on Euclidean Space 263 Surfaces in Euclidean Space 287 Nonorientable Surfaces 331 Metrics on Surfaces 361 Shape and Curvature 385 Ruled Surfaces 431 Surfaces of Revolution and Constant Curvature 461 A Selection of Minimal Surfaces 501
 Rotation and Animation Using Quaternions 767 Differentiate Manifolds 809 Riemannian Manifolds 847 Abstract Surfaces and Their Geodesies 871 The GaussBonnet Theorem 901 Bibliography 931 Name Index 953 Notebook Index 977 Direitos autorais

### Referências de páginas web

JSTOR: Modern Differential Geometry of Curves and Surfaces with ...
Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd edi- tion. By Alfred Gray. CRC Press, Boca Raton, FL, 1998. \$84.95. xxiv+1053 pp., ...

Modern Differential Geometry of Curves and Surfaces with ...
Modern Differential Geometry of Curves and Surfaces with Mathematica, Third Edition. Alfred Gray, Elsa Abbena, and Simon Salamon, 2006, Chapman & Hall/CRC, ...
www.mathematica-journal.com/ issue/ v10i2/ newpublications/ ISBN1584884487.html

Modern Differential Geometry of Curves and Surfaces with ...
Modern Differential Geometry of Curves and Surfaces with Mathematica, ... Modern Differential Geometry of Curves and Surfaces with Mathematica, ...
library.wolfram.com/ infocenter/ Books/ 3759/

Submarino.com.br Importados: Modern Differential Geometry of ...
Modern Differential Geometry of Curves And Surfaces With Mathematica Cód. do Produto: 1251552 Gray, Alfred Gray, Alfred/ Salamon, Simon/ Abbena, Elsa ...
lojaabril.com.br/ imports_productdetails.asp?Query=& ProdTypeId=9& CatId=31560& PrevCatId=31557& ProdId=1251552& ST=BL3156...

Modern Differential Geometry of Curves and Surfaces with ...
Ideal for both classroom use and self-study, Modern Differential Geometry of Curves and Surfaces with Mathematica has been tested extensively in the ...
portal.acm.org/ citation.cfm?id=524240

NCSU Libraries - Modern differential geometry of curves and ...
Title: Modern differential geometry of curves and surfaces with Mathematica. Published: Boca Raton, FL : Chapman & Hall CRC, 2006. Edition: 3rd ed. ...
catalog.lib.ncsu.edu/ web2/ tramp2.exe/ do_ccl_search/ guest?setting_key=files& record_screen=record_brief.html& *search_b...

Modern differential geometry of curves and surfaces with ...
Modern differential geometry of curves and surfaces with Mathematica. 3rd ed. Boca Raton, FL: Chapman & Hall CRC, 2006. 984 p.
volterra.impa.br/ arquivos/ 30000/ 31500/ 105_31565.htm

Differential Geometry References
Gray, Alfred, Elsa Abbena, and Simon Salamon, Modern Differential Geometry of Curves and Surfaces with Mathematica (3e), CRC Press, 2006 (1e, 1993; 2e, ...
www.math.wayne.edu/ ~drucker/ diffgeomrefsF07.html

diff geo images page
Modern Differential Geometry of Curves and Surfaces with Mathematica (Second Edition). by Alfred Gray. Click here for additional materials of Gray related ...
www.math.uiowa.edu/ ~wseaman/ DGImage53100.htm

differential geometry :: Visualizing curves and surfaces ...
Alfred Gray, Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. (1998), allows exploration of the subject through ...
www.britannica.com/ eb/ article-235559/ differential-geometry