Flatland: An Edition with Notes and Commentary (Spectrum)

Flatland, Edwin Abbott Abbott's story of a two-dimensional universe, as told by one of its inhabitants who is introduced to the mysteries of three-dimensional space, has enjoyed an enduring popularity from the time of its publication in 1884. This fully annotated edition enables the modern-day reader to understand and appreciate the many "dimensions" of this classic satire. Mathematical notes and illustrations enhance the usefulness of Flatland as an elementary introduction to higher-dimensional geometry. Historical notes show connections to late-Victorian England and to classical Greece. Citations from Abbott's other writings as well as the works of Plato and Aristotle serve to interpret the text. Commentary on language and literary style includes numerous definitions of obscure words. An appendix gives a comprehensive account of the life and work of Flatland's remarkable author.

Literature & Fiction

Banchoff, Thomas F.

Abbott, Edwin A.

Lindgren, William F.

United States

American Mathematical Society

Cambridge University Press

This work investigates ways of picturing and understanding dimensions below and above our own. What would a two-dimensional universe be like? How can we even attempt to picture objects of four, five or six dimensions? Such are the questions examined in this text.

Beyond the Third Dimension: Geometry, Computer Graphics, and Higher Dimensions (Scientific American Library Series)

W.H.Freeman & Co.

Differential Geometry of Curves and Surfaces

Science & Math

Lovett, Stephen

Mathematics

Chapman and Hall/CRC

Through two previous editions, the third edition of this popular and intriguing text takes both an analytical/theoretical approach and a visual/intuitive approach to the local and global properties of curves and surfaces. 
Requiring only multivariable calculus and linear algebra, it develops students’ geometric intuition through interactive graphics applets. Applets are presented in Maple workbook format, which readers can access using the free Maple Player. 
The book explains the reasons for various definitions while the interactive applets offer motivation for definitions, allowing students to explore examples further, and give a visual explanation of complicated theorems. The ability to change parametric curves and parametrized surfaces in an applet lets students probe the concepts far beyond what static text permits. Investigative project ideas promote student research. 
At users of the previous editions' request, this third edition offers a broader list of exercises. More elementary exercises are added and some challenging problems are moved later in exercise sets to assure more graduated progress. The authors also add hints to motivate students grappling with the more difficult exercises. 
This student-friendly and readable approach offers additional examples, well-placed to assist student comprehension. In the presentation of the Gauss-Bonnet Theorem, the authors provide more intuition and stepping-stones to help students grasp phenomena behind it. Also, the concept of a homeomorphism is new to students even though it is a key theoretical component of the definition of a regular surface. Providing more examples show students how to prove certain functions are homeomorphisms.

Students and professors of an undergraduate course in differential geometry will appreciate the clear exposition and comprehensive exercises in this book that focuses on the geometric properties of curves and surfaces, one- and two-dimensional objects in Euclidean space. The problems generally relate to questions of local properties (the properties observed at a point on the curve or surface) or global properties (the properties of the object as a whole). Some of the more interesting theorems explore relationships between local and global properties.  A special feature is the availability of accompanying online interactive java applets coordinated with each section. The applets allow students to investigate and manipulate curves and surfaces to develop intuition and to help analyze geometric phenomena.

Lovett, Stephen T.

A K Peters/CRC Press

Differential Geometry of Curves and Surfaces, Second Edition takes both an analytical/theoretical approach and a visual/intuitive approach to the local and global properties of curves and surfaces. Requiring only multivariable calculus and linear algebra, it develops students’ geometric intuition through interactive computer graphics applets supported by sound theory. The book explains the reasons for various definitions while the interactive applets offer motivation for certain definitions, allow students to explore examples further, and give a visual explanation of complicated theorems. The ability to change parametric curves and parametrized surfaces in an applet lets students probe the concepts far beyond what static text permits. New to the Second Edition <ul>
<li>Reworked presentation to make it more approachable</li> <li>More exercises, both introductory and advanced</li> <li>New section on the application of differential geometry to cartography</li> <li>Additional investigative project ideas</li> <li>Significantly reorganized material on the Gauss–Bonnet theorem</li> <li>Two new sections dedicated to hyperbolic and spherical geometry as applications of intrinsic geometry</li> <li>A new chapter on curves and surfaces in Rn
</li>
</ul> Suitable for an undergraduate-level course or self-study, this self-contained textbook and online software applets provide students with a rigorous yet intuitive introduction to the field of differential geometry. The text gives a detailed introduction of definitions, theorems, and proofs and includes many types of exercises appropriate for daily or weekly assignments. The applets can be used for computer labs, in-class illustrations, exploratory exercises, or self-study aids.

Students and professors of an undergraduate course in differential geometry will appreciate the clear exposition and comprehensive exercises in this book that focuses on the geometric properties of curves and surfaces, one- and two-dimensional objects in Euclidean space. The problems generally relate to questions of local properties (the properties observed at a point on the curve or surface) or global properties (the properties of the object as a whole). Some of the more interesting theorems explore relationships between local and global properties. A special feature is the availability of accompanying online interactive java applets coordinated with each section. The applets allow students to investigate and manipulate curves and surfaces to develop intuition and to help analyze geometric phenomena.

See the best price to sell, buy, or rent books by Banchoff, Thomas F.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Banchoff, Thomas F.

See the best price to sell, buy, or rent books by Banchoff, Thomas F.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Flatland: An Edition with Notes and Commentary (Spectrum)

Flatland: An Edition with Notes and Commentary (Spectrum)

Beyond the Third Dimension: Geometry, Computer Graphics, and Higher Dimensions (Scientific American Library Series)

Differential Geometry of Curves and Surfaces

Differential Geometry of Curves and Surfaces

Differential Geometry of Curves and Surfaces

Differential Geometry of Curves and Surfaces

Differential Geometry of Curves and Surfaces