Methods of Geometry

ISBN-13: 9780471251835 / Angielski / Twarda / 2000 / 486 str.

James T. Smith; Whitney Smith

Opis

A practical, accessible introduction to advanced geometry Exceptionally well-written and filled with historical and bibliographic notes, Methods of Geometry presents a practical and proof-oriented approach. The author develops a wide range of subject areas at an intermediate level and explains how theories that underlie many fields of advanced mathematics ultimately lead to applications in science and engineering. Foundations, basic Euclidean geometry, and transformations are discussed in detail and applied to study advanced plane geometry, polyhedra, isometries, similarities, and symmetry. An excellent introduction to advanced concepts as well as a reference to techniques for use in independent study and research, Methods of Geometry also features:

• Ample exercises designed to promote effective problem-solving strategies
  
• Insight into novel uses of Euclidean geometry
  
• More than 300 figures accompanying definitions and proofs
  
• A comprehensive and annotated bibliography
  
• Appendices reviewing vector and matrix algebra, least upper bound principle, and equivalence relations
  
  An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department.

Recenzje

"It should be emphasized that the book is filled with historical and bibliographic notes, good motivations and a number of exercises. Altogether, it can be regarded as a good approach to a special part of geometry on an intermediate level." (Zentralblatt Math, Volume 955, No 5, 2001)

"Fine interweaving of history, foundations, and geometry.... Useful as a source of exercises." (American Mathematical Monthly, November 2001)

Spis treści

Foundations.

Elementary Euclidean Geometry.

Exercises on Elementary Geometry.

Some Triangle and Circle Geometry.

Plane Isometries and Similarities.

Three Dimensional Isometries and Similarities.

Symmetry.

Appendices.

Bibliography.

Index.

O autorze

JAMES T. SMITH, PhD, is Professor of Mathematics at San Francisco State University.

Blurb

A practical, accessible introduction to advanced geometry

Exceptionally well–written and filled with historical and bibliographic notes, Methods of Geometry presents a practical and proof–oriented approach. The author develops a wide range of subject areas at an intermediate level and explains how theories that underlie many fields of advanced mathematics ultimately lead to applications in science and engineering. Foundations, basic Euclidean geometry, and transformations are discussed in detail and applied to study advanced plane geometry, polyhedra, isometries, similarities, and symmetry. An excellent introduction to advanced concepts as well as a reference to techniques for use in independent study and research, Methods of Geometry also features:

• Ample exercises designed to promote effective problem–solving strategies
• Insight into novel uses of Euclidean geometry
• More than 300 figures accompanying definitions and proofs
• A comprehensive and annotated bibliography
• Appendices reviewing vector and matrix algebra, least upper bound principle, and equivalence relations