Invitation to Geometry

Author: Z. A. Melzak
Publisher: Courier Corporation
ISBN: 9780486789484
Release Date: 2014-01-15
Genre: Mathematics

Intended for students of many different backgrounds with only a modest knowledge of mathematics, this text features self-contained chapters that can be adapted to several types of geometry courses. Only a slight acquaintance with mathematics beyond the high-school level is necessary, including some familiarity with calculus and linear algebra. This text's introductions to several branches of geometry feature topics and treatments based on memorability and relevance. The author emphasizes connections with calculus and simple mechanics, focusing on developing students' grasp of spatial relationships. Subjects include classical Euclidean material, polygonal and circle isoperimetry, conics and Pascal's theorem, geometrical optimization, geometry and trigonometry on a sphere, graphs, convexity, and elements of differential geometry of curves. Additional material may be conveniently introduced in several places, and each chapter concludes with exercises of varying degrees of difficulty.

Geometry A Comprehensive Course

Author: Dan Pedoe
Publisher: Courier Corporation
ISBN: 9780486131733
Release Date: 2013-04-02
Genre: Mathematics

Introduction to vector algebra in the plane; circles and coaxial systems; mappings of the Euclidean plane; similitudes, isometries, Moebius transformations, much more. Includes over 500 exercises.

Linear Geometry

Author: Rafael Artzy
Publisher:
ISBN: 0486466272
Release Date: 2008
Genre: Mathematics

Most linear algebra texts neglect geometry in general and linear geometry in particular. This text for advanced undergraduates and graduate students stresses the relationship between algebra and linear geometry. It begins by using the complex number plane as an introduction to a variety of transformations and their groups in the Euclidean plane, explaining algebraic concepts as they arise. A brief account of Poincaré's model of the hyperbolic plane and its transformation group follow. Succeeding chapters contain a systematic treatment of affine, Euclidean, and projective spaces over fields that emphasizes transformations and their groups, along with an outline of results involving other geometries. An examination of the foundations of geometry starts from rudimentary projective incidence planes, then gradually adjoins axioms and develops various non-Desarguesian, Desarguesian, and Pappian planes, their corresponding algebraic structures, and their collineation groups. The axioms of order, continuity, and congruence make their appearance and lead to Euclidean and non-Euclidean planes. Lists of books for suggested further reading follow the third and fourth chapters, and the Appendix provides lists of notations, axioms, and transformation groups.

Invitation to Combinatorial Topology

Author: Maurice Fréchet
Publisher: Courier Corporation
ISBN: 0486427862
Release Date: 2003
Genre: Mathematics

Elementary text, accessible to anyone with a background in high school geometry, covers problems inherent to coloring maps, homeomorphism, applications of Descartes' theorem, topological polygons, more. Includes 108 figures. 1967 edition.

Differential Geometry

Author: Erwin Kreyszig
Publisher: Courier Corporation
ISBN: 0486667219
Release Date: 1959
Genre: Mathematics

Text from preface: "This book provides an introduction to the differential geometry of curves and surfaces in three-dimensional Euclidean space"

Foundations of Geometry

Author: C. R. Wylie
Publisher: Courier Corporation
ISBN: 9780486472140
Release Date: 2009-05-21
Genre: Education

Explains geometric theories and shows many examples.

Geometry of Complex Numbers

Author: Hans Schwerdtfeger
Publisher: Courier Corporation
ISBN: 9780486135861
Release Date: 2012-05-23
Genre: Mathematics

Illuminating, widely praised book on analytic geometry of circles, the Moebius transformation, and 2-dimensional non-Euclidean geometries.

Differential Geometry

Author: Heinrich W. Guggenheimer
Publisher: Courier Corporation
ISBN: 9780486157207
Release Date: 2012-04-27
Genre: Mathematics

This text contains an elementary introduction to continuous groups and differential invariants; an extensive treatment of groups of motions in euclidean, affine, and riemannian geometry; more. Includes exercises and 62 figures.

Curvature in Mathematics and Physics

Author: Shlomo Sternberg
Publisher: Courier Corporation
ISBN: 9780486292717
Release Date: 2013-04-17
Genre: Mathematics

Expert treatment introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Prerequisites include linear algebra and advanced calculus. 2012 edition.

Introduction to Projective Geometry

Author: C. R. Wylie
Publisher: Courier Corporation
ISBN: 9780486141701
Release Date: 2011-09-12
Genre: Mathematics

This introductory volume offers strong reinforcement for its teachings, with detailed examples and numerous theorems, proofs, and exercises, plus complete answers to all odd-numbered end-of-chapter problems. 1970 edition.

Introductory Non Euclidean Geometry

Author: Henry Parker Manning
Publisher: Courier Corporation
ISBN: 9780486154640
Release Date: 2013-01-30
Genre: Mathematics

This fine and versatile introduction begins with the theorems common to Euclidean and non-Euclidean geometry, and then it addresses the specific differences that constitute elliptic and hyperbolic geometry. 1901 edition.

Coordinate Geometry

Author: Luther Pfahler Eisenhart
Publisher: Courier Corporation
ISBN: 9780486442617
Release Date: 2005-03-04
Genre: Mathematics

A thorough, complete, and unified introduction, this volume affords exceptional insights into coordinate geometry. Invariants of conic sections and quadric surfaces receive full treatments. Algebraic equations on the first degree in two and three unknowns are carefully reviewed. Throughout the book, results are formulated precisely, with clearly stated theorems. More than 500 helpful exercises. 1939 edition.

Fundamental Concepts of Geometry

Author: Bruce E. Meserve
Publisher: Courier Corporation
ISBN: 9780486152264
Release Date: 2014-12-08
Genre: Mathematics

Demonstrates relationships between different types of geometry. Provides excellent overview of the foundations and historical evolution of geometrical concepts. Exercises (no solutions). Includes 98 illustrations.

College Geometry

Author: Nathan Altshiller-Court
Publisher: Courier Corporation
ISBN: 9780486141374
Release Date: 2012-06-29
Genre: Mathematics

The standard university-level text for decades, this volume offers exercises in construction problems, harmonic division, circle and triangle geometry, and other areas. 1952 edition, revised and enlarged by the author.

Taxicab Geometry

Author: Eugene F. Krause
Publisher: Courier Corporation
ISBN: 9780486136066
Release Date: 2012-04-30
Genre: Mathematics

Fascinating, accessible introduction to unusual mathematical system in which distance is not measured by straight lines. Illustrated topics include applications to urban geography and comparisons to Euclidean geometry. Selected answers to problems.