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.

Differential Geometry

Author: Erwin Kreyszig
Publisher: Courier Corporation
ISBN: 0486667219
Release Date: 1991-06
Genre: Mathematics

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

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: 9780486147888
Release Date: 2012-08-13
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.

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.

Geometry and the Visual Arts

Author: Daniel Pedoe
Publisher: Courier Corporation
ISBN: 048624458X
Release Date: 1976
Genre: Mathematics

This survey traces the effects of geometry on artistic achievement and clearly discusses its importance to artists and scientists. It also surveys projective geometry, mathematical curves, theories of perspective, architectural form, and concepts of space.

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.

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.

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.

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.

Differential Geometric Structures

Author: Walter A. Poor
Publisher: Courier Corporation
ISBN: 9780486151915
Release Date: 2015-04-27
Genre: Mathematics

This introductory text defines geometric structure by specifying parallel transport in an appropriate fiber bundle and focusing on simplest cases of linear parallel transport in a vector bundle. 1981 edition.

Euclidean Geometry and Transformations

Author: Clayton W. Dodge
Publisher: Courier Corporation
ISBN: 9780486138428
Release Date: 2012-04-26
Genre: Mathematics

This introduction to Euclidean geometry emphasizes transformations, particularly isometries and similarities. Suitable for undergraduate courses, it includes numerous examples, many with detailed answers. 1972 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.

Beyond Geometry

Author: Peter Pesic
Publisher: Courier Corporation
ISBN: 9780486453507
Release Date: 2007
Genre: Mathematics

Eight essays trace seminal ideas about the foundations of geometry that led to the development of Einstein's general theory of relativity. This is the only English-language collection of these important papers, some of which are extremely hard to find. Contributors include Helmholtz, Klein, Clifford, Poincaré, and Cartan.

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.