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Spherical Models

by Magnus J. Wenninger Dover Publications (May 05, 2014)

Well-illustrated, practical approach to creating star-faced spherical forms that can serve as basic structures for geodesic domes. Complete instructions for making models from circular bands of paper with just...

Lectures on Analytic and Projective Geometry

by Dirk J. Struik Dover Publications (March 05, 2014)

This undergraduate text develops the geometry of plane and space, leading up to conics and quadrics, within the context of metrical, affine, and projective transformations. 1953 edition.

Advanced Euclidean Geometry

by Roger A. Johnson Dover Publications (December 11, 2012)

This classic text explores the geometry of the triangle and the circle, concentrating on extensions of Euclidean theory, and examining in detail many relatively recent theorems. 1929 edition.

Ruler and the Round: Classic Problems in Geometric Constructions

by Nicholas D. Kazarinoff Dover Publications (August 14, 2012)

An intriguing look at the "impossible" geometric constructions (those that defy completion with just a ruler and a compass), this book covers angle trisection and circle division. 1970 edition.

Euclidean Geometry and Transformations

by Clayton W. Dodge Dover Publications (March 29, 2012)

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

Lie Algebras

by Nathan Jacobson Dover Publications (August 19, 2013)

Definitive treatment of important subject in modern mathematics. Covers split semi-simple Lie algebras, universal enveloping algebras, classification of irreducible modules, automorphisms, simple Lie algebras...

Introduction to Non-Euclidean Geometry

by Harold E. Wolfe Dover Publications (September 26, 2013)

College-level text for elementary courses covers the fifth postulate, hyperbolic plane geometry and trigonometry, and elliptic plane geometry and trigonometry. Appendixes offer background on Euclidean geometry....

Existence Theorems for Ordinary Differential Equations

by Francis J. Murray & Kenneth S. Miller Dover Publications (October 10, 2013)

This text examines fundamental and general existence theorems, along with uniqueness theorems and Picard iterants, and applies them to properties of solutions and linear differential equations. 1954 edition....

Proof in Geometry: With "Mistakes in Geometric Proofs"

by A. I. Fetisov & Ya. S. Dubnov Dover Publications (May 14, 2012)

This single-volume compilation of 2 books explores the construction of geometric proofs. It offers useful criteria for determining correctness and presents examples of faulty proofs that illustrate common errors....

The Geometry of Geodesics

by Herbert Busemann Dover Publications (June 14, 2012)

A comprehensive approach to qualitative problems in intrinsic differential geometry, this text examines Desarguesian spaces, perpendiculars and parallels, covering spaces, the influence of the sign of the curvature...

A Catalog of Special Plane Curves

by J. Dennis Lawrence Dover Publications (December 31, 2013)

One of the most beautiful aspects of geometry. Information on general properties, derived curves, geometric and analytic properties of each curve. 89 illus.

Analytical Geometry of Three Dimensions

by William H. McCrea Dover Publications (January 27, 2012)

Geared toward advanced undergraduates and graduate students, this text covers the coordinate system, planes and lines, spheres, homogeneous coordinates, general equations, quadric in Cartesian coordinates, and...

Non-Euclidean Geometry

by Stefan Kulczycki Dover Publications (June 08, 2012)

This accessible approach features stereometric and planimetric proofs, and elementary proofs employing only the simplest properties of the plane. A short history of geometry precedes the systematic exposition....

Projective Geometry

by T. Ewan Faulkner Dover Publications (January 23, 2013)

Highlighted by numerous examples, this book explores methods of the projective geometry of the plane. Examines the conic, the general equation of the 2nd degree, and the relationship between Euclidean and projective...

General Investigations of Curved Surfaces: Edited with an Introduction and Notes by Peter Pesic

by Karl Friedrich Gauss, James Morehead, Adam Hiltebeitel & Peter Pesic Dover Publications (January 23, 2013)

This influential work defines the concept of surface curvature and presents the important theorem stating that the "Gauss curvature" is invariant under arbitrary isometric deformation of a curved surface. 1902...

Introductory Non-Euclidean Geometry

by Henry Parker Manning Dover Publications (January 02, 2013)

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....

The Elements of Non-Euclidean Geometry

by D. M.Y. Sommerville Dover Publications (April 26, 2012)

Renowned for its lucid yet meticulous exposition, this classic allows students to follow the development of non-Euclidean geometry from a fundamental analysis of the concept of parallelism to more advanced topics....

History of Analytic Geometry

by Carl B. Boyer Dover Publications (May 31, 2012)

This study presents the concepts and contributions from before the Alexandrian Age through to Fermat and Descartes, and on through Newton and Euler to the "Golden Age," from 1789 to 1850. 1956 edition. Analytical...

The Complete Book of Holograms: How They Work and How to Make Them

by Joseph E. Kasper & Steven A. Feller Dover Publications (June 06, 2012)

Clear, thorough account, without complicated mathematics, explains geometric and zone plate holography and the different types of holograms, along with step-by-step instructions for making holograms. 116 illustrations....

Projective Geometry and Projective Metrics

by Herbert Busemann & Paul J. Kelly Dover Publications (October 17, 2012)

This text examines the 3 classical geometries and their relationship to general geometric structures, with particular focus on affine geometry, projective metrics, non-Euclidean geometry, and spatial geometry....

Fundamental Concepts of Geometry

by Bruce E. Meserve Dover Publications (June 08, 2012)

Fundamental Concepts of Geometry demonstrates in a clear and lucid manner the relationships of several types of geometry to one another. This highly regarded work is a superior teaching text, especially valuable...

Inversive Geometry

by Frank Morley & F.V. Morley Dover Publications (November 05, 2013)

This introduction to algebraic geometry makes particular reference to the operation of inversion. Topics include Euclidean group; inversion; quadratics; finite inversive groups; parabolic, hyperbolic, and elliptic...

Theory of Linear Operators in Hilbert Space

by N. I. Akhiezer & I. M. Glazman Dover Publications (March 18, 2013)

This classic textbook introduces linear operators in Hilbert Space, and presents the geometry of Hilbert space and the spectral theory of unitary and self-adjoint operators. Invaluable for every mathematician...

Differential Geometry

by Erwin Kreyszig Dover Publications (March 29, 2013)

An introductory textbook on the differential geometry of curves and surfaces in 3-dimensional Euclidean space, presented in its simplest, most essential form. With problems and solutions. Includes 99 illustrations....

Differential Manifolds

by Antoni A. Kosinski Dover Publications (June 04, 2013)

Introductory text for advanced undergraduates and graduate students presents systematic study of the topological structure of smooth manifolds, starting with elements of theory and concluding with method of...

Extremal Graph Theory

by Bela Bollobas Dover Publications (June 04, 2013)

Concise yet comprehensive, this treatment of extremal graph theory is appropriate for undergraduate and graduate students and features numerous exercises and complete proofs. 1978 edition.

Invariants of Quadratic Differential Forms

by Joseph Edmund Wright Dover Publications (September 23, 2013)

Classic monograph offers a brief account of the invariant theory connected with a single quadratic differential form. Includes historical overview; methods of Christoffel, Lie, Maschke; and geometrical, dynamical...

An Introduction to Differential Geometry

by T. J. Willmore Dover Publications (April 15, 2013)

This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian...

Pythagorean Triangles

by Waclaw Sierpinski Dover Publications (March 13, 2013)

This classic text, written by a distinguished mathematician and teacher, focuses on a fundamental theory of geometry. Topics include all types of Pythagorean triangles.

The Green Book of Mathematical Problems

by Kenneth Hardy & Kenneth S. Williams Dover Publications (November 26, 2013)

Rich selection of 100 practice problems — with hints and solutions — for students preparing for the William Lowell Putnam and other undergraduate-level mathematical competitions. Features real numbers, differential...

A Survey of Minimal Surfaces

by Robert Osserman Dover Publications (November 10, 2013)

Newly updated accessible study covers parametric and non-parametric surfaces, isothermal parameters, Bernstein’s theorem, much more, including such recent developments as new work on Plateau’s problem and...

Mathematical Foundations of Quantum Statistics

by A. Y. Khinchin Dover Publications (January 24, 2013)

A coherent, well-organized look at the basis of quantum statistics’ computational methods, the determination of the mean values of occupation numbers, the foundations of the statistics of photons and material...

Elementary Mathematics from an Advanced Standpoint: Geometry

by Felix Klein Dover Publications (February 10, 2012)

This comprehensive treatment features analytic formulas, enabling precise formulation of geometric facts, and it covers geometric manifolds and transformations, concluding with a systematic discussion of fundamentals....

The Fourth Dimension Simply Explained

by Henry P. Manning Dover Publications (October 12, 2012)

Twenty-two essays examine the fourth dimension: how it may be studied, its relationship to non-Euclidean geometry, analogues to three-dimensional space, its absurdities and curiosities, and its simpler properties....

A Treatise on the Differential Geometry of Curves and Surfaces

by Luther Pfahler Eisenhart Dover Publications (March 28, 2013)

Created especially for graduate students by a leading writer on mathematics, this introduction to the geometry of curves and surfaces concentrates on problems that students will find most helpful.

The Geometry of René Descartes

by René Descartes Dover Publications (August 22, 2012)

The great work that founded analytical geometry. Includes the original French text, Descartes' own diagrams, and the definitive Smith-Latham translation. "The greatest single step ever made in the progress of...

Introduction to the Geometry of Complex Numbers

by Roland Deaux & Howard Eves Dover Publications (December 26, 2012)

Geared toward readers unfamiliar with complex numbers, this text explains how to solve problems that frequently arise in the applied sciences and emphasizes constructions related to algebraic operations. 1956...

Mathematics: Its Content, Methods and Meaning

by A. D. Aleksandrov, A. N. Kolmogorov & M. A. Lavrent’ev Dover Publications (April 09, 2012)

Major survey offers comprehensive, coherent discussions of analytic geometry, algebra, differential equations, calculus of variations, functions of a complex variable, prime numbers, linear and non-Euclidean...

Differential Geometry

by Heinrich W. Guggenheimer Dover Publications (March 30, 2012)

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...

Einstein's Legacy: The Unity of Space and Time

by Julian Schwinger Dover Publications (April 26, 2012)

A Nobel Laureate relates the fascinating story of Einstein and relativity theory in well-illustrated, nontechnical terms, discussing the meaning of time, gravity and its effect on light, the curving of space-time,...

Symmetry Discovered: Concepts and Applications in Nature and Science

by Joe Rosen Dover Publications (September 18, 2012)

Newly enlarged classic covers basic concepts and terminology, lucid discussions of geometric symmetry, other symmetries and approximate symmetry, symmetry in nature, in science, more. Solutions to problems....

Technical Calculus with Analytic Geometry

by Judith L. Gersting Dover Publications (May 17, 2012)

Well-conceived text with many special features covers functions and graphs, straight lines and conic sections, new coordinate systems, the derivative, much more. Many examples, exercises, practice problems,...

Taxicab Geometry: An Adventure in Non-Euclidean Geometry

by Eugene F. Krause Dover Publications (April 02, 2012)

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 of Complex Numbers

by Hans Schwerdtfeger Dover Publications (April 25, 2012)

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

Geometry from Euclid to Knots

by Saul Stahl Dover Publications (April 25, 2012)

This text provides a historical perspective on plane geometry and covers non-neutral Euclidean geometry, circles and regular polygons, projective geometry, symmetries, inversions, informal topology, and more....

Challenging Problems in Geometry

by Alfred S. Posamentier & Charles T. Salkind Dover Publications (April 02, 2012)

Collection of nearly 200 unusual problems dealing with congruence and parallelism, the Pythagorean theorem, circles, area relationships, Ptolemy and the cyclic quadrilateral, collinearity and concurrency and...

Geometry: A Comprehensive Course

by Dan Pedoe Dover Publications (March 05, 2013)

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.

The Penrose Transform

by Robert J. Baston & Michael G. Eastwood Dover Publications (October 28, 2016)

"Brings to the reader a huge amount of information, well organized and condensed into less than two hundred pages." — Mathematical Reviews

In recent decades twistor theory has become an important focus for...

Cohomology and Differential Forms

by Izu Vaisman Dover Publications (July 28, 2016)

This monograph explores the cohomological theory of manifolds with various sheaves and its application to differential geometry. Based on lectures given by author Izu Vaisman at Romania's University of Iasi,...

The Theory and Practice of Conformal Geometry

by Steven G. Krantz Dover Publications (March 17, 2016)

In this original text, prolific mathematics author Steven G. Krantz addresses conformal geometry, a subject that has occupied him for four decades and for which he helped to develop some of the modern theory....