This lucid introductory text offers both an analytic and an axiomatic approach to plane projective geometry. The analytic treatment builds and expands upon students' familiarity with elementary plane analytic geometry and provides a well-motivated approach to projective geometry. Subsequent chapters ... read more
Geometry: A Comprehensive Course by Dan Pedoe 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 from Euclid to Knots by Saul Stahl 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. Includes 1,000 practice problems. Solutions available. 2003 edition.
Taxicab Geometry: An Adventure in Non-Euclidean Geometry by Eugene F. Krause 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.
Fundamental Concepts of Geometry by Bruce E. Meserve 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.
A Vector Space Approach to Geometry by Melvin Hausner This examination of geometry's correlation with other branches of math and science features a review of systematic geometric motivations in vector space theory and matrix theory; more. 1965 edition.
Problems and Solutions in Euclidean Geometry by M. N. Aref, William Wernick Based on classical principles, this book is intended for a second course in Euclidean geometry and can be used as a refresher. More than 200 problems include hints and solutions. 1968 edition.
Advanced Euclidean Geometry by Roger A. Johnson 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.
Foundations of Geometry by C. R. Wylie, Jr. Geared toward students preparing to teach high school mathematics, this text explores the principles of Euclidean and non-Euclidean geometry and covers both generalities and specifics of the axiomatic method. 1964 edition.
Non-Euclidean Geometry by Roberto Bonola Examines various attempts to prove Euclid's parallel postulate — by the Greeks, Arabs, and Renaissance mathematicians. It considers forerunners and founders such as Saccheri, Lambert, Legendre, W. Bolyai, Gauss, others. Includes 181 diagrams.
Lectures in Projective Geometry by A. Seidenberg An ideal text for undergraduate courses, this volume takes an axiomatic approach that covers relations between the basic theorems, conics, coordinate systems and linear transformations, quadric surfaces, and the Jordan canonical form. 1962 edition.
Lectures on Analytic and Projective Geometry by Dirk J. Struik 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.
Linear Algebra and Projective Geometry by Reinhold Baer Geared toward upper-level undergraduates and graduate students, this text establishes that projective geometry and linear algebra are essentially identical. The supporting evidence consists of theorems offering an algebraic demonstration of certain geometric concepts. 1952 edition.
Projective Geometry by T. Ewan Faulkner 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 geometry. 1960 edition.
Projective Geometry and Projective Metrics by Herbert Busemann, Paul J. Kelly 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. 1953 edition.
The Beauty of Geometry: Twelve Essays by H. S. M. Coxeter Absorbing essays demonstrate the charms of mathematics. Stimulating and thought-provoking treatment of geometry's crucial role in a wide range of mathematical applications, for students and mathematicians.
Challenging Problems in Geometry by Alfred S. Posamentier, Charles T. Salkind 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 more. Arranged in order of difficulty. Detailed solutions.
Linear Geometry by Rafael Artzy This text stresses the relationship between algebra and linear geometry, examining transformations in the Euclidean plane, affine and Euclidean geometry, projective geometry and non-Euclidean geometries, and axiomatic plane geometry. 1974 edition.
Non-Euclidean Geometry by Stefan Kulczycki 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. 1961 edition.
Proof in Geometry: With "Mistakes in Geometric Proofs" by A. I. Fetisov, Ya. S. Dubnov 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. 1963 editions.
Vector Geometry by Gilbert de B. Robinson Concise undergraduate-level text by a prominent mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement. Includes answers to exercises. 1962 edition.
This lucid introductory text offers both an analytic and an axiomatic approach to plane projective geometry. The analytic treatment builds and expands upon students' familiarity with elementary plane analytic geometry and provides a well-motivated approach to projective geometry. Subsequent chapters explore Euclidean and non-Euclidean geometry as specializations of the projective plane, revealing the existence of an infinite number of geometries, each Euclidean in nature but characterized by a different set of distance- and angle-measurement formulas. Outstanding pedagogical features include worked-through examples, introductions and summaries for each topic, and numerous theorems, proofs, and exercises that reinforce each chapter's precepts. Two helpful indexes conclude the text, along with answers to all odd-numbered exercises. In addition to its value to undergraduate students of mathematics, computer science, and secondary mathematics education, this volume provides an excellent reference for computer science professionals.
Reprint of the McGraw-Hill Book Company, Inc., New York, 1970 edition.
Clarence Raymond Wylie, Jr., had a long career as a writer of mathematics and engineering textbooks. His Advanced Engineering Mathematics was the standard text in that field starting in the 1950s and for many decades thereafter. He also wrote widely used textbooks on geometry directed at students preparing to become secondary school teachers, which also serve as very useful reviews for college undergraduates even today. Dover reprinted two of these books in recent years, Introduction to Projective Geometry in 2008 and Foundations ofGeometry in 2009.
The author is important to our program for another reason, as well. In 1957, when Dover was publishing very few original books of any kind, we published Wylie's original manuscript 101 Puzzles in Thought and Logic. The book is still going strong after 55 years, and the gap between its first appearance in 1957 and Introduction to Projective Geometry in 2008 may be the longest period of time between the publication of two books by the same author in the history of the Dover mathematics program. Wylie's 1957 book launched the Dover category of intriguing logic puzzles, which has seen the appearance of many books by some of the most popular authors in the field including Martin Gardner and, more recently, Raymond Smullyan.
Here's a quick one from 101 Puzzles in Thought and Logic:
If it takes twice as long for a passenger train to pass a freight train after it first overtakes it as it takes the two trains to pass when going in opposite directions, how many times faster than the freight train is the passenger train?
Answer: The passenger train is three times as fast as the freight train.
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