Geometry A Comprehensive Course

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 is a mathematical branch that deals with the questions of size, shape, relative position of figures and the properties of space. Some of the fundamental concepts of geometry include concepts of line, surface, point, plane, angle and curve as well as the notions of manifold and topology. Geometry is applied in many fields such as architecture, physics, art and other branches of mathematics. A few of the sub-disciplines within this field are Euclidean geometry, differential geometry and algebraic geometry. Euclidean geometry is applied in the fields of computer graphics, computational geometry, incidence, geodesy and navigation. Differential geometry involves the usage of techniques of calculus and linear algebra for studying geometric problems. The topics included in this book on geometry are of utmost significance and bound to provide incredible insights to readers. It elucidates new techniques and their applications in a multidisciplinary approach. Those in search of information to further their knowledge will be greatly assisted by this book.

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.

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

A straightedge, compass, and a little thought are all that's needed to discover the intellectual excitement of geometry. Harmonic division and Apollonian circles, inversive geometry, hexlet, Golden Section, more. 132 illustrations.

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.

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.

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.