Classical Geometry Euclidean, Transformational, Inversive, and Projective

Features the classical themes of geometry with plentiful applications in mathematics, education, engineering, and science

Accessible and reader-friendly, Classical Geometry: Euclidean, Transformational, Inversive, and Projective introduces readers to a valuable discipline that is crucial to understanding bothspatial relationships and logical reasoning. Focusing on the development of geometric intuitionwhile avoiding the axiomatic method, a problem solving approach is encouraged throughout.

The book is strategically divided into three sections: Part One focuses on Euclidean geometry, which provides the foundation for the rest of the material covered throughout; Part Two discusses Euclidean transformations of the plane, as well as groups and their use in studying transformations; and Part Three covers inversive and projective geometry as natural extensions of Euclidean geometry. In addition to featuring real-world applications throughout, Classical Geometry: Euclidean, Transformational, Inversive, and Projective includes:

• Multiple entertaining and elegant geometry problems at the end of each section for every level of study
• Fully worked examples with exercises to facilitate comprehension and retention
• Unique topical coverage, such as the theorems of Ceva and Menalaus and their applications
• An approach that prepares readers for the art of logical reasoning, modeling, and proofs

The book is an excellent textbook for courses in introductory geometry, elementary geometry, modern geometry, and history of mathematics at the undergraduate level for mathematics majors, as well as for engineering and secondary education majors. The book is also ideal for anyone who would like to learn the various applications of elementary geometry.

Preface v

Part I Euclidean Geometry

1 Congruency 3

2 Concurrency 41

3 Similarity 59

4 Theorems of Ceva and Menelaus 95

5 Area 133

6 Miscellaneous Topics 159

Part II Transformational Geometry

7 The Euclidean Transformations or Isometries 207

8 The Algebra of Isometries 235

9 The Product of Direct Isometries 255

10 Symmetry and Groups 271

11 Homotheties 289

12 Tessellations 313

Part III Inversive And Projective Geometries

13 Introduction to Inversive Geometry 339

14 Reciprocation and the Extended Plane 375

15 Cross Ratios 411

16 Introduction to Projective Geometry 435

Bibliography 466

Index 471

I. E. LEONARD, PHD, is Lecturer in the Department of Mathematical and Statistical Sciences at the University of Alberta, Canada. The author of over fifteen journal articles, his areas of research interest include real analysis and discrete mathematics.

J. E. LEWIS, PHD, is Professor Emeritus in the Department of Mathematical Sciences at the University of Alberta, Canada. He was the recipient of the Faculty of Science Award for Excellence in Teaching in 2004.

A. C. F. LIU, PHD, is Professor in the Department of Mathematical and Statistical Sciences at the University of Alberta, Canada. He has authored over thirty journal articles.

G. W. TOKARSKY, MSC, is Faculty Lecturer in the Department of Mathematical and Statistical Sciences at the University of Alberta, Canada. His areas of research interest include polygonal billiards and symbolic logic.