Classical Geometry

Euclidean, Transformational, Inversive, and Projective

Inbunden, Engelska, 2014

AvI. E. Leonard,J. E. Lewis,A. C. F. Liu,G. W. Tokarsky

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Features the classical themes of geometry with plentiful applications in mathematics, education, engineering, and scienceAccessible 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 studyFully worked examples with exercises to facilitate comprehension and retentionUnique topical coverage, such as the theorems of Ceva and Menalaus and their applicationsAn approach that prepares readers for the art of logical reasoning, modeling, and proofsThe 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.

Produktinformation

Utgivningsdatum2014-05-09
Mått158 x 236 x 31 mm
Vikt839 g
FormatInbunden
SpråkEngelska
Antal sidor496
FörlagJohn Wiley & Sons Inc
ISBN9781118679197

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Matematik inom Naturvetenskap och teknik

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.

Preface vPart I Euclidean Geometry1 Congruency 32 Concurrency 413 Similarity 594 Theorems of Ceva and Menelaus 955 Area 1336 Miscellaneous Topics 159Part II Transformational Geometry7 The Euclidean Transformations or Isometries 2078 The Algebra of Isometries 2359 The Product of Direct Isometries 25510 Symmetry and Groups 27111 Homotheties 28912 Tessellations 313Part III Inversive And Projective Geometries13 Introduction to Inversive Geometry 33914 Reciprocation and the Extended Plane 37515 Cross Ratios 41116 Introduction to Projective Geometry 435Bibliography 466Index 471