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Classical Geometry
Euclidean, Transformational, Inversive, and Projective
I. E. Leonard (Author), J. E. Lewis (Author), A. C. F. Liu (Author), G. W. Tokarsky (Author)
9781118679197, Wiley
Hardback, published 9 May 2014
496 pages
23.6 x 15.8 x 3 cm, 0.839 kg
“The book is an extremely valuable compendium of elementary constructions of Euclidean geometry. The text, especially the proofs, is clearly structured and move forward in simple steps, and thus are at the one hand very suitable for a beginner in geometry and at the other hand exemplary for a teacher of geometry.” (Zentralblatt MATH, 1 October 2014)
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: 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
Subject Areas: Mathematics [PB]
