{"product_id":"classical-geometry-9781118679197","title":"Classical Geometry","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eFeatures the classical themes of geometry with plentiful applications in mathematics, education, engineering, and science\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eAccessible and reader-friendly, \u003ci\u003eClassical Geometry: Euclidean, Transformational, Inversive, and Projective \u003c\/i\u003eintroduces 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.\u003c\/p\u003e \u003cp\u003eThe 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, \u003ci\u003eClassical Geome\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003c\/i\u003e\u003c\/p\u003e\u003cp\u003e“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.”  (\u003ci\u003eZentralblatt MATH\u003c\/i\u003e, 1 October 2014)\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface v\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART I EUCLIDEAN GEOMETRY\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Congruency 3\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction 3\u003c\/p\u003e \u003cp\u003e1.2 Congruent Figures 6\u003c\/p\u003e \u003cp\u003e1.3 Parallel Lines 12\u003c\/p\u003e \u003cp\u003e1.3.1 Angles in a Triangle 13\u003c\/p\u003e \u003cp\u003e1.3.2 Thales' Theorem 14\u003c\/p\u003e \u003cp\u003e1.3.3 Quadrilaterals 17\u003c\/p\u003e \u003cp\u003e1.4 More About Congruency 21\u003c\/p\u003e \u003cp\u003e1.5 Perpendiculars and Angle Bisectors 24\u003c\/p\u003e \u003cp\u003e1.6 Construction Problems 28\u003c\/p\u003e \u003cp\u003e1.6.1 The Method of Loci 31\u003c\/p\u003e \u003cp\u003e1.7 Solutions to Selected Exercises 33\u003c\/p\u003e \u003cp\u003e1.8 Problems 38\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Concurrency 41\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Perpendicular Bisectors 41\u003c\/p\u003e \u003cp\u003e2.2 Angle Bisectors 43\u003c\/p\u003e \u003cp\u003e2.3 Altitudes 46\u003c\/p\u003e \u003cp\u003e2.4 Medians 48\u003c\/p\u003e \u003cp\u003e2.5 Construction Problems 50\u003c\/p\u003e \u003cp\u003e2.6 Solutions to the Exercises 54\u003c\/p\u003e \u003cp\u003e2.7 Problems 56\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Similarity 59\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Similar Triangles 59\u003c\/p\u003e \u003cp\u003e3.2 Parallel Lines and Similarity 60\u003c\/p\u003e \u003cp\u003e3.3 Other Conditions Implying Similarity 64\u003c\/p\u003e \u003cp\u003e3.4 Examples 67\u003c\/p\u003e \u003cp\u003e3.5 Construction Problems 75\u003c\/p\u003e \u003cp\u003e3.6 The Power of a Point 82\u003c\/p\u003e \u003cp\u003e3.7 Solutions to the Exercises 87\u003c\/p\u003e \u003cp\u003e3.8 Problems 90\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Theorems of Ceva and Menelaus 95\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Directed Distances, Directed Ratios 95\u003c\/p\u003e \u003cp\u003e4.2 The Theorems 97\u003c\/p\u003e \u003cp\u003e4.3 Applications of Ceva's Theorem 99\u003c\/p\u003e \u003cp\u003e4.4 Applications of Menelaus' Theorem 103\u003c\/p\u003e \u003cp\u003e4.5 Proofs of the Theorems 115\u003c\/p\u003e \u003cp\u003e4.6 Extended Versions of the Theorems 125\u003c\/p\u003e \u003cp\u003e4.6.1 Ceva's Theorem in the Extended Plane 127\u003c\/p\u003e \u003cp\u003e4.6.2 Menelaus' Theorem in the Extended Plane 129\u003c\/p\u003e \u003cp\u003e4.7 Problems 131\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Area 133\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Basic Properties 133\u003c\/p\u003e \u003cp\u003e5.1.1 Areas of Polygons 134\u003c\/p\u003e \u003cp\u003e5.1.2 Finding the Area of Polygons 138\u003c\/p\u003e \u003cp\u003e5.1.3 Areas of Other Shapes 139\u003c\/p\u003e \u003cp\u003e5.2 Applications of the Basic Properties 140\u003c\/p\u003e \u003cp\u003e5.3 Other Formulae for the Area of a Triangle 147\u003c\/p\u003e \u003cp\u003e5.4 Solutions to the Exercises 153\u003c\/p\u003e \u003cp\u003e5.5 Problems 153\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Miscellaneous Topics 159\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 The Three Problems of Antiquity 159\u003c\/p\u003e \u003cp\u003e6.2 Constructing Segments of Specific Lengths 161\u003c\/p\u003e \u003cp\u003e6.3 Construction of Regular Polygons 166\u003c\/p\u003e \u003cp\u003e6.3.1 Construction of the Regular Pentagon 168\u003c\/p\u003e \u003cp\u003e6.3.2 Construction of Other Regular Polygons 169\u003c\/p\u003e \u003cp\u003e6.4 Miquel's Theorem 171\u003c\/p\u003e \u003cp\u003e6.5 Morley's Theorem 178\u003c\/p\u003e \u003cp\u003e6.6 The Nine-Point Circle 185\u003c\/p\u003e \u003cp\u003e6.6.1 Special Cases 188\u003c\/p\u003e \u003cp\u003e6.7 The Steiner-Lehmus Theorem 193\u003c\/p\u003e \u003cp\u003e6.8 The Circle of Apollonius 197\u003c\/p\u003e \u003cp\u003e6.9 Solutions to the Exercises 200\u003c\/p\u003e \u003cp\u003e6.10 Problems 201\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART II TRANSFORMATIONAL GEOMETRY\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 The Euclidean Transformations or Isometries 207\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Rotations, Reflections, and Translations 207\u003c\/p\u003e \u003cp\u003e7.2 Mappings and Transformations 211\u003c\/p\u003e \u003cp\u003e7.2.1 Isometries 213\u003c\/p\u003e \u003cp\u003e7.3 Using Rotations, Reflections, and Translations 217\u003c\/p\u003e \u003cp\u003e7.4 Problems 227\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 The Algebra of Isometries 231\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Basic Algebraic Properties 231\u003c\/p\u003e \u003cp\u003e8.2 Groups of Isometries 236\u003c\/p\u003e \u003cp\u003e8.2.1 Direct and Opposite Isometries 237\u003c\/p\u003e \u003cp\u003e8.3 The Product of Reflections 241\u003c\/p\u003e \u003cp\u003e8.4 Problems 246\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 The Product of Direct Isometries 253\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Angles 253\u003c\/p\u003e \u003cp\u003e9.2 Fixed Points 255\u003c\/p\u003e \u003cp\u003e9.3 The Product of Two Translations 256\u003c\/p\u003e \u003cp\u003e9.4 The Product of a Translation and a Rotation 257\u003c\/p\u003e \u003cp\u003e9.5 The Product of Two Rotations 260\u003c\/p\u003e \u003cp\u003e9.6 Problems 263\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Symmetry and Groups 269\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 More About Groups 269\u003c\/p\u003e \u003cp\u003e10.1.1 Cyclic and Dihedral Groups 273\u003c\/p\u003e \u003cp\u003e10.2 Leonardo's Theorem 277\u003c\/p\u003e \u003cp\u003e10.3 Problems 281\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Homotheties 287\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 The Pantograph 287\u003c\/p\u003e \u003cp\u003e11.2 Some Basic Properties 288\u003c\/p\u003e \u003cp\u003e11.2.1 Circles 291\u003c\/p\u003e \u003cp\u003e11.3 Construction Problems 293\u003c\/p\u003e \u003cp\u003e11.4 Using Homotheties in Proofs 298\u003c\/p\u003e \u003cp\u003e11.5 Dilatation 302\u003c\/p\u003e \u003cp\u003e11.6 Problems 304\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Tessellations 311\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Tilings 311\u003c\/p\u003e \u003cp\u003e12.2 Monohedral Tilings 312\u003c\/p\u003e \u003cp\u003e12.3 Tiling with Regular Polygons 317\u003c\/p\u003e \u003cp\u003e12.4 Platonic and Archimedean Tilings 323\u003c\/p\u003e \u003cp\u003e12.5 Problems 330\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART III INVERSIVE AND PROJECTIVE GEOMETRIES\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Introduction to Inversive Geometry 337\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Inversion in the Euclidean Plane 337\u003c\/p\u003e \u003cp\u003e13.2 The Effect of Inversion on Euclidean Properties 343\u003c\/p\u003e \u003cp\u003e13.3 Orthogonal Circles 351\u003c\/p\u003e \u003cp\u003e13.4 Compass-Only Constructions 360\u003c\/p\u003e \u003cp\u003e13.5 Problems 369\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Reciprocation and the Extended Plane 373\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Harmonic Conjugates 373\u003c\/p\u003e \u003cp\u003e14.2 The Projective Plane and Reciprocation 383\u003c\/p\u003e \u003cp\u003e14.3 Conjugate Points and Lines 393\u003c\/p\u003e \u003cp\u003e14.4 Conics 399\u003c\/p\u003e \u003cp\u003e14.5 Problems 406\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Cross Ratios 409\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Cross Ratios 409\u003c\/p\u003e \u003cp\u003e15.2 Applications of Cross Ratios 420\u003c\/p\u003e \u003cp\u003e15.3 Problems 429\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Introduction to Projective Geometry 433\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Straightedge Constructions 433\u003c\/p\u003e \u003cp\u003e16.2 Perspectivities and Projectivities 443\u003c\/p\u003e \u003cp\u003e16.3 Line Perspectivities and Line Projectivities 448\u003c\/p\u003e \u003cp\u003e16.4 Projective Geometry and Fixed Points 448\u003c\/p\u003e \u003cp\u003e16.5 Projecting a Line to Infinity 451\u003c\/p\u003e \u003cp\u003e16.6 The Apollonian Definition of a Conic 455\u003c\/p\u003e \u003cp\u003e16.7 Problems 461\u003c\/p\u003e \u003cp\u003e\u003cb\u003eBibliography 464\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIndex 469\u003c\/b\u003e\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default 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