{"product_id":"classical-geometry-9781118903674","title":"Classical Geometry","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cstrong\u003eThe combination text and Student Solutions Manual that features the classical themes of geometry with plentiful applications\u003c\/strong\u003e \u003c\/p\u003e\u003cp\u003eAccessible and reader-friendly, \u003cem\u003eClassical Geometry: Euclidean, Transformational, Inversive, and Projective\u003c\/em\u003e and the companion \u003cem\u003eStudent Solutions Manual introduces\u003c\/em\u003e a valuable discipline that is crucial to understanding both spatial relationships and logical reasoning. Focusing on the development of geometric intuition while avoiding the axiomatic method, a problem solving approach is encouraged throughout. The books address Euclidean geometry, Euclidean transformations, and inversive and projective geometry.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003c\/p\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 Title","offer_id":53515637260631,"sku":"9781118903674","price":999.99,"currency_code":"GBP","in_stock":false}],"url":"https:\/\/bookcurl.com\/products\/classical-geometry-9781118903674","provider":"Book Curl","version":"1.0","type":"link"}